Metrics for invcot (example 3.9)

analyze7.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 16 to 11 computations (31.3% saved)

Precisions

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

...c/correct-round.rkt:119:19: 2.0ms (46.7% of total)

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

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

ival-<: 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)

sample7.3s (60%)

Results

5.0s	4424×	2	valid
1.3s	1327×	3	valid
671.0ms	2469×	1	valid
9.0ms	36×	0	valid

Precisions

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

ival-tan: 4.8s (76.6% of total)

ival-div: 488.0ms (7.8% of total)

...c/correct-round.rkt:119:19: 439.0ms (7% of total)

backward-pass: 221.0ms (3.5% of total)

ival-sub: 196.0ms (3.1% of total)

ival-<: 87.0ms (1.4% of total)

const: 16.0ms (0.3% of total)

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

Bogosity

preprocess39.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

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

Symmetry

(negabs x)

explain419.0ms (3.4%)

FPErrors

Click to see full error table

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

Results

297.0ms	282×	2	valid
47.0ms	82×	3	valid
26.0ms	148×	1	valid

Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 324.0ms

ival-tan: 274.0ms (84.6% of total)

ival-div: 27.0ms (8.3% of total)

backward-pass: 14.0ms (4.3% of total)

ival-sub: 8.0ms (2.5% 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
▶	6.1%	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify50.0ms (0.4%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize218.0ms (1.8%)

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	6.1%	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

128.0ms	141×	2	valid
25.0ms	41×	3	valid
12.0ms	74×	1	valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 131.0ms

ival-tan: 107.0ms (81.7% of total)

ival-div: 13.0ms (9.9% of total)

backward-pass: 7.0ms (5.3% of total)

ival-sub: 4.0ms (3.1% of total)

const: 1.0ms (0.8% 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))

rewrite254.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	47	13
2	483	13
3	6182	13
0	8127	13

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 222

Calls

Call 1

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

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

simplify172.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

2522×	`-lowering-.f32`
2522×	`-lowering-.f64`
2470×	`sum3-define`
1924×	`+-lowering-+.f64`
1924×	`+-lowering-+.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	67	302
1	186	287
2	559	281
3	1807	281
4	2717	281
5	4432	281
6	6049	281
7	6591	281
0	8079	281

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval30.0ms (0.2%)

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

prune28.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	268	2	270
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	269	2	271

Accuracy

99.5%

Counts

271 → 2

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) #s(literal -1/45 binary64))))
▶	99.2%	(*.f64 #s(literal 1/3 binary64) x)

Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify50.0ms (0.4%)

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Program
✓	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

756×	`fma-define`
722×	`fnmadd-define`
546×	`sum3-define`
488×	`fmsub-define`
478×	`fnmsub-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	32
1	18	32
2	45	30
3	103	30
4	192	30
5	278	30
6	442	30
7	584	30
8	1160	30
9	1606	30
10	1859	30
11	2411	30
12	2467	30
0	2467	30

Stop Event

1×	iter limit
1×	saturated

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

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)

localize65.0ms (0.5%)

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	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

54.0ms

256×

valid

Compiler

Compiled 34 to 9 computations (73.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-mult: 33.0ms (77.2% of total)

...c/correct-round.rkt:119:19: 8.0ms (18.7% of total)

ival-sub: 1.0ms (2.3% of total)

const: 0.0ms (0% of total)

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

series4.0ms (0%)

Counts

5 → 60

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)>

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)>

Calls

15 calls:

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

rewrite281.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

3558×	`-lowering-.f32`
3558×	`-lowering-.f64`
2356×	`/-lowering-/.f32`
2356×	`/-lowering-/.f64`
1586×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	35	27
2	227	25
3	2058	25
0	8459	25

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 215

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)

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

simplify462.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

5544×	`-lowering-.f32`
5544×	`-lowering-.f64`
3086×	`cube-prod`
2994×	`pow-lowering-pow.f64`
2994×	`pow-lowering-pow.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	300
1	53	282
2	134	282
3	315	282
4	640	282
5	1718	282
6	1911	282
7	2216	282
8	2512	282
9	2902	282
10	3388	282
11	3983	282
12	4241	282
13	4418	282
14	4530	282
15	4649	282
16	4788	282
17	5526	282
18	6545	282
19	6987	282
20	7206	282
21	7320	282
22	7432	282
23	7557	282
24	7682	282
25	7789	282
26	7896	282
0	8003	282

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

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)

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

eval34.0ms (0.3%)

Compiler: Compiled 10883 to 821 computations (92.5% saved)

prune26.0ms (0.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	272	3	275
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	272	5	277

Accuracy

100.0%

Counts

277 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64)))))
▶	99.5%	(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
▶	99.7%	(.f64 (-.f64 #s(literal 1/9 binary64) (.f64 x (.f64 x (.f64 (.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))))))
✓	99.5%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
✓	99.2%	(*.f64 #s(literal 1/3 binary64) x)

Compiler

Compiled 60 to 42 computations (30% saved)

simplify138.0ms (1.1%)

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

Rules

2218×	`fma-define`
2172×	`fnmadd-define`
2008×	`sum3-define`
1698×	`fma-lowering-fma.f32`
1698×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	153
1	62	134
2	154	132
3	401	126
4	1016	126
5	1857	126
6	3430	126
7	5151	126
0	8105	126

Stop Event

1×	iter limit
1×	node limit

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

localize198.0ms (1.6%)

Localize:

Found 12 expressions of interest:

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

Results

75.0ms	44×	3	valid
52.0ms	174×	0	valid
20.0ms	19×	2	valid
11.0ms	19×	1	valid

Compiler

Compiled 158 to 25 computations (84.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 91.0ms

...c/correct-round.rkt:119:19: 33.0ms (36.4% of total)

ival-mult: 28.0ms (30.9% of total)

ival-div: 9.0ms (9.9% of total)

backward-pass: 8.0ms (8.8% of total)

ival-sub: 8.0ms (8.8% of total)

ival-add: 4.0ms (4.4% of total)

const: 0.0ms (0% of total)

series13.0ms (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) 1/2025))>
#<alt (- (* 1/3 x) (* x (* x (* x -1/45))))>
#<alt (* 1/3 x)>
#<alt (* x (* x (* x -1/45)))>
#<alt (* x (* x -1/45))>
#<alt (/ x (/ 1 (+ 1/3 (* (* x x) 1/45))))>
#<alt (/ 1 (+ 1/3 (* (* x x) 1/45)))>
#<alt (+ 1/3 (* (* x x) 1/45))>
#<alt (* (* x x) 1/45)>
#<alt (* x -1/45)>
#<alt (/ x (+ 1/3 (* x (* x -1/45))))>
#<alt (* x x)>

Outputs
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt 1/9>
#<alt (+ 1/9 (* -1/2025 (pow x 4)))>
#<alt (+ 1/9 (* -1/2025 (pow x 4)))>
#<alt (+ 1/9 (* -1/2025 (pow x 4)))>
#<alt (* -1/2025 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* -1/2025 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 3))>
#<alt (* 1/2025 (pow x 3))>
#<alt (* 1/2025 (pow x 3))>
#<alt (* 1/2025 (pow x 3))>
#<alt (* 1/2025 (pow x 3))>
#<alt (* 1/2025 (pow x 3))>
#<alt (* 1/2025 (pow x 3))>
#<alt (* 1/2025 (pow x 3))>
#<alt (* 1/2025 (pow x 3))>
#<alt (* 1/2025 (pow x 3))>
#<alt (* 1/2025 (pow x 3))>
#<alt (* 1/2025 (pow x 3))>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt 3>
#<alt (+ 3 (* -1/5 (pow x 2)))>
#<alt (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))>
#<alt (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))>
#<alt (/ 45 (pow x 2))>
#<alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))>
#<alt (/ 45 (pow x 2))>
#<alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))>
#<alt 1/3>
#<alt (+ 1/3 (* 1/45 (pow x 2)))>
#<alt (+ 1/3 (* 1/45 (pow x 2)))>
#<alt (+ 1/3 (* 1/45 (pow x 2)))>
#<alt (* 1/45 (pow x 2))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 2))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (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 (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* 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 (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

45 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(* x (* (* x x) 1/2025))
2.0ms	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 x) 1/2025)))
0.0ms	x	@	-inf	(* x (* (* x x) 1/2025))

rewrite398.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

3424×	`-lowering-.f32`
3424×	`-lowering-.f64`
2780×	`/-lowering-/.f32`
2780×	`/-lowering-/.f64`
1926×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	140
1	140	90
2	1140	85
0	8514	85

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 1051

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

Outputs
(+.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))))
(+.f64 (.f64 x #s(literal 1/3 binary64)) (+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) (+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))))
(+.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x #s(literal -1/45 binary64))) (.f64 x x)))
(+.f64 (.f64 x #s(literal 1/3 binary64)) (neg.f64 (-.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64))))))))
(+.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 (neg.f64 (.f64 x (.f64 x x))) #s(literal -1/45 binary64)))
(+.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))) (+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))))
(+.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))) (+.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x #s(literal -1/45 binary64))) (.f64 x x)) (.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))))
(+.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))) (+.f64 (+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64))))) (+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64)))))))
(+.f64 (+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64))))) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64))))))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 x #s(literal 1/3 binary64)))
(+.f64 (/.f64 (.f64 #s(literal 1/27 binary64) (.f64 x (.f64 x x))) (+.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))))) (neg.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/91125 binary64)) (.f64 x (.f64 x x))) (+.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))))))))
(+.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))) (neg.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.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))))))))
(+.f64 (.f64 (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))) #s(literal 1/9 binary64)) (.f64 (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))) (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64))))))
(+.f64 (/.f64 #s(literal 1/9 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) x)) (/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) x)))
(+.f64 (fma.f64 x #s(literal 1/3 binary64) (neg.f64 (.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x x))))) (fma.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x x)) (.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x x)))))
(+.f64 (fma.f64 #s(literal 1/3 binary64) x (neg.f64 (.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x x))))) (fma.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x x)) (.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x x)))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64))))) #s(literal -1 binary64)))
(-.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
(-.f64 (.f64 x #s(literal 1/3 binary64)) (-.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))))
(-.f64 (+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64))))) (.f64 x (+.f64 (.f64 x (*.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64))))
(-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (.f64 x (*.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64))))
(-.f64 (/.f64 (.f64 #s(literal 1/27 binary64) (.f64 x (.f64 x x))) (+.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))))) (/.f64 (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/91125 binary64)) (.f64 x (.f64 x x))) (+.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))))))
(-.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.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)))))))
(-.f64 (/.f64 #s(literal 1/9 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 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 x (.f64 x #s(literal -1/45 binary64)))) x)))
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(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))) (/.f64 #s(literal 1/9 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))) (+.f64 (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))) (/.f64 (.f64 (.f64 x x) (.f64 (.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 #s(literal 1/9 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))) (/.f64 #s(literal 1/9 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))) (/.f64 (.f64 (.f64 x x) (.f64 (.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 #s(literal 1/9 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))))
(pow.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (+.f64 (.f64 x (*.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))
(.f64 #s(literal -1 binary64) (pow.f64 (+.f64 (.f64 x (*.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64)) #s(literal 1 binary64)))
(.f64 (+.f64 (.f64 x (*.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64)) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/91125 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64))))))
(.f64 (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/91125 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 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 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 (.f64 x (*.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))))))
(.f64 (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/91125 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x 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 x) (.f64 (.f64 x x) #s(literal 1/2025 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 #s(literal -1 binary64) (+.f64 (.f64 x (*.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/91125 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64)))))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/2025 binary64) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (*.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64))))
(.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (*.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64))))
(.f64 (pow.f64 (+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))) #s(literal 1 binary64)))
(.f64 (pow.f64 (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/91125 binary64))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64))))) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/91125 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64))))))
(.f64 (/.f64 (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/8303765625 binary64))))) (+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/2025 binary64) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 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 x (.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/8303765625 binary64))))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 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 x (.f64 x #s(literal -1/45 binary64))))))
(.f64 (/.f64 (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4100625 binary64)))) #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 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))))
(.f64 (/.f64 (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4100625 binary64)))) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/91125 binary64)))) (/.f64 (/.f64 #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 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))))))
(.f64 (pow.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) #s(literal 1/2 binary64)) (pow.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 (.f64 x (*.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64))) #s(literal -1/2 binary64)))
(+.f64 #s(literal 0 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))
(neg.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (+.f64 #s(literal 0 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 (-.f64 #s(literal 0 binary64) (*.f64 x #s(literal -1/45 binary64))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/91125 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) (.f64 #s(literal 0 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(.f64 x (-.f64 #s(literal 0 binary64) (.f64 x #s(literal -1/45 binary64))))
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(.f64 (.f64 x #s(literal -1/45 binary64)) (-.f64 #s(literal 0 binary64) x))
(.f64 #s(literal 1/45 binary64) (.f64 x x))
(.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x #s(literal -1/45 binary64)))
(.f64 (.f64 x #s(literal 1/45 binary64)) x)
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x #s(literal -1/45 binary64))) x)
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal -1/45 binary64))
(/.f64 #s(literal -1/45 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 x #s(literal -1/45 binary64))
(*.f64 #s(literal -1/45 binary64) x)
(exp.f64 (.f64 (log.f64 (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))) x)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64))) (/.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64))))
(neg.f64 (/.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64))))
(/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) x))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) x))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) x)))
(/.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/2025 binary64) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 #s(literal -1 binary64) (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64))))
(pow.f64 (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 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 x (*.f64 x #s(literal -1/45 binary64))))))
(.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))))
(.f64 #s(literal -1 binary64) (/.f64 x (+.f64 (.f64 x (*.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64))))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))) x))))
(.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (*.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64))))) x)
(.f64 (/.f64 x (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/91125 binary64)))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))))
(.f64 (/.f64 x (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/91125 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))))))
(.f64 (/.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/2025 binary64) (.f64 (.f64 x x) (.f64 x x))))) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64)))) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))) x) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(/.f64 x (/.f64 #s(literal 1 binary64) x))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))

simplify237.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

2318×	`fma-lowering-fma.f32`
2318×	`fma-lowering-fma.f64`
1976×	`fma-define`
1904×	`-lowering-.f32`
1904×	`-lowering-.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	113	1138
1	313	1074
2	882	1068
3	2340	1067
4	5524	1067
0	8356	1067

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))
(* 1/2025 (pow x 3))
(* 1/2025 (pow x 3))
(* 1/2025 (pow x 3))
(* 1/2025 (pow x 3))
(* 1/2025 (pow x 3))
(* 1/2025 (pow x 3))
(* 1/2025 (pow x 3))
(* 1/2025 (pow x 3))
(* 1/2025 (pow x 3))
(* 1/2025 (pow x 3))
(* 1/2025 (pow x 3))
(* 1/2025 (pow x 3))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (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))
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* 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))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

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

eval154.0ms (1.3%)

Compiler: Compiled 49073 to 1767 computations (96.4% saved)

prune66.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	1284	2	1286
Fresh	0	0	0
Picked	3	0	3
Done	1	1	2
Total	1288	3	1291

Accuracy

100.0%

Counts

1291 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

▶

100.0%

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

▶

99.7%

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

✓

99.5%

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

Compiler

Compiled 24 to 17 computations (29.2% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

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

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
8×	`fma-lowering-fma.f32`
8×	`fma-define`
8×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	32
1	12	30
2	18	30
3	19	30
0	19	30

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize37.0ms (0.3%)

Localize:

Found 5 expressions of interest:

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

Results

26.0ms

256×

valid

Compiler

Compiled 34 to 9 computations (73.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-div: 4.0ms (29.3% of total)

ival-mult: 4.0ms (29.3% of total)

...c/correct-round.rkt:119:19: 4.0ms (29.3% of total)

ival-add: 1.0ms (7.3% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0%)

Counts

5 → 60

Calls

Call 1

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

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

Calls

15 calls:

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

rewrite274.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

3304×	`-lowering-.f32`
3304×	`-lowering-.f64`
2288×	`fma-lowering-fma.f32`
2288×	`fma-lowering-fma.f64`
2154×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	44	25
2	280	25
3	2516	25
0	8466	25

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 284

Calls

Call 1

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

Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 3 binary64) x)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 x #s(literal -3 binary64)))
(neg.f64 (/.f64 x #s(literal -3 binary64)))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 x #s(literal -3 binary64))))
(/.f64 x #s(literal 3 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -3 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3 binary64) x))
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -3 binary64) x))
(/.f64 #s(literal -1/3 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) #s(literal -3 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))) #s(literal 3 binary64))
(pow.f64 (/.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 3 binary64) x) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 3 binary64) x) (/.f64 #s(literal 3 binary64) x)) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 #s(literal 3 binary64) x))) #s(literal -1 binary64))
(*.f64 x #s(literal 1/3 binary64))
(*.f64 (/.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/3 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 x #s(literal 3 binary64)))
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 #s(literal 1/3 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 x #s(literal -3 binary64)))
(*.f64 #s(literal -1/3 binary64) (-.f64 #s(literal 0 binary64) x))
(*.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) #s(literal -1/3 binary64))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) #s(literal -1/3 binary64))
(+.f64 (.f64 (/.f64 x (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64))))) #s(literal 9 binary64)) (.f64 (/.f64 x (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64))))) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64)))))
(+.f64 (.f64 (/.f64 x (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64))))) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64)))) (.f64 (/.f64 x (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64))))) #s(literal 9 binary64)))
(+.f64 (.f64 (/.f64 x (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/25 binary64)))) #s(literal 3 binary64)) (.f64 (/.f64 x (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/25 binary64)))) (.f64 (.f64 x x) #s(literal 1/5 binary64))))
(+.f64 (.f64 #s(literal 9 binary64) (/.f64 x (+.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 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))) (/.f64 x (+.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 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))) (/.f64 x (+.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 x (+.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 3 binary64) (/.f64 x (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/25 binary64))))) (.f64 (.f64 (.f64 x x) #s(literal 1/5 binary64)) (/.f64 x (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/25 binary64))))))
(exp.f64 (.f64 (log.f64 (/.f64 (+.f64 #s(literal 3 binary64) (.f64 (*.f64 x x) #s(literal -1/5 binary64))) x)) #s(literal -1 binary64)))
(exp.f64 (+.f64 (log.f64 x) (.f64 (log.f64 (+.f64 #s(literal 3 binary64) (.f64 (*.f64 x x) #s(literal -1/5 binary64)))) #s(literal -1 binary64))))
(exp.f64 (+.f64 (.f64 (log.f64 (+.f64 #s(literal 3 binary64) (.f64 (*.f64 x x) #s(literal -1/5 binary64)))) #s(literal -1 binary64)) (log.f64 x)))
(-.f64 #s(literal 0 binary64) (/.f64 x (+.f64 #s(literal -3 binary64) (.f64 (.f64 x x) #s(literal 1/5 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))) (/.f64 x (+.f64 #s(literal -3 binary64) (.f64 (.f64 x x) #s(literal 1/5 binary64)))))
(fma.f64 #s(literal 3 binary64) (/.f64 x (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/25 binary64)))) (.f64 (.f64 (.f64 x x) #s(literal 1/5 binary64)) (/.f64 x (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/25 binary64))))))
(fma.f64 #s(literal 9 binary64) (/.f64 x (+.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 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))) (/.f64 x (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/125 binary64)))))))
(fma.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))) (/.f64 x (+.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 x (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/125 binary64)))))))
(fma.f64 (/.f64 x (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64))))) #s(literal 9 binary64) (.f64 (/.f64 x (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64))))) (.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64)))))
(fma.f64 (/.f64 x (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64))))) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))) (.f64 (/.f64 x (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/125 binary64))))) #s(literal 9 binary64)))
(fma.f64 (/.f64 x (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/25 binary64)))) #s(literal 3 binary64) (.f64 (/.f64 x (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/25 binary64)))) (.f64 (*.f64 x x) #s(literal 1/5 binary64))))
(neg.f64 (/.f64 x (+.f64 #s(literal -3 binary64) (.f64 (.f64 x x) #s(literal 1/5 binary64)))))
(neg.f64 (.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal -3 binary64) (.f64 (*.f64 x x) #s(literal 1/5 binary64))))))
(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal -3 binary64) (.f64 (.f64 x x) #s(literal 1/5 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64))) x))
(/.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -3 binary64) (.f64 (.f64 x x) #s(literal 1/5 binary64))) x))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -3 binary64) (.f64 (.f64 x x) #s(literal 1/5 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) x)))
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(pow.f64 (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (.f64 (.f64 x x) #s(literal -1/5 binary64)) #s(literal -3 binary64)) (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/25 binary64)))) #s(literal -9 binary64))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal 3 binary64) (.f64 (*.f64 x x) #s(literal -1/5 binary64))) #s(literal 1 binary64))
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(.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 x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))))) #s(literal 1 binary64)))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 (*.f64 x 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 (*.f64 x 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 (*.f64 x x) #s(literal 1/5 binary64)))) #s(literal 1 binary64)))
(.f64 #s(literal -1 binary64) (+.f64 #s(literal -3 binary64) (.f64 (*.f64 x x) #s(literal 1/5 binary64))))
(.f64 (+.f64 #s(literal -27 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/125 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (neg.f64 (.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64)))) #s(literal -9 binary64))))
(.f64 (+.f64 #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 (*.f64 x x) #s(literal 1/5 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))))) (+.f64 #s(literal 27 binary64) (.f64 (.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 x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/125 binary64))))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal 1/5 binary64)))) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/25 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal 1/5 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/25 binary64)))) #s(literal -1 binary64)))
(.f64 (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/25 binary64)))) #s(literal -9 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (*.f64 x 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 (*.f64 x 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 x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))))))) (+.f64 #s(literal 81 binary64) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))) #s(literal 9 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 27 binary64) (.f64 (.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 x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64)))))) (-.f64 #s(literal 9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 9 binary64) (.f64 (.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 x) (+.f64 (.f64 (*.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64)))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/25 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 (*.f64 x x) #s(literal 1/5 binary64)))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/25 binary64)))) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 (*.f64 x x) #s(literal 1/5 binary64))))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64))))) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64)))))) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 3 binary64) (.f64 (*.f64 x x) #s(literal -1/5 binary64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64)))) (+.f64 #s(literal 19683 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.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 -1/1953125 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 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 (pow.f64 (/.f64 (+.f64 #s(literal 9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64)))) (+.f64 #s(literal 729 binary64) (.f64 (.f64 (.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)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/125 binary64))))))
(.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 27 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (neg.f64 (.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64)))) #s(literal -9 binary64))))
(.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/25 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 3 binary64) (.f64 (*.f64 x x) #s(literal 1/5 binary64))))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/25 binary64)))) #s(literal -9 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (*.f64 x x) #s(literal -1/5 binary64)) #s(literal -3 binary64))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal 1/5 binary64))) (+.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)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 81 binary64) (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/25 binary64)))) (+.f64 #s(literal 9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/25 binary64)))))))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal 1/5 binary64))) (-.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)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 1/25 binary64)))))))
(exp.f64 (log.f64 (.f64 (.f64 x x) #s(literal -1/5 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 x x) #s(literal -1/5 binary64))) #s(literal 1 binary64)))
(pow.f64 (.f64 (.f64 x x) #s(literal -1/5 binary64)) #s(literal 1 binary64))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(.f64 x (pow.f64 (.f64 x #s(literal -1/5 binary64)) #s(literal 1 binary64)))
(.f64 x (exp.f64 (log.f64 (.f64 x #s(literal -1/5 binary64)))))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(.f64 (.f64 x x) (exp.f64 (log.f64 #s(literal -1/5 binary64))))
(.f64 #s(literal -1/5 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal -1/5 binary64)) x)
(.f64 (pow.f64 (.f64 x #s(literal -1/5 binary64)) #s(literal 1 binary64)) x)
(.f64 (exp.f64 (log.f64 (.f64 x #s(literal -1/5 binary64)))) x)
(.f64 (exp.f64 (log.f64 #s(literal -1/5 binary64))) (.f64 x x))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 2 binary64)))

simplify191.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

2036×	`sum4-define`
1798×	`fnmsub-define`
1662×	`-lowering-.f32`
1662×	`-lowering-.f64`
1394×	`+-lowering-+.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	72	356
1	194	339
2	559	333
3	1501	332
4	3225	330
5	5884	330
0	8191	330

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

Inputs
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 1/675 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 1/675 (* 1/10125 (pow x 2))))))))
(/ -5 x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(/ (- (* -1 (/ (+ 75 (* 1125 (/ 1 (pow x 2)))) (pow x 2))) 5) x)
(/ (- (* -1 (/ (+ 1125 (* 16875 (/ 1 (pow x 2)))) (pow x 4))) (+ 5 (* 75 (/ 1 (pow x 2))))) x)
(/ -5 x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (/ 1125 (pow x 4)))) x))
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (+ (* 16875 (/ 1 (pow x 6))) (/ 1125 (pow x 4))))) x))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* -1/5 (pow x 2)))
(* -1/5 (pow x 2))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* -1/5 (pow x 2))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

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 (* (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 x (*.f64 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 #s(literal -1 binary64) (.f64 x x)) (+.f64 (/.f64 (+.f64 #s(literal 1125 binary64) (/.f64 #s(literal 16875 binary64) (.f64 x x))) (.f64 x x)) #s(literal 75 binary64)))) 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 #s(literal -5 binary64) (+.f64 (/.f64 (+.f64 #s(literal -75 binary64) (/.f64 #s(literal -1125 binary64) (.f64 x x))) (.f64 x x)) (/.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))
(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)

eval46.0ms (0.4%)

Compiler: Compiled 9062 to 915 computations (89.9% saved)

prune45.0ms (0.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	343	1	344
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	343	4	347

Accuracy

100.0%

Counts

347 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64))))
✓	99.7%	(/.f64 x #s(literal 3 binary64))
	99.0%	(/.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) #s(literal -1/45 binary64))))

Compiler

Compiled 111 to 61 computations (45% saved)

regimes6.0ms (0.1%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	x
2.0ms	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

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 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 #s(literal 3 binary64))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
99.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	13	15

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness863.0ms (7.1%)

Rules

3558×	`-lowering-.f32`
3558×	`-lowering-.f64`
2522×	`-lowering-.f32`
2522×	`-lowering-.f64`
2470×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	35	27
2	227	25
3	2058	25
0	8459	25
0	113	1138
1	313	1074
2	882	1068
3	2340	1067
4	5524	1067
0	8356	1067
0	67	302
1	186	287
2	559	281
3	1807	281
4	2717	281
5	4432	281
6	6049	281
7	6591	281
0	8079	281

Stop Event

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

Compiler

Compiled 78 to 55 computations (29.5% saved)

preprocess43.0ms (0.4%)

Remove: (negabs x)
Compiler: Compiled 140 to 94 computations (32.9% saved)

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

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

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

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

analyze7.0ms (0.1%)

sample7.3s (60%)

preprocess39.0ms (0.3%)

explain419.0ms (3.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify50.0ms (0.4%)

localize218.0ms (1.8%)

series4.0ms (0%)

rewrite254.0ms (2.1%)

simplify172.0ms (1.4%)

eval30.0ms (0.2%)

prune28.0ms (0.2%)

simplify50.0ms (0.4%)

localize65.0ms (0.5%)

series4.0ms (0%)

rewrite281.0ms (2.3%)

simplify462.0ms (3.8%)

eval34.0ms (0.3%)

prune26.0ms (0.2%)

simplify138.0ms (1.1%)

localize198.0ms (1.6%)

series13.0ms (0.1%)

rewrite398.0ms (3.3%)

simplify237.0ms (1.9%)

eval154.0ms (1.3%)

prune66.0ms (0.5%)

simplify13.0ms (0.1%)

localize37.0ms (0.3%)

series2.0ms (0%)

rewrite274.0ms (2.2%)

simplify191.0ms (1.6%)

eval46.0ms (0.4%)

prune45.0ms (0.4%)

regimes6.0ms (0.1%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify7.0ms (0.1%)

soundness863.0ms (7.1%)

preprocess43.0ms (0.4%)

end0.0ms (0%)

Profiling

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

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