Metrics for invcot (example 3.9)

analyze8.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 16 to 11 computations (31.3% saved)

Precisions

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

...c/correct-round.rkt:119:19: 2.0ms (45.9% of total)

ival-div: 1.0ms (22.9% of total)

ival-tan: 1.0ms (22.9% of total)

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

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

const: 0.0ms (0% of total)

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

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

sample7.6s (54.2%)

Results

5.3s	4479×	2	valid
1.3s	1358×	3	valid
606.0ms	2369×	1	valid
5.0ms	50×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.5s

ival-tan: 4.8s (74.6% of total)

ival-div: 614.0ms (9.5% of total)

backward-pass: 440.0ms (6.8% of total)

...c/correct-round.rkt:119:19: 349.0ms (5.4% of total)

ival-sub: 138.0ms (2.1% of total)

ival-<: 68.0ms (1.1% of total)

const: 19.0ms (0.3% of total)

ival-and: 16.0ms (0.2% of total)

Bogosity

preprocess43.0ms (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	17
1	37	16
2	72	15
3	156	15
4	311	15
5	480	15
6	523	15
7	531	15
0	6	5
1	16	5
2	24	5
3	36	5
4	50	5
5	87	5
6	158	5
7	255	5
8	356	5
9	499	5
10	621	5
11	653	5
0	653	5

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

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

Symmetry

(negabs x)

explain560.0ms (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

409.0ms	288×	2	valid
79.0ms	88×	3	valid
34.0ms	134×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 429.0ms

ival-tan: 362.0ms (84.4% of total)

ival-div: 33.0ms (7.7% of total)

backward-pass: 19.0ms (4.4% of total)

ival-sub: 13.0ms (3% of total)

const: 2.0ms (0.5% of total)

eval0.0ms (0%)

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

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.0%	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify22.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize495.0ms (3.5%)

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	6.0%	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

429.0ms	144×	2	valid
38.0ms	44×	3	valid
15.0ms	67×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 442.0ms

ival-tan: 411.0ms (93.1% of total)

ival-div: 15.0ms (3.4% of total)

backward-pass: 11.0ms (2.5% of total)

ival-sub: 4.0ms (0.9% of total)

const: 1.0ms (0.2% 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))

rewrite217.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 225

Calls

Call 1

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

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

simplify198.0ms (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	189	269
2	564	266
3	1805	266
4	2707	266
5	4420	266
6	6039	266
7	6587	266
0	8075	266

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval31.0ms (0.2%)

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

prune29.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Accuracy

99.4%

Counts

274 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))))
▶	99.4%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
▶	99.1%	(*.f64 #s(literal 1/3 binary64) x)

Status

Accuracy

Program

▶

99.4%

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

▶

99.4%

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

▶

99.1%

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

Compiler

Compiled 30 to 21 computations (30% saved)

simplify137.0ms (1%)

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize118.0ms (0.8%)

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal -2/945 binary64)))
✓	accuracy	99.8%	(.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64)))))
✓	accuracy	99.5%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))))
✓	accuracy	99.3%	(*.f64 x #s(literal -2/945 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal -1/45 binary64))
✓	accuracy	99.5%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
✓	accuracy	99.4%	(*.f64 #s(literal 1/3 binary64) x)

Results

69.0ms

256×

valid

Compiler

Compiled 95 to 16 computations (83.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-mult: 16.0ms (51.9% of total)

...c/correct-round.rkt:119:19: 11.0ms (35.7% of total)

ival-sub: 3.0ms (9.7% of total)

ival-add: 1.0ms (3.2% of total)

const: 0.0ms (0% of total)

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

series24.0ms (0.2%)

Counts

10 → 120

Calls

Call 1

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

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

Calls

30 calls:

Time	Variable		Point	Expression
10.0ms	x	@	inf	(* x (* x -2/945))
1.0ms	x	@	-inf	(* x (- 1/3 (* (* x x) (+ -1/45 (* x (* x -2/945))))))
1.0ms	x	@	0	(* 1/3 x)
1.0ms	x	@	inf	(* x (- 1/3 (* (* x x) (+ -1/45 (* x (* x -2/945))))))
1.0ms	x	@	inf	(* x (- 1/3 (* (* x x) -1/45)))

rewrite289.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 287

Calls

Call 1

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

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

simplify173.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

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

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

eval52.0ms (0.4%)

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

prune71.0ms (0.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

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

Accuracy

100.0%

Counts

428 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.9%	(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 #s(literal 1/3 binary64) x)) (.f64 (.f64 (.f64 x x) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))) (.f64 (.f64 x x) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))))) (-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x x) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64))))))
▶	100.0%	(/.f64 x (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))))))
▶	100.0%	(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64)))))
✓	99.4%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))))
✓	99.4%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
✓	99.1%	(*.f64 #s(literal 1/3 binary64) x)

Compiler

Compiled 114 to 58 computations (49.1% saved)

simplify214.0ms (1.5%)

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	128	(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x x) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))))
✓	cost-diff	128	(.f64 (.f64 #s(literal 1/3 binary64) x) (*.f64 #s(literal 1/3 binary64) x))
✓	cost-diff	256	(-.f64 (.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 #s(literal 1/3 binary64) x)) (.f64 (.f64 (.f64 x x) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))) (.f64 (.f64 x x) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64))))))
✓	cost-diff	1920	(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 #s(literal 1/3 binary64) x)) (.f64 (.f64 (.f64 x x) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))) (.f64 (.f64 x x) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))))) (-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x x) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64))))))
✓	cost-diff	0	(.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64)))))
✓	cost-diff	0	(-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64)))))))
✓	cost-diff	128	(/.f64 x (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))))))
✓	cost-diff	0	(.f64 (.f64 x x) #s(literal 1/45 binary64))
✓	cost-diff	0	(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64))))
✓	cost-diff	128	(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64)))))

Rules

4354×	`-lowering-.f32`
4354×	`-lowering-.f64`
1530×	`fma-define`
1466×	`fma-lowering-fma.f32`
1466×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	191
1	111	177
2	464	170
3	2564	169
0	8441	169

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize189.0ms (1.3%)

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(.f64 (.f64 #s(literal 1/3 binary64) x) (*.f64 #s(literal 1/3 binary64) x))
✓	accuracy	99.6%	(.f64 x (+.f64 (.f64 (*.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))
✓	accuracy	99.4%	(*.f64 #s(literal 1/3 binary64) x)
✓	accuracy	52.9%	(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 #s(literal 1/3 binary64) x)) (.f64 (.f64 (.f64 x x) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))) (.f64 (.f64 x x) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))))) (-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x x) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64))))))
✓	accuracy	100.0%	(-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))))
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal -2/945 binary64)))
✓	accuracy	99.8%	(.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64)))))
✓	accuracy	99.3%	(*.f64 x #s(literal -2/945 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64))))
✓	accuracy	100.0%	(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64)))
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal 1/45 binary64))

Results

108.0ms

256×

valid

Compiler

Compiled 303 to 30 computations (90.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 52.0ms

ival-mult: 18.0ms (34.5% of total)

...c/correct-round.rkt:119:19: 18.0ms (34.5% of total)

ival-div: 8.0ms (15.3% of total)

ival-sub: 4.0ms (7.7% of total)

ival-add: 4.0ms (7.7% of total)

const: 0.0ms (0% of total)

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

series9.0ms (0.1%)

Counts

17 → 204

Calls

Call 1

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

Outputs
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt 3>
#<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 (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))>
#<alt (* 2/945 (pow x 5))>
#<alt (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* 2/945 (pow x 5))>
#<alt (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))>
#<alt 3>
#<alt (+ 3 (* -1/5 (pow x 2)))>
#<alt (+ 3 (* (pow x 2) (- (* -1/175 (pow x 2)) 1/5)))>
#<alt (+ 3 (* (pow x 2) (- (* (pow x 2) (- (* 13/7875 (pow x 2)) 1/175)) 1/5)))>
#<alt (/ 945/2 (pow x 4))>
#<alt (/ (- 945/2 (* 19845/4 (/ 1 (pow x 2)))) (pow x 4))>
#<alt (/ (+ 945/2 (* -1 (/ (+ 19845/4 (* 178605/8 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 4))>
#<alt (/ (- (+ 945/2 (* 16253055/16 (/ 1 (pow x 6)))) (+ (* 19845/4 (/ 1 (pow x 2))) (/ 178605/8 (pow x 4)))) (pow x 4))>
#<alt (/ 945/2 (pow x 4))>
#<alt (/ (- 945/2 (* 19845/4 (/ 1 (pow x 2)))) (pow x 4))>
#<alt (/ (+ 945/2 (* -1 (/ (+ 19845/4 (* 178605/8 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 4))>
#<alt (/ (- (+ 945/2 (* 16253055/16 (/ 1 (pow x 6)))) (+ (* 19845/4 (/ 1 (pow x 2))) (/ 178605/8 (pow x 4)))) (pow x 4))>
#<alt 1/3>
#<alt (+ 1/3 (* 1/45 (pow x 2)))>
#<alt (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))>
#<alt (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))>
#<alt (* 2/945 (pow x 4))>
#<alt (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* 2/945 (pow x 4))>
#<alt (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1/45 (pow x 2))>
#<alt (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))>
#<alt (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))>
#<alt (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))>
#<alt (* -2/945 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -2/945 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))>
#<alt (* 2/945 (pow x 5))>
#<alt (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* 2/945 (pow x 5))>
#<alt (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))>
#<alt (* 1/9 (pow x 2))>
#<alt (* (pow x 2) (+ 1/9 (* -1/2025 (pow x 4))))>
#<alt (* (pow x 2) (+ 1/9 (* (pow x 4) (- (* -4/42525 (pow x 2)) 1/2025))))>
#<alt (* (pow x 2) (+ 1/9 (* (pow x 4) (- (* (pow x 2) (- (* -4/893025 (pow x 2)) 4/42525)) 1/2025))))>
#<alt (* -4/893025 (pow x 10))>
#<alt (* -1 (* (pow x 10) (+ 4/893025 (* 4/42525 (/ 1 (pow x 2))))))>
#<alt (* (pow x 10) (- (* -1 (/ (+ 4/42525 (* 1/2025 (/ 1 (pow x 2)))) (pow x 2))) 4/893025))>
#<alt (* (pow x 10) (- (* 1/9 (/ 1 (pow x 8))) (+ 4/893025 (+ (/ 1/2025 (pow x 4)) (* 4/42525 (/ 1 (pow x 2)))))))>
#<alt (* -4/893025 (pow x 10))>
#<alt (* -1 (* (pow x 10) (+ 4/893025 (* 4/42525 (/ 1 (pow x 2))))))>
#<alt (* (pow x 10) (- (* -1 (/ (+ 4/42525 (* 1/2025 (/ 1 (pow x 2)))) (pow x 2))) 4/893025))>
#<alt (* (pow x 10) (- (* 1/9 (/ 1 (pow x 8))) (+ 4/893025 (+ (/ 1/2025 (pow x 4)) (* 4/42525 (/ 1 (pow x 2)))))))>
#<alt (* 1/9 (pow x 2))>
#<alt (* 1/9 (pow x 2))>
#<alt (* 1/9 (pow x 2))>
#<alt (* 1/9 (pow x 2))>
#<alt (* 1/9 (pow x 2))>
#<alt (* 1/9 (pow x 2))>
#<alt (* 1/9 (pow x 2))>
#<alt (* 1/9 (pow x 2))>
#<alt (* 1/9 (pow x 2))>
#<alt (* 1/9 (pow x 2))>
#<alt (* 1/9 (pow x 2))>
#<alt (* 1/9 (pow x 2))>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* -1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))))>
#<alt (* x (+ 1/3 (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))))>
#<alt (* -2/945 (pow x 5))>
#<alt (* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* (pow x 5) (- (/ 1/3 (pow x 4)) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* (pow x 5) (- (/ 1/3 (pow x 4)) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -2/945 (pow x 5))>
#<alt (* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (- (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (/ 1/3 (pow x 4)))))>
#<alt (* -1 (* (pow x 5) (- (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (/ 1/3 (pow x 4)))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* -2/945 x)>
#<alt (* -2/945 x)>
#<alt (* -2/945 x)>
#<alt (* -2/945 x)>
#<alt (* -2/945 x)>
#<alt (* -2/945 x)>
#<alt (* -2/945 x)>
#<alt (* -2/945 x)>
#<alt (* -2/945 x)>
#<alt (* -2/945 x)>
#<alt (* -2/945 x)>
#<alt (* -2/945 x)>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<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 x)>
#<alt (* x (+ 1/45 (* 2/945 (pow x 2))))>
#<alt (* x (+ 1/45 (* 2/945 (pow x 2))))>
#<alt (* x (+ 1/45 (* 2/945 (pow x 2))))>
#<alt (* 2/945 (pow x 3))>
#<alt (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* 2/945 (pow x 3))>
#<alt (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>

Calls

51 calls:

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

rewrite470.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

3416×	`-lowering-.f32`
3416×	`-lowering-.f64`
2354×	`/-lowering-/.f32`
2354×	`/-lowering-/.f64`
1936×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	154
1	229	124
2	2102	121
0	8864	121

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 646

Calls

Call 1

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

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

simplify280.0ms (2%)

Algorithm

1×	egg-herbie

Rules

3678×	`-lowering-.f32`
3678×	`-lowering-.f64`
2856×	`+-lowering-+.f64`
2856×	`+-lowering-+.f32`
1380×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	182	1705
1	525	1447
2	1505	1421
3	4111	1415
0	8247	1415

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
3
(+ 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))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* (pow x 2) (- (* -1/175 (pow x 2)) 1/5)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (- (* 13/7875 (pow x 2)) 1/175)) 1/5)))
(/ 945/2 (pow x 4))
(/ (- 945/2 (* 19845/4 (/ 1 (pow x 2)))) (pow x 4))
(/ (+ 945/2 (* -1 (/ (+ 19845/4 (* 178605/8 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 4))
(/ (- (+ 945/2 (* 16253055/16 (/ 1 (pow x 6)))) (+ (* 19845/4 (/ 1 (pow x 2))) (/ 178605/8 (pow x 4)))) (pow x 4))
(/ 945/2 (pow x 4))
(/ (- 945/2 (* 19845/4 (/ 1 (pow x 2)))) (pow x 4))
(/ (+ 945/2 (* -1 (/ (+ 19845/4 (* 178605/8 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 4))
(/ (- (+ 945/2 (* 16253055/16 (/ 1 (pow x 6)))) (+ (* 19845/4 (/ 1 (pow x 2))) (/ 178605/8 (pow x 4)))) (pow x 4))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(* 2/945 (pow x 4))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* 2/945 (pow x 4))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* -1/45 (pow x 2))
(* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))
(* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))
(* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))
(* -2/945 (pow x 4))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -2/945 (pow x 4))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* 1/9 (pow x 2))
(* (pow x 2) (+ 1/9 (* -1/2025 (pow x 4))))
(* (pow x 2) (+ 1/9 (* (pow x 4) (- (* -4/42525 (pow x 2)) 1/2025))))
(* (pow x 2) (+ 1/9 (* (pow x 4) (- (* (pow x 2) (- (* -4/893025 (pow x 2)) 4/42525)) 1/2025))))
(* -4/893025 (pow x 10))
(* -1 (* (pow x 10) (+ 4/893025 (* 4/42525 (/ 1 (pow x 2))))))
(* (pow x 10) (- (* -1 (/ (+ 4/42525 (* 1/2025 (/ 1 (pow x 2)))) (pow x 2))) 4/893025))
(* (pow x 10) (- (* 1/9 (/ 1 (pow x 8))) (+ 4/893025 (+ (/ 1/2025 (pow x 4)) (* 4/42525 (/ 1 (pow x 2)))))))
(* -4/893025 (pow x 10))
(* -1 (* (pow x 10) (+ 4/893025 (* 4/42525 (/ 1 (pow x 2))))))
(* (pow x 10) (- (* -1 (/ (+ 4/42525 (* 1/2025 (/ 1 (pow x 2)))) (pow x 2))) 4/893025))
(* (pow x 10) (- (* 1/9 (/ 1 (pow x 8))) (+ 4/893025 (+ (/ 1/2025 (pow x 4)) (* 4/42525 (/ 1 (pow x 2)))))))
(* 1/9 (pow x 2))
(* 1/9 (pow x 2))
(* 1/9 (pow x 2))
(* 1/9 (pow x 2))
(* 1/9 (pow x 2))
(* 1/9 (pow x 2))
(* 1/9 (pow x 2))
(* 1/9 (pow x 2))
(* 1/9 (pow x 2))
(* 1/9 (pow x 2))
(* 1/9 (pow x 2))
(* 1/9 (pow x 2))
(* 1/3 x)
(* x (+ 1/3 (* -1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))))
(* x (+ 1/3 (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))))
(* -2/945 (pow x 5))
(* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 5) (- (/ 1/3 (pow x 4)) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 5) (- (/ 1/3 (pow x 4)) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -2/945 (pow x 5))
(* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (/ 1/3 (pow x 4)))))
(* -1 (* (pow x 5) (- (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (/ 1/3 (pow x 4)))))
(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)
(* -2/945 x)
(* -2/945 x)
(* -2/945 x)
(* -2/945 x)
(* -2/945 x)
(* -2/945 x)
(* -2/945 x)
(* -2/945 x)
(* -2/945 x)
(* -2/945 x)
(* -2/945 x)
(* -2/945 x)
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* 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 x)
(* x (+ 1/45 (* 2/945 (pow x 2))))
(* x (+ 1/45 (* 2/945 (pow x 2))))
(* x (+ 1/45 (* 2/945 (pow x 2))))
(* 2/945 (pow x 3))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* 2/945 (pow x 3))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))

Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/5 binary64) (.f64 x (.f64 x #s(literal 1/75 binary64)))))))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/5 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/75 binary64) (.f64 (.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 10125 binary64) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal -675 binary64) (.f64 x x))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (-.f64 (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (/.f64 #s(literal 675 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 151875 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal -45 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 10125 binary64) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal -675 binary64) (.f64 x x))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (-.f64 (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (/.f64 #s(literal 675 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 151875 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal -45 binary64)))) (*.f64 x x))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 1/45 (pow x 2)))
(+.f64 #s(literal 1/3 binary64) (.f64 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)))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(* 2/945 (pow x 5))
(.f64 x (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 2/945 binary64)))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) x) (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/45 binary64) (.f64 x x))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) x) (+.f64 (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/45 binary64) (.f64 x x))) (/.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) x) (+.f64 (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/45 binary64) (.f64 x x))) (/.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* 2/945 (pow x 5))
(.f64 x (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 2/945 binary64)))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
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(*.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 x)
(*.f64 x #s(literal 1/45 binary64))
(* x (+ 1/45 (* 2/945 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* x (+ 1/45 (* 2/945 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* x (+ 1/45 (* 2/945 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* 2/945 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 2/945 binary64)))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* 2/945 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 2/945 binary64)))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))

eval173.0ms (1.2%)

Compiler: Compiled 69942 to 2746 computations (96.1% saved)

prune186.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	1088	3	1091
Fresh	0	0	0
Picked	3	0	3
Done	2	1	3
Total	1093	4	1097

Accuracy

100.0%

Counts

1097 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.0%	(/.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))))) (-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x x) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64))))))
▶	100.0%	(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64)))))
▶	99.7%	(/.f64 x #s(literal 3 binary64))
✓	99.4%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))))

Compiler

Compiled 64 to 41 computations (35.9% saved)

simplify174.0ms (1.2%)

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/2025 binary64))))
✓	cost-diff	0	(.f64 x (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))))
✓	cost-diff	128	(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x x) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))))
✓	cost-diff	256	(/.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))))) (-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x x) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64))))))
✓	cost-diff	0	(*.f64 x #s(literal -1/5 binary64))
✓	cost-diff	0	(.f64 x (.f64 x #s(literal -1/5 binary64)))
✓	cost-diff	0	(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
✓	cost-diff	0	(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64)))))
✓	cost-diff	0	(/.f64 x #s(literal 3 binary64))

Rules

3066×	`-lowering-.f32`
3066×	`-lowering-.f64`
1518×	`fma-lowering-fma.f32`
1518×	`fma-lowering-fma.f64`
1184×	`fma-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	27	149
1	75	131
2	249	131
3	694	128
4	1368	126
5	2547	126
6	5424	126
0	8102	126

Stop Event

1×	iter limit
1×	node limit

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 -1/5)
-1/5
(/ (* x (* x (+ 1/9 (* (* x (* x (* x x))) -1/2025)))) (- (* 1/3 x) (* (* x x) (* x (+ (* (* x x) 2/945) 1/45)))))
(* x (* x (+ 1/9 (* (* x (* x (* x x))) -1/2025))))
x
(* x (+ 1/9 (* (* x (* x (* x x))) -1/2025)))
(+ 1/9 (* (* x (* x (* x x))) -1/2025))
1/9
(* (* x (* x (* x x))) -1/2025)
(* x (* x (* x x)))
(* x (* x x))
(* x x)
-1/2025
(- (* 1/3 x) (* (* x x) (* x (+ (* (* x x) 2/945) 1/45))))
(* 1/3 x)
1/3
(* (* x x) (* x (+ (* (* x x) 2/945) 1/45)))
(* x (+ (* (* x x) 2/945) 1/45))
(+ (* (* x x) 2/945) 1/45)
(* (* x x) 2/945)
2/945
1/45

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

localize232.0ms (1.7%)

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(.f64 x (+.f64 (.f64 (*.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))
✓	accuracy	99.4%	(*.f64 #s(literal 1/3 binary64) x)
✓	accuracy	99.4%	(.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/2025 binary64))))
✓	accuracy	52.9%	(/.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))))) (-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x x) (.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64))))))
✓	accuracy	100.0%	(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
✓	accuracy	100.0%	(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64)))))
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal -1/5 binary64)))
✓	accuracy	99.4%	(*.f64 x #s(literal -1/5 binary64))
✓	accuracy	100.0%	(/.f64 x #s(literal 3 binary64))

Results

164.0ms

256×

valid

Compiler

Compiled 190 to 28 computations (85.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 90.0ms

ival-mult: 48.0ms (53.2% of total)

...c/correct-round.rkt:119:19: 28.0ms (31% of total)

ival-div: 7.0ms (7.8% of total)

ival-add: 5.0ms (5.5% of total)

ival-sub: 2.0ms (2.2% of total)

const: 0.0ms (0% of total)

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

series18.0ms (0.1%)

Counts

11 → 132

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 -1/5)>
#<alt (/ (* x (* x (+ 1/9 (* (* x (* x (* x x))) -1/2025)))) (- (* 1/3 x) (* (* x x) (* x (+ (* (* x x) 2/945) 1/45)))))>
#<alt (- (* 1/3 x) (* (* x x) (* x (+ (* (* x x) 2/945) 1/45))))>
#<alt (* x (* x (+ 1/9 (* (* x (* x (* x x))) -1/2025))))>
#<alt (* x (+ 1/9 (* (* x (* x (* x x))) -1/2025)))>
#<alt (* 1/3 x)>
#<alt (* x (+ (* (* x x) 2/945) 1/45))>

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 (* -1/5 x)>
#<alt (* -1/5 x)>
#<alt (* -1/5 x)>
#<alt (* -1/5 x)>
#<alt (* -1/5 x)>
#<alt (* -1/5 x)>
#<alt (* -1/5 x)>
#<alt (* -1/5 x)>
#<alt (* -1/5 x)>
#<alt (* -1/5 x)>
#<alt (* -1/5 x)>
#<alt (* -1/5 x)>
#<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 (* 4/14175 (pow x 2))))))))>
#<alt (* 7/30 x)>
#<alt (* x (- 7/30 (* 49/20 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 7/30 (/ 399/40 (pow x 4))) (* 49/20 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 7/30 (/ 399/40 (pow x 4))) (+ (* 49/20 (/ 1 (pow x 2))) (* 39249/80 (/ 1 (pow x 6))))))>
#<alt (* 7/30 x)>
#<alt (* -1 (* x (- (* 49/20 (/ 1 (pow x 2))) 7/30)))>
#<alt (* -1 (* x (- (* 49/20 (/ 1 (pow x 2))) (+ 7/30 (/ 399/40 (pow x 4))))))>
#<alt (* -1 (* x (- (+ (* 49/20 (/ 1 (pow x 2))) (* 39249/80 (/ 1 (pow x 6)))) (+ 7/30 (/ 399/40 (pow x 4))))))>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* -1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))))>
#<alt (* x (+ 1/3 (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))))>
#<alt (* -2/945 (pow x 5))>
#<alt (* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* (pow x 5) (- (/ 1/3 (pow x 4)) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* (pow x 5) (- (/ 1/3 (pow x 4)) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -2/945 (pow x 5))>
#<alt (* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (- (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (/ 1/3 (pow x 4)))))>
#<alt (* -1 (* (pow x 5) (- (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (/ 1/3 (pow x 4)))))>
#<alt (* 1/9 (pow x 2))>
#<alt (* (pow x 2) (+ 1/9 (* -1/2025 (pow x 4))))>
#<alt (* (pow x 2) (+ 1/9 (* -1/2025 (pow x 4))))>
#<alt (* (pow x 2) (+ 1/9 (* -1/2025 (pow x 4))))>
#<alt (* -1/2025 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* (pow x 6) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* (pow x 6) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* -1/2025 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* (pow x 6) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* (pow x 6) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* 1/9 x)>
#<alt (* x (+ 1/9 (* -1/2025 (pow x 4))))>
#<alt (* x (+ 1/9 (* -1/2025 (pow x 4))))>
#<alt (* x (+ 1/9 (* -1/2025 (pow x 4))))>
#<alt (* -1/2025 (pow x 5))>
#<alt (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))>
#<alt (* -1/2025 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4))))))>
#<alt (* -1 (* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4))))))>
#<alt (* -1 (* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4))))))>
#<alt (* 1/3 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 x)>
#<alt (* x (+ 1/45 (* 2/945 (pow x 2))))>
#<alt (* x (+ 1/45 (* 2/945 (pow x 2))))>
#<alt (* x (+ 1/45 (* 2/945 (pow x 2))))>
#<alt (* 2/945 (pow x 3))>
#<alt (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* 2/945 (pow x 3))>
#<alt (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>

Calls

33 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	(* x (* x -1/5))
2.0ms	x	@	0	(/ (* x (* x (+ 1/9 (* (* x (* x (* x x))) -1/2025)))) (- (* 1/3 x) (* (* x x) (* x (+ (* (* x x) 2/945) 1/45)))))
1.0ms	x	@	inf	(* x (* x (+ 1/9 (* (* x (* x (* x x))) -1/2025))))
1.0ms	x	@	inf	(/ x (+ 3 (* x (* x -1/5))))
1.0ms	x	@	inf	(/ (* x (* x (+ 1/9 (* (* x (* x (* x x))) -1/2025)))) (- (* 1/3 x) (* (* x x) (* x (+ (* (* x x) 2/945) 1/45)))))

rewrite385.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

5010×	`-lowering-.f32`
5010×	`-lowering-.f64`
3914×	`/-lowering-/.f32`
3914×	`/-lowering-/.f64`
1802×	`frac-times`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	94
1	159	83
2	1309	83
0	8959	83

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 370

Calls

Call 1

Inputs
(/ x 3)
(/ x (+ 3 (* x (* x -1/5))))
(+ 3 (* x (* x -1/5)))
(* x (* x -1/5))
(* x -1/5)
(/ (* x (* x (+ 1/9 (* (* x (* x (* x x))) -1/2025)))) (- (* 1/3 x) (* (* x x) (* x (+ (* (* x x) 2/945) 1/45)))))
(- (* 1/3 x) (* (* x x) (* x (+ (* (* x x) 2/945) 1/45))))
(* x (* x (+ 1/9 (* (* x (* x (* x x))) -1/2025))))
(* x (+ 1/9 (* (* x (* x (* x x))) -1/2025)))
(* 1/3 x)
(* x (+ (* (* x x) 2/945) 1/45))

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)))
(/.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))
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(/.f64 (neg.f64 (.f64 x (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 4/893025 binary64)) #s(literal -1/2025 binary64)))) (neg.f64 (+.f64 (.f64 (*.f64 x x) #s(literal 2/945 binary64)) #s(literal -1/45 binary64))))
(/.f64 (neg.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8/843908625 binary64))) #s(literal 1/91125 binary64)) x)) (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 4/893025 binary64)) (-.f64 #s(literal 1/2025 binary64) (.f64 (*.f64 x x) #s(literal 2/42525 binary64))))))
(/.f64 (neg.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 4/893025 binary64)) #s(literal -1/2025 binary64)) x)) (neg.f64 (+.f64 (.f64 (*.f64 x x) #s(literal 2/945 binary64)) #s(literal -1/45 binary64))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8/843908625 binary64))))) (+.f64 (.f64 (.f64 x #s(literal 1/45 binary64)) (.f64 x #s(literal 1/45 binary64))) (-.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 2/945 binary64))) (.f64 x (.f64 (.f64 x x) #s(literal 2/945 binary64)))) (.f64 (.f64 x #s(literal 1/45 binary64)) (.f64 x (.f64 (*.f64 x x) #s(literal 2/945 binary64)))))))
(.f64 x (+.f64 (.f64 (*.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))
(.f64 (+.f64 (.f64 (*.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) x)

simplify243.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

3150×	`+-lowering-+.f64`
3150×	`+-lowering-+.f32`
2946×	`-lowering-.f32`
2946×	`-lowering-.f64`
1262×	`sum3-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	158	992
1	481	873
2	1452	859
3	4216	858
0	8170	858

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

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))
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* -1/5 x)
(* 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 (* 4/14175 (pow x 2))))))))
(* 7/30 x)
(* x (- 7/30 (* 49/20 (/ 1 (pow x 2)))))
(* x (- (+ 7/30 (/ 399/40 (pow x 4))) (* 49/20 (/ 1 (pow x 2)))))
(* x (- (+ 7/30 (/ 399/40 (pow x 4))) (+ (* 49/20 (/ 1 (pow x 2))) (* 39249/80 (/ 1 (pow x 6))))))
(* 7/30 x)
(* -1 (* x (- (* 49/20 (/ 1 (pow x 2))) 7/30)))
(* -1 (* x (- (* 49/20 (/ 1 (pow x 2))) (+ 7/30 (/ 399/40 (pow x 4))))))
(* -1 (* x (- (+ (* 49/20 (/ 1 (pow x 2))) (* 39249/80 (/ 1 (pow x 6)))) (+ 7/30 (/ 399/40 (pow x 4))))))
(* 1/3 x)
(* x (+ 1/3 (* -1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))))
(* x (+ 1/3 (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))))
(* -2/945 (pow x 5))
(* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 5) (- (/ 1/3 (pow x 4)) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 5) (- (/ 1/3 (pow x 4)) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -2/945 (pow x 5))
(* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (/ 1/3 (pow x 4)))))
(* -1 (* (pow x 5) (- (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (/ 1/3 (pow x 4)))))
(* 1/9 (pow x 2))
(* (pow x 2) (+ 1/9 (* -1/2025 (pow x 4))))
(* (pow x 2) (+ 1/9 (* -1/2025 (pow x 4))))
(* (pow x 2) (+ 1/9 (* -1/2025 (pow x 4))))
(* -1/2025 (pow x 6))
(* (pow x 6) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* (pow x 6) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* (pow x 6) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* -1/2025 (pow x 6))
(* (pow x 6) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* (pow x 6) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* (pow x 6) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* 1/9 x)
(* x (+ 1/9 (* -1/2025 (pow x 4))))
(* x (+ 1/9 (* -1/2025 (pow x 4))))
(* x (+ 1/9 (* -1/2025 (pow x 4))))
(* -1/2025 (pow x 5))
(* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* -1/2025 (pow x 5))
(* -1 (* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4))))))
(* -1 (* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4))))))
(* -1 (* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4))))))
(* 1/3 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 x)
(* x (+ 1/45 (* 2/945 (pow x 2))))
(* x (+ 1/45 (* 2/945 (pow x 2))))
(* x (+ 1/45 (* 2/945 (pow x 2))))
(* 2/945 (pow x 3))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* 2/945 (pow x 3))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))

Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 1/675 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 1/675 binary64))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 1/675 (* 1/10125 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/675 binary64) (.f64 (*.f64 x x) #s(literal 1/10125 binary64)))))))))
(/ -5 x)
(/.f64 #s(literal -5 binary64) x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -5 binary64) (/.f64 #s(literal -75 binary64) (*.f64 x x))) x)
(/ (- (* -1 (/ (+ 75 (* 1125 (/ 1 (pow x 2)))) (pow x 2))) 5) x)
(/.f64 (-.f64 #s(literal -5 binary64) (/.f64 (+.f64 #s(literal 75 binary64) (/.f64 #s(literal 1125 binary64) (.f64 x x))) (.f64 x x))) x)
(/ (- (* -1 (/ (+ 1125 (* 16875 (/ 1 (pow x 2)))) (pow x 4))) (+ 5 (* 75 (/ 1 (pow x 2))))) x)
(/.f64 (+.f64 #s(literal -5 binary64) (+.f64 (/.f64 (+.f64 #s(literal -1125 binary64) (/.f64 #s(literal -16875 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -75 binary64) (*.f64 x x)))) x)
(/ -5 x)
(/.f64 #s(literal -5 binary64) x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -5 binary64) (/.f64 #s(literal -75 binary64) (*.f64 x x))) x)
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (/ 1125 (pow x 4)))) x))
(/.f64 (+.f64 #s(literal -5 binary64) (+.f64 (/.f64 #s(literal -75 binary64) (.f64 x x)) (/.f64 #s(literal -1125 binary64) (.f64 x (.f64 x (.f64 x x)))))) x)
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (+ (* 16875 (/ 1 (pow x 6))) (/ 1125 (pow x 4))))) x))
(/.f64 (+.f64 (+.f64 (/.f64 #s(literal -75 binary64) (.f64 x x)) (/.f64 #s(literal -1125 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal -5 binary64) (/.f64 #s(literal -16875 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x)))))))) x)
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
(+ 3 (* -1/5 (pow x 2)))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
(+ 3 (* -1/5 (pow x 2)))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64))))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 x (.f64 x #s(literal -1/5 binary64)))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* -1/5 x)
(*.f64 x #s(literal -1/5 binary64))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 4/14175 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (+.f64 #s(literal 2/945 binary64) (.f64 (*.f64 x x) #s(literal 4/14175 binary64)))))))))
(* 7/30 x)
(*.f64 x #s(literal 7/30 binary64))
(* x (- 7/30 (* 49/20 (/ 1 (pow x 2)))))
(+.f64 (.f64 x #s(literal 7/30 binary64)) (.f64 #s(literal 1 binary64) (/.f64 #s(literal -49/20 binary64) x)))
(* x (- (+ 7/30 (/ 399/40 (pow x 4))) (* 49/20 (/ 1 (pow x 2)))))
(+.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal -49/20 binary64) x)) (.f64 x (-.f64 #s(literal 7/30 binary64) (/.f64 #s(literal -399/40 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* x (- (+ 7/30 (/ 399/40 (pow x 4))) (+ (* 49/20 (/ 1 (pow x 2))) (* 39249/80 (/ 1 (pow x 6))))))
(+.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal -49/20 binary64) x)) (.f64 x (+.f64 (/.f64 #s(literal 399/40 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 7/30 binary64) (/.f64 #s(literal -39249/80 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))))))
(* 7/30 x)
(*.f64 x #s(literal 7/30 binary64))
(* -1 (* x (- (* 49/20 (/ 1 (pow x 2))) 7/30)))
(+.f64 (.f64 x #s(literal 7/30 binary64)) (.f64 #s(literal 1 binary64) (/.f64 #s(literal -49/20 binary64) x)))
(* -1 (* x (- (* 49/20 (/ 1 (pow x 2))) (+ 7/30 (/ 399/40 (pow x 4))))))
(+.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal -49/20 binary64) x)) (.f64 x (-.f64 #s(literal 7/30 binary64) (/.f64 #s(literal -399/40 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* -1 (* x (- (+ (* 49/20 (/ 1 (pow x 2))) (* 39249/80 (/ 1 (pow x 6)))) (+ 7/30 (/ 399/40 (pow x 4))))))
(+.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal -49/20 binary64) x)) (.f64 x (+.f64 (/.f64 #s(literal 399/40 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 7/30 binary64) (/.f64 #s(literal -39249/80 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))))))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* -1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(* x (+ 1/3 (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
(* x (+ 1/3 (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
(* -2/945 (pow x 5))
(.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x x)))))
(* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal -2/945 binary64) (/.f64 #s(literal 1/45 binary64) (.f64 x x))))
(* (pow x 5) (- (/ 1/3 (pow x 4)) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -2/945 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/45 binary64) (*.f64 x x)))))
(* (pow x 5) (- (/ 1/3 (pow x 4)) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -2/945 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/45 binary64) (*.f64 x x)))))
(* -2/945 (pow x 5))
(.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x x)))))
(* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal -2/945 binary64) (/.f64 #s(literal 1/45 binary64) (.f64 x x))))
(* -1 (* (pow x 5) (- (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (/ 1/3 (pow x 4)))))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -2/945 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/45 binary64) (*.f64 x x)))))
(* -1 (* (pow x 5) (- (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (/ 1/3 (pow x 4)))))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -2/945 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/45 binary64) (*.f64 x x)))))
(* 1/9 (pow x 2))
(.f64 x (.f64 x #s(literal 1/9 binary64)))
(* (pow x 2) (+ 1/9 (* -1/2025 (pow x 4))))
(.f64 x (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(* (pow x 2) (+ 1/9 (* -1/2025 (pow x 4))))
(.f64 x (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(* (pow x 2) (+ 1/9 (* -1/2025 (pow x 4))))
(.f64 x (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(* -1/2025 (pow x 6))
(.f64 x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/2025 binary64)))
(* (pow x 6) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal -1/2025 binary64) (/.f64 #s(literal 1/9 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* (pow x 6) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal -1/2025 binary64) (/.f64 #s(literal 1/9 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* (pow x 6) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal -1/2025 binary64) (/.f64 #s(literal 1/9 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* -1/2025 (pow x 6))
(.f64 x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/2025 binary64)))
(* (pow x 6) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal -1/2025 binary64) (/.f64 #s(literal 1/9 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* (pow x 6) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal -1/2025 binary64) (/.f64 #s(literal 1/9 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* (pow x 6) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal -1/2025 binary64) (/.f64 #s(literal 1/9 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* 1/9 x)
(*.f64 x #s(literal 1/9 binary64))
(* x (+ 1/9 (* -1/2025 (pow x 4))))
(.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* x (+ 1/9 (* -1/2025 (pow x 4))))
(.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* x (+ 1/9 (* -1/2025 (pow x 4))))
(.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/2025 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* -1/2025 (pow x 5))
(.f64 (.f64 x (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1/2025 binary64))
(* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -1/2025 binary64) (/.f64 #s(literal 1/9 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -1/2025 binary64) (/.f64 #s(literal 1/9 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -1/2025 binary64) (/.f64 #s(literal 1/9 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* -1/2025 (pow x 5))
(.f64 (.f64 x (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1/2025 binary64))
(* -1 (* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4))))))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -1/2025 binary64) (/.f64 #s(literal 1/9 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* -1 (* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4))))))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -1/2025 binary64) (/.f64 #s(literal 1/9 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* -1 (* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4))))))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal -1/2025 binary64) (/.f64 #s(literal 1/9 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* x (+ 1/45 (* 2/945 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* x (+ 1/45 (* 2/945 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* x (+ 1/45 (* 2/945 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* 2/945 (pow x 3))
(.f64 #s(literal 2/945 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* 2/945 (pow x 3))
(.f64 #s(literal 2/945 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))

eval98.0ms (0.7%)

Compiler: Compiled 23729 to 1436 computations (93.9% saved)

prune64.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	501	1	502
Fresh	0	0	0
Picked	1	2	3
Done	0	1	1
Total	502	4	506

Accuracy

100.0%

Counts

506 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
	53.0%	(/.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))))) (.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 (.f64 (*.f64 x x) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))))))
✓	100.0%	(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 x (.f64 x #s(literal -1/5 binary64)))))
✓	99.7%	(/.f64 x #s(literal 3 binary64))
✓	99.4%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))))

Compiler

Compiled 255 to 98 computations (61.6% saved)

regimes7.0ms (0.1%)

Counts

11 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes3.0ms (0%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
100.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

3 → 1

Calls

Call 1

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

Outputs
(/.f64 x #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)

regimes10.0ms (0.1%)

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:

10.0ms

Results

Accuracy	Segments	Branch
99.1%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

28×	`*-commutative_binary64`
22×	`+-commutative_binary64`
18×	`sub-neg_binary64`
16×	`neg-sub0_binary64`
16×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	32
1	37	32
2	51	32
3	63	32
4	80	32
5	93	32
6	99	32
7	102	32
8	103	32

Stop Event

1×

saturated

Calls

Call 1

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

soundness1.1s (8%)

Rules

5384×	`-lowering-.f32`
5384×	`-lowering-.f64`
3678×	`-lowering-.f32`
3678×	`-lowering-.f64`
2856×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	63
1	84	60
2	680	56
0	8206	56
0	182	1705
1	525	1447
2	1505	1421
3	4111	1415
0	8247	1415
0	67	302
1	189	269
2	564	266
3	1805	266
4	2707	266
5	4420	266
6	6039	266
7	6587	266
0	8075	266

Stop Event

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

Compiler

Compiled 97 to 68 computations (29.9% saved)

preprocess64.0ms (0.5%)

Remove: (negabs x)
Compiler: Compiled 206 to 140 computations (32% saved)

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

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

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

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

analyze8.0ms (0.1%)

sample7.6s (54.2%)

preprocess43.0ms (0.3%)

explain560.0ms (4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify22.0ms (0.2%)

localize495.0ms (3.5%)

series4.0ms (0%)

rewrite217.0ms (1.5%)

simplify198.0ms (1.4%)

eval31.0ms (0.2%)

prune29.0ms (0.2%)

simplify137.0ms (1%)

localize118.0ms (0.8%)

series24.0ms (0.2%)

rewrite289.0ms (2.1%)

simplify173.0ms (1.2%)

eval52.0ms (0.4%)

prune71.0ms (0.5%)

simplify214.0ms (1.5%)

localize189.0ms (1.3%)

series9.0ms (0.1%)

rewrite470.0ms (3.3%)

simplify280.0ms (2%)

eval173.0ms (1.2%)

prune186.0ms (1.3%)

simplify174.0ms (1.2%)

localize232.0ms (1.7%)

series18.0ms (0.1%)

rewrite385.0ms (2.7%)

simplify243.0ms (1.7%)

eval98.0ms (0.7%)

prune64.0ms (0.5%)

regimes7.0ms (0.1%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes10.0ms (0.1%)

simplify10.0ms (0.1%)

soundness1.1s (8%)

preprocess64.0ms (0.5%)

end0.0ms (0%)

Profiling

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

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