Metrics for invcot (example 3.9)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze5.0ms (0%)

Memory

9.2MiB live, 9.2MiB allocated

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 12 computations (25% saved)

sample10.3s (62%)

Memory

-31.4MiB live, 8 774.4MiB allocated

Samples

8.1s	3 868×	2	valid
1.6s	4 313×	1	valid
7.0ms	75×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 9.0s

ival-tan: 7.5s (83.1% of total)

ival-div: 677.0ms (7.5% of total)

adjust: 329.0ms (3.6% of total)

const: 289.0ms (3.2% of total)

ival-<: 118.0ms (1.3% of total)

ival-sub: 96.0ms (1.1% of total)

ival-and: 13.0ms (0.1% of total)

exact: 6.0ms (0.1% of total)

ival-assert: 4.0ms (0% of total)

Bogosity

explain494.0ms (3%)

Memory

10.4MiB live, 482.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
256	-	1	(-9.047100790562084e-309)	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`
0	-	0	-	`(/.f64 #s(literal 1 binary64) x)`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(tan.f64 x)`
0	-	0	-	`(/.f64 #s(literal 1 binary64) (tan.f64 x))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`	cancellation	255	0

Confusion

	Predicted +	Predicted -
+	255	1
-	0	0

Precision

1.0

Recall

0.99609375

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	255	0	1
-	0	0	0

Precision?

1.0

Recall?

0.99609375

Freqs

test

number	freq
0	1
1	255

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

347.0ms	254×	2	valid
62.0ms	250×	1	valid
0.0ms	8×	0	valid

Compiler

Compiled 107 to 52 computations (51.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 385.0ms

ival-tan: 346.0ms (89.9% of total)

ival-div: 20.0ms (5.2% of total)

adjust: 12.0ms (3.1% of total)

ival-sub: 6.0ms (1.6% of total)

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

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

exact: 0.0ms (0% of total)

preprocess21.0ms (0.1%)

Memory

17.1MiB live, 17.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	21	19
2	54	16
3	131	16
4	204	16
5	228	16
6	230	16
0	6	8
0	10	8
1	14	8
2	22	8
3	31	8
4	43	8
5	63	8
6	102	8
7	134	8
8	192	8
9	225	8
10	247	8
0	247	8

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

Outputs
(-.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) x))

Symmetry

(negabs x)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.7%	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify8.0ms (0%)

Memory

5.1MiB live, 5.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(tan.f64 x)
cost-diff	0	(/.f64 #s(literal 1 binary64) (tan.f64 x))
cost-diff	0	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
0	10	19
1	14	19
2	22	19
3	31	19
4	43	19
5	63	19
6	102	19
7	134	19
8	192	19
9	225	19
10	247	19
0	247	19

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize225.0ms (1.4%)

Memory

-17.5MiB live, 253.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	0	(tan.f64 x)
accuracy	0.015625	(/.f64 #s(literal 1 binary64) (tan.f64 x))
accuracy	59.639913169424005	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Samples

173.0ms	127×	2	valid
44.0ms	125×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 40 to 14 computations (65% saved)

Precisions

Click to see histograms. Total time spent on operations: 206.0ms

ival-tan: 185.0ms (89.9% of total)

ival-div: 11.0ms (5.3% of total)

adjust: 6.0ms (2.9% of total)

ival-sub: 3.0ms (1.5% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0%)

Memory

4.1MiB live, 4.1MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())
#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())

Outputs
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) (taylor 0 x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) (taylor 0 x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1/3 (pow x 2))) x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/3 (pow x 2)))) (taylor 0 x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (taylor 0 x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) (taylor 0 x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (cos x) (sin x))) (taylor inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (cos x) (sin x))) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor -inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor -inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor -inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (cos x)) (taylor -inf x) (#s(alt (tan.f64 x) (patch (tan.f64 x) #<representation binary64>) () ())) ())

Calls

3 calls:

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

simplify300.0ms (1.8%)

Memory

23.8MiB live, 178.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	324
1	179	324
2	458	318
3	1332	318
4	2094	318
5	3093	318
6	3682	318
7	3949	318
8	5089	318
9	7269	318
0	8431	300

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 47

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 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)
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))))))))
(* -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)
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos 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)
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))

Outputs
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 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 (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/.f64 (fma.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -2/945 binary64) (.f64 x x) #s(literal -1/45 binary64)) (.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
x
(* x (+ 1 (* 1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/15 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 5 binary64)) (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (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)
(/ (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))
(/ (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))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (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)
(/ (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))
(/ (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))

rewrite102.0ms (0.6%)

Memory

11.1MiB live, 118.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
0	10	17
1	49	17
2	454	17
3	5706	17
0	9203	17

Stop Event

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

Counts

4 → 277

Calls

Call 1

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

Outputs
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eval47.0ms (0.3%)

Memory: -24.9MiB live, 63.2MiB allocated
Compiler: Compiled 5 442 to 762 computations (86% saved)

prune5.0ms (0%)

Memory

16.7MiB live, 16.7MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	321	3	324
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	322	3	325

Accuracy

99.4%

Counts

325 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
▶	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
▶	98.7%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))

Status

Accuracy

Program

▶

99.4%

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

▶

99.3%

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

▶

98.7%

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

Compiler

Compiled 27 to 20 computations (25.9% saved)

simplify74.0ms (0.4%)

Memory

2.8MiB live, 41.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	113
0	29	113
1	48	113
2	83	113
3	145	113
4	237	113
5	263	113
6	305	113
7	337	113
8	586	113
9	1998	113
10	2707	113
11	2791	113
12	2791	113
13	2793	113
14	2794	113
0	2794	113

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize606.0ms (3.7%)

Memory

-59.8MiB live, 257.6MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
accuracy	0.00390625	(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
accuracy	0.00390625	(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
accuracy	0.3515625	(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
accuracy	0.10621703111186122	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
accuracy	0.34765625	(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
accuracy	0.35546875	(*.f64 x #s(literal 1/3 binary64))
accuracy	0.49720355326799853	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))

Samples

359.0ms	125×	1	valid
215.0ms	127×	2	valid
1.0ms	4×	0	valid

Compiler

Compiled 184 to 35 computations (81% saved)

Precisions

Click to see histograms. Total time spent on operations: 252.0ms

ival-tan: 174.0ms (69% of total)

adjust: 20.0ms (7.9% of total)

const: 17.0ms (6.7% of total)

ival-mult: 17.0ms (6.7% of total)

ival-div: 14.0ms (5.6% of total)

ival-add: 6.0ms (2.4% of total)

ival-sub: 3.0ms (1.2% of total)

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

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

exact: 0.0ms (0% of total)

series9.0ms (0.1%)

Memory

13.1MiB live, 13.1MiB allocated

Counts

10 → 120

Calls

Call 1

Inputs
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 1/3 binary64)) (patch (.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/3 binary64)) (patch (.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/3 binary64)) (patch (.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/3 binary64)) (patch (.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/3 binary64)) (patch (.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1/3 (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 (* 1/45 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 (* 1/45 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 (* 1/45 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1/3 (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 (* 1/45 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt 1/45 (taylor 0 x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/45 (* 2/945 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/45 (* 2/945 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/45 (* 2/945 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (cos x) (sin x))) (taylor inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/3 binary64)) (patch (.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/3 binary64)) (patch (.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/3 binary64)) (patch (.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/3 binary64)) (patch (.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (cos x) (sin x))) (taylor inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/45 (pow x 3)) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 1/45 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (cos x) (sin x))) (taylor inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 2/945 (pow x 5)) (taylor inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 2/945 (pow x 4)) (taylor inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/945 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/3 binary64)) (patch (.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/3 binary64)) (patch (.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/3 binary64)) (patch (.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/3 binary64)) (patch (.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/45 (pow x 3)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 1/45 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 2/945 (pow x 5)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 2/945 (pow x 4)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/945 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

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

Time

Variable

Point

Expression

2.0ms

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

2.0ms

inf

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

2.0ms

-inf

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

simplify155.0ms (0.9%)

Memory

23.7MiB live, 138.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	908
1	185	908
2	477	908
3	1163	908
4	2339	908
5	5675	908
0	8126	833

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

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

Outputs
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 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)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
1/45
#s(literal 1/45 binary64)
(+ 1/45 (* 2/945 (pow x 2)))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(+ 1/45 (* 2/945 (pow x 2)))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(+ 1/45 (* 2/945 (pow x 2)))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* 1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 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)
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 2/945 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/945 binary64))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/945 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* 2/945 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/945 binary64))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x)
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(* 2/945 (pow x 2))
(.f64 #s(literal 2/945 binary64) (.f64 x x))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* 1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 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)
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 2/945 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/945 binary64))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/945 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* 2/945 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/945 binary64))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x)
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(* 2/945 (pow x 2))
(.f64 #s(literal 2/945 binary64) (.f64 x x))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))

rewrite142.0ms (0.9%)

Memory

-14.0MiB live, 177.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	101
0	29	101
1	123	101
2	933	101
0	8742	101

Stop Event

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

Counts

10 → 309

Calls

Call 1

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

Outputs
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eval62.0ms (0.4%)

Memory: 22.5MiB live, 141.5MiB allocated
Compiler: Compiled 9 610 to 1 398 computations (85.5% saved)

prune72.0ms (0.4%)

Memory

-28.9MiB live, 48.0MiB allocated

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	473	6	479
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	473	9	482

Accuracy

100.0%

Counts

482 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x)))
▶	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
▶	99.4%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))))
▶	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))))
▶	99.8%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
✓	99.4%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
✓	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/945 binary64))) x))
✓	98.7%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))

Compiler

Compiled 215 to 158 computations (26.5% saved)

simplify160.0ms (1%)

Memory

27.5MiB live, 110.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))))
cost-diff	6848	(/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64)))
cost-diff	0	(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))
cost-diff	0	(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x)
cost-diff	0	(/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))))
cost-diff	0	(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
cost-diff	0	(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x)))
cost-diff	320	(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x))
cost-diff	0	(*.f64 #s(literal 1/45 binary64) x)
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
cost-diff	320	(fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))
cost-diff	0	(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
cost-diff	1088	(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	292
0	61	292
1	98	276
2	154	276
3	276	276
4	404	276
5	520	276
6	649	276
7	792	276
8	1390	276
9	4611	276
10	6068	276
11	6713	276
12	6872	276
13	7183	276
14	7470	276
0	8021	276

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))
x
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
#s(literal 1 binary64)
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
#s(literal 1/45 binary64)
(*.f64 x x)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
(fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))
(*.f64 x x)
x
(*.f64 #s(literal 1/45 binary64) x)
#s(literal 1/45 binary64)
(*.f64 #s(literal 1/3 binary64) x)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x)))
(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
#s(literal 2/945 binary64)
(*.f64 x x)
x
#s(literal 1/45 binary64)
(*.f64 #s(literal 1/3 binary64) x)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))))
(/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))
(pow.f64 x #s(literal 4 binary64))
x
#s(literal 4 binary64)
#s(literal 1/2025 binary64)
#s(literal -1/9 binary64)
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))
#s(literal 1/45 binary64)
(*.f64 x x)
#s(literal -1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))))
(/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64)))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
#s(literal 2/945 binary64)
(*.f64 x x)
x
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)
(pow.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
x
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)))
#s(literal 1 binary64)
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
#s(literal 1/45 binary64)
(*.f64 x x)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
(fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(*.f64 x x)
x
(*.f64 #s(literal 1/45 binary64) x)
#s(literal 1/45 binary64)
(*.f64 #s(literal 1/3 binary64) x)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)) x))
(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x))
(.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)) x)
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
#s(literal 2/945 binary64)
(*.f64 x x)
x
#s(literal 1/45 binary64)
(*.f64 #s(literal 1/3 binary64) x)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (/.f64 x (fma.f64 (.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))))
(/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))
(.f64 (/.f64 x (fma.f64 (.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/2025 binary64) (*.f64 #s(literal -1/9 binary64) x))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))
(pow.f64 x #s(literal 4 binary64))
x
#s(literal 4 binary64)
#s(literal 1/2025 binary64)
#s(literal -1/9 binary64)
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))
(fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))
#s(literal 1/45 binary64)
(*.f64 x x)
#s(literal -1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)) x))
(/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64)))
(.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)) x)
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
#s(literal 2/945 binary64)
(*.f64 x x)
x
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)
(pow.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)

localize483.0ms (2.9%)

Memory

14.5MiB live, 431.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))))
accuracy	0.00390625	(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
accuracy	0.00390625	(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
accuracy	0.3984375	(/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64)))
accuracy	0.01171875	(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))
accuracy	0.10621703111186122	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))))
accuracy	0.39453125	(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x)
accuracy	0.453125	(/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))
accuracy	0.00390625	(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
accuracy	0.01171875	(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x))
accuracy	0.22265625	(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
accuracy	0.35546875	(*.f64 #s(literal 1/3 binary64) x)
accuracy	0.0078125	(fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))
accuracy	0.10621703111186122	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
accuracy	0.21875	(*.f64 #s(literal 1/45 binary64) x)
accuracy	0.35546875	(*.f64 #s(literal 1/3 binary64) x)
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
accuracy	0.0078125	(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))
accuracy	0.10621703111186122	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))

Samples

261.0ms	127×	2	valid
148.0ms	125×	1	valid
1.0ms	4×	0	valid

Compiler

Compiled 494 to 73 computations (85.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 367.0ms

ival-tan: 170.0ms (46.3% of total)

adjust: 76.0ms (20.7% of total)

ival-mult: 33.0ms (9% of total)

ival-div: 29.0ms (7.9% of total)

const: 29.0ms (7.9% of total)

ival-add: 20.0ms (5.4% of total)

ival-pow: 6.0ms (1.6% of total)

ival-sub: 3.0ms (0.8% of total)

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

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

exact: 0.0ms (0% of total)

series26.0ms (0.2%)

Memory

-13.8MiB live, 31.6MiB allocated

Counts

21 → 252

Calls

Call 1

Inputs
#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (.f64 #s(literal 1/3 binary64) x)) (patch (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (.f64 #s(literal 1/3 binary64) x))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (.f64 #s(literal 1/3 binary64) x))) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/45 binary64) x) (patch (.f64 #s(literal 1/45 binary64) x) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x)) (patch (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x)) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x))) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (patch (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) (patch (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (patch (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) (patch (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))) (patch (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/3 binary64) x) (patch (.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (patch (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))))) #<representation binary64>) () ())) ())
#s(alt 3 (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -1/5 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt 1/3 (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 (* 1/45 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/3 (* 1/45 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* 1/2025 (pow x 4)) (taylor -inf x) (#s(alt (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) (patch (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4))))) (taylor -inf x) (#s(alt (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) (patch (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4))))) (taylor -inf x) (#s(alt (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) (patch (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4))))) (taylor -inf x) (#s(alt (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) (patch (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/945 (pow x 5)) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))) (patch (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))) (patch (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))) (patch (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))) (patch (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 2/945 (pow x 4)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (patch (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/3 binary64) x) (patch (.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/3 binary64) x) (patch (.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/3 binary64) x) (patch (.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/3 binary64) x) (patch (.f64 #s(literal 1/3 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/45 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (patch (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (patch (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (patch (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (patch (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

9.0ms

-inf

((/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (- (/ 1 x) (/ 1 (tan x))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* 1/45 (* x x)) 1/3) (+ (* (* x x) (* 1/45 x)) (* 1/3 x)) (- (/ 1 x) (/ 1 (tan x))) (* x x) (* 1/45 x) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) (* x x)) (* 1/3 x)) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* 2/945 (* x x)) 1/45) x) (+ (* 2/945 (* x x)) 1/45) (- (/ 1 x) (/ 1 (tan x))) (/ (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* 1/45 (* x x)) -1/3)) (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* (pow x 4) 1/2025) -1/9) (/ (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) (pow x -1)) (- (/ 1 x) (/ 1 (tan x))) (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) (* 1/3 x) (+ (* 1/45 (* x x)) -1/3))

4.0ms

inf

((/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (- (/ 1 x) (/ 1 (tan x))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* 1/45 (* x x)) 1/3) (+ (* (* x x) (* 1/45 x)) (* 1/3 x)) (- (/ 1 x) (/ 1 (tan x))) (* x x) (* 1/45 x) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) (* x x)) (* 1/3 x)) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* 2/945 (* x x)) 1/45) x) (+ (* 2/945 (* x x)) 1/45) (- (/ 1 x) (/ 1 (tan x))) (/ (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* 1/45 (* x x)) -1/3)) (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* (pow x 4) 1/2025) -1/9) (/ (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) (pow x -1)) (- (/ 1 x) (/ 1 (tan x))) (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) (* 1/3 x) (+ (* 1/45 (* x x)) -1/3))

4.0ms

((/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (- (/ 1 x) (/ 1 (tan x))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* 1/45 (* x x)) 1/3) (+ (* (* x x) (* 1/45 x)) (* 1/3 x)) (- (/ 1 x) (/ 1 (tan x))) (* x x) (* 1/45 x) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) (* x x)) (* 1/3 x)) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* 2/945 (* x x)) 1/45) x) (+ (* 2/945 (* x x)) 1/45) (- (/ 1 x) (/ 1 (tan x))) (/ (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* 1/45 (* x x)) -1/3)) (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* (pow x 4) 1/2025) -1/9) (/ (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) (pow x -1)) (- (/ 1 x) (/ 1 (tan x))) (+ (* (+ (* 2/945 (* x x)) 1/45) (* x x)) 1/3) (* 1/3 x) (+ (* 1/45 (* x x)) -1/3))

simplify146.0ms (0.9%)

Memory

4.4MiB live, 166.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	119	2018
1	334	2014
2	840	2014
3	1991	2010
4	4659	2010
0	8108	1866

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 252

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 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 (* (pow x 2) (+ 2/945 (* 1/4725 (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)))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/3 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))))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* 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))))))))
(* 1/45 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))))
1/45
(+ 1/45 (* 2/945 (pow x 2)))
(+ 1/45 (* 2/945 (pow x 2)))
(+ 1/45 (* 2/945 (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 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* -1/9 x)
(* x (- (* 1/2025 (pow x 4)) 1/9))
(* x (- (* 1/2025 (pow x 4)) 1/9))
(* x (- (* 1/2025 (pow x 4)) 1/9))
-1/9
(- (* 1/2025 (pow x 4)) 1/9)
(- (* 1/2025 (pow x 4)) 1/9)
(- (* 1/2025 (pow x 4)) 1/9)
(* 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))))))
(* 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))))))))
1/3
(+ 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)))))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
-1/3
(- (* 1/45 (pow x 2)) 1/3)
(- (* 1/45 (pow x 2)) 1/3)
(- (* 1/45 (pow x 2)) 1/3)
(* 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 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(/ 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))
(* 1/45 (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 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 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 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))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 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 2))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 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)))))
(* 1/2025 (pow x 5))
(* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* 1/2025 (pow x 4))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* 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))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 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))))))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 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 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 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(/ 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))
(* 1/45 (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 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 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 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 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 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 2))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 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)))))
(* 1/2025 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))
(* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))
(* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))
(* 1/2025 (pow x 4))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* 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 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 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))))))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 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)))))

Outputs
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(fma.f64 (fma.f64 #s(literal 1/75 binary64) (.f64 x x) #s(literal -1/5 binary64)) (.f64 x x) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/1125 binary64) (.f64 x x) #s(literal 1/75 binary64)) (.f64 x x) #s(literal -1/5 binary64)) (*.f64 x x) #s(literal 3 binary64))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) 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)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* x (+ 1/45 (* 2/945 (pow x 2))))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(* x (+ 1/45 (* 2/945 (pow x 2))))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(* x (+ 1/45 (* 2/945 (pow x 2))))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
1/45
#s(literal 1/45 binary64)
(+ 1/45 (* 2/945 (pow x 2)))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(+ 1/45 (* 2/945 (pow x 2)))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(+ 1/45 (* 2/945 (pow x 2)))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* -1/9 x)
(*.f64 #s(literal -1/9 binary64) x)
(* x (- (* 1/2025 (pow x 4)) 1/9))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x)
(* x (- (* 1/2025 (pow x 4)) 1/9))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x)
(* x (- (* 1/2025 (pow x 4)) 1/9))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x)
-1/9
#s(literal -1/9 binary64)
(- (* 1/2025 (pow x 4)) 1/9)
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))
(- (* 1/2025 (pow x 4)) 1/9)
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))
(- (* 1/2025 (pow x 4)) 1/9)
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
-1/3
#s(literal -1/3 binary64)
(- (* 1/45 (pow x 2)) 1/3)
(fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))
(- (* 1/45 (pow x 2)) 1/3)
(fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))
(- (* 1/45 (pow x 2)) 1/3)
(fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 45 binary64) (/.f64 #s(literal 675 binary64) (*.f64 x x))) x) x)
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 10125 binary64) (pow.f64 x #s(literal 4 binary64))) #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))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (/.f64 (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 10125 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 45 binary64)) (/.f64 #s(literal 675 binary64) (*.f64 x x))) (/.f64 #s(literal 151875 binary64) (pow.f64 x #s(literal 6 binary64)))) x) x)
(* 1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 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)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 2/945 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/945 binary64))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(fma.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 2/945 binary64)) (pow.f64 x #s(literal 5 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(fma.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 2/945 binary64)) (pow.f64 x #s(literal 5 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 2/945 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 2/945 binary64))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(* 2/945 (pow x 2))
(.f64 #s(literal 2/945 binary64) (.f64 x x))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* 1/2025 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/2025 binary64))
(* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(*.f64 (-.f64 #s(literal 1/2025 binary64) (/.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(*.f64 (-.f64 #s(literal 1/2025 binary64) (/.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(*.f64 (-.f64 #s(literal 1/2025 binary64) (/.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 5 binary64)))
(* 1/2025 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))
(* 2/945 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/945 binary64))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(fma.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 2/945 binary64)) (pow.f64 x #s(literal 5 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(fma.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 2/945 binary64)) (pow.f64 x #s(literal 5 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64)))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 2/945 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/945 binary64))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x)
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (- 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))
(* (pow x 2) (- 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))
(* (pow x 2) (- 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 45 binary64) (/.f64 #s(literal 675 binary64) (*.f64 x x))) x) x)
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 10125 binary64) (pow.f64 x #s(literal 4 binary64))) #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))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (/.f64 (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 10125 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 45 binary64)) (/.f64 #s(literal 675 binary64) (*.f64 x x))) (/.f64 #s(literal 151875 binary64) (pow.f64 x #s(literal 6 binary64)))) x) x)
(* 1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 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)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 1/45 x)
(*.f64 #s(literal 1/45 binary64) x)
(* 2/945 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/945 binary64))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.f64 (-.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (.f64 x x)) #s(literal -1/45 binary64)) x) x) #s(literal -2/945 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.f64 (-.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (.f64 x x)) #s(literal -1/45 binary64)) x) x) #s(literal -2/945 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 2/945 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 2/945 binary64))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(* 2/945 (pow x 2))
(.f64 #s(literal 2/945 binary64) (.f64 x x))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* 1/2025 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/2025 binary64))
(* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))
(*.f64 (-.f64 #s(literal 1/2025 binary64) (/.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))
(*.f64 (-.f64 #s(literal 1/2025 binary64) (/.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))
(*.f64 (-.f64 #s(literal 1/2025 binary64) (/.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 5 binary64)))
(* 1/2025 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))
(* 2/945 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/945 binary64))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.f64 (-.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (.f64 x x)) #s(literal -1/45 binary64)) x) x) #s(literal -2/945 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.f64 (-.f64 (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (.f64 x x)) #s(literal -1/45 binary64)) x) x) #s(literal -2/945 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 2/945 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/945 binary64))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x)
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* 1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (- 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))
(* (pow x 2) (- 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))
(* (pow x 2) (- 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 #s(literal 1/45 binary64) x) x #s(literal -1/3 binary64))

rewrite177.0ms (1.1%)

Memory

-4.8MiB live, 225.8MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	243
0	61	233
1	252	213
2	1872	213
0	8477	213

Stop Event

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

Counts

21 → 813

Calls

Call 1

Inputs
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
(*.f64 x x)
(*.f64 #s(literal 1/45 binary64) x)
(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x)))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))))
(/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))
(/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))

Outputs
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eval150.0ms (0.9%)

Memory: 28.2MiB live, 263.8MiB allocated
Compiler: Compiled 27 802 to 2 587 computations (90.7% saved)

prune84.0ms (0.5%)

Memory

-11.7MiB live, 65.4MiB allocated

Pruning

10 alts after pruning (5 fresh and 5 done)

	Pruned	Kept	Total
New	1 252	5	1 257
Fresh	1	0	1
Picked	3	2	5
Done	0	3	3
Total	1 256	10	1 266

Accuracy

100.0%

Counts

1 266 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x)))
✓	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
▶	99.4%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))))
▶	99.4%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x)))
▶	99.9%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
▶	99.2%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
▶	99.0%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))))
✓	99.4%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
✓	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
✓	98.7%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))

Compiler

Compiled 178 to 138 computations (22.5% saved)

simplify97.0ms (0.6%)

Memory

17.3MiB live, 55.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 x #s(literal -1 binary64))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))))
cost-diff	1792	(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))))
cost-diff	5760	(/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))
cost-diff	0	(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
cost-diff	0	(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x)))
cost-diff	7232	(/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x))
cost-diff	0	#s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64))
cost-diff	0	(.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x)
cost-diff	0	(/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))))
cost-diff	0	#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))
cost-diff	0	(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
cost-diff	0	(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
cost-diff	0	#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))
cost-diff	0	(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	383
0	67	381
1	105	381
2	187	369
3	441	369
4	1500	369
5	3883	369
6	5811	369
7	7192	369
8	7899	369
0	8011	358

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))
x
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
#s(literal -1/5 binary64)
(*.f64 x x)
#s(literal 3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
x
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))
#s(literal 3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))))
(/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)))
(.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x)
#s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64))
#s(literal -1/9 binary64)
x
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))
#s(literal 1/45 binary64)
(*.f64 x x)
#s(literal -1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x)))
(/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x))
(neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))
(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
#s(literal 2/945 binary64)
(*.f64 x x)
x
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)
(/.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))))
#s(literal 1 binary64)
(/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))
(pow.f64 x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
#s(literal 2/945 binary64)
(*.f64 x x)
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))
x
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))
#s(literal -1/5 binary64)
(*.f64 x x)
#s(literal 3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
x
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))
#s(literal 3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (/.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64))))
(/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)))
(.f64 (/.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)))
(.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x)
#s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64))
#s(literal -1/9 binary64)
x
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))
#s(literal 1/45 binary64)
(*.f64 x x)
#s(literal -1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)) x))
(/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x))
(.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)) x)
(neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -2/945 binary64) (fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)))
(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
#s(literal 2/945 binary64)
(*.f64 x x)
x
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)
(/.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)) x))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))))
(.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)) x)
#s(literal 1 binary64)
(/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) x)
(pow.f64 x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
#s(literal 2/945 binary64)
(*.f64 x x)
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)

localize1.3s (7.7%)

Memory

-22.1MiB live, 374.7MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
accuracy	0.22265625	(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
accuracy	0.43014340516871985	(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))))
accuracy	0.4453125	(/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))
accuracy	0.00390625	(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))
accuracy	0.00390625	(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
accuracy	0.22265625	(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
accuracy	0.3984375	(/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x))
accuracy	0.09897078940174665	#s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64))
accuracy	0.10621703111186122	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))))
accuracy	0.39453125	(.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x)
accuracy	0.453125	(/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)))
accuracy	0.0078125	(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
accuracy	0.10621703111186122	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
accuracy	0.49490682071700154	#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))
accuracy	0.09630810821123671	#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))
accuracy	0.10621703111186122	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))

Samples

762.0ms	127×	2	valid
356.0ms	125×	1	valid
1.0ms	4×	0	valid

Compiler

Compiled 554 to 76 computations (86.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 935.0ms

const: 291.0ms (31.1% of total)

ival-neg: 229.0ms (24.5% of total)

ival-tan: 223.0ms (23.9% of total)

ival-div: 127.0ms (13.6% of total)

adjust: 25.0ms (2.7% of total)

ival-mult: 18.0ms (1.9% of total)

ival-add: 12.0ms (1.3% of total)

ival-pow: 6.0ms (0.6% of total)

ival-sub: 3.0ms (0.3% of total)

exact: 1.0ms (0.1% of total)

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

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

series19.0ms (0.1%)

Memory

0.3MiB live, 38.8MiB allocated

Counts

21 → 252

Calls

Call 1

Inputs
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64)) (patch (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) (patch (/.f64 (.f64 #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (patch (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) (patch #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x)) (patch (/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)) (patch (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (patch (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) #<representation binary64>) () ())
#s(alt (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (patch (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))))) #<representation binary64>) () ())
#s(alt (pow.f64 x #s(literal -1 binary64)) (patch (pow.f64 x #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt 3 (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -1/5 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5))) (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5))) (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ ( 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt 3 (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64)) (patch (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -1/5 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64)) (patch (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -1/5 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64)) (patch (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -1/5 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64)) (patch (fma.f64 #s(literal -1/5 binary64) (.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt 3 (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -1/5 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5))) (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5))) (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) (patch #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) (patch (/.f64 (.f64 #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) (patch (/.f64 (.f64 #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) (patch (/.f64 (.f64 #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))) (patch (/.f64 (.f64 #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/9 x) (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (patch (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/2025 (pow x 4)) 1/9)) (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (patch (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/2025 (pow x 4)) 1/9)) (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (patch (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/2025 (pow x 4)) 1/9)) (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (patch (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) #<representation binary64>) () ())) ())
#s(alt -1/9 (taylor 0 x) (#s(alt #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) (patch #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2025 (pow x 4)) 1/9) (taylor 0 x) (#s(alt #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) (patch #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2025 (pow x 4)) 1/9) (taylor 0 x) (#s(alt #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) (patch #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2025 (pow x 4)) 1/9) (taylor 0 x) (#s(alt #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) (patch #s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) #<representation binary64>) () ())) ())
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#s(alt (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (pow.f64 x #s(literal -1 binary64)) (patch (pow.f64 x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (pow.f64 x #s(literal -1 binary64)) (patch (pow.f64 x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (pow.f64 x #s(literal -1 binary64)) (patch (pow.f64 x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (pow.f64 x #s(literal -1 binary64)) (patch (pow.f64 x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2/945 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (patch (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

-inf

((- (/ 1 x) (/ 1 (tan x))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* -1/5 (* x x)) 3) (- (/ 1 x) (/ 1 (tan x))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (- (/ 1 x) (/ 1 (tan x))) (/ (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* 1/45 (* x x)) -1/3)) (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* (pow x 4) 1/2025) -1/9) (/ (neg (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3)) (/ -1 x)) (- (/ 1 x) (/ 1 (tan x))) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3) (* (+ (* 2/945 (* x x)) 1/45) x) (/ (pow x -1) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3)) (/ 1 (/ (pow x -1) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3))) (- (/ 1 x) (/ 1 (tan x))) (pow x -1) (* x x) (+ (* 2/945 (* x x)) 1/45))

3.0ms

inf

((- (/ 1 x) (/ 1 (tan x))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* -1/5 (* x x)) 3) (- (/ 1 x) (/ 1 (tan x))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (- (/ 1 x) (/ 1 (tan x))) (/ (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* 1/45 (* x x)) -1/3)) (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* (pow x 4) 1/2025) -1/9) (/ (neg (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3)) (/ -1 x)) (- (/ 1 x) (/ 1 (tan x))) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3) (* (+ (* 2/945 (* x x)) 1/45) x) (/ (pow x -1) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3)) (/ 1 (/ (pow x -1) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3))) (- (/ 1 x) (/ 1 (tan x))) (pow x -1) (* x x) (+ (* 2/945 (* x x)) 1/45))

2.0ms

((- (/ 1 x) (/ 1 (tan x))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* -1/5 (* x x)) 3) (- (/ 1 x) (/ 1 (tan x))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (- (/ 1 x) (/ 1 (tan x))) (/ (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* 1/45 (* x x)) -1/3)) (* (+ (* (pow x 4) 1/2025) -1/9) x) (+ (* (pow x 4) 1/2025) -1/9) (/ (neg (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3)) (/ -1 x)) (- (/ 1 x) (/ 1 (tan x))) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3) (* (+ (* 2/945 (* x x)) 1/45) x) (/ (pow x -1) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3)) (/ 1 (/ (pow x -1) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3))) (- (/ 1 x) (/ 1 (tan x))) (pow x -1) (* x x) (+ (* 2/945 (* x x)) 1/45))

simplify129.0ms (0.8%)

Memory

14.4MiB live, 168.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	163	2222
1	441	2220
2	1107	2216
3	2669	2212
4	5752	2212
0	8223	2073

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 252

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
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)))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* -1/5 (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 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
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)))
(* 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))))))))
(* 1/3 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))))
(* -1/9 x)
(* x (- (* 1/2025 (pow x 4)) 1/9))
(* x (- (* 1/2025 (pow x 4)) 1/9))
(* x (- (* 1/2025 (pow x 4)) 1/9))
-1/9
(- (* 1/2025 (pow x 4)) 1/9)
(- (* 1/2025 (pow x 4)) 1/9)
(- (* 1/2025 (pow x 4)) 1/9)
(* 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))))))
(* 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))))))))
1/3
(+ 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)))))
(* 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))))
(/ 3 x)
(/ (+ 3 (* -1/5 (pow x 2))) x)
(/ (+ 3 (* (pow x 2) (- (* -1/175 (pow x 2)) 1/5))) x)
(/ (+ 3 (* (pow x 2) (- (* (pow x 2) (- (* 13/7875 (pow x 2)) 1/175)) 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 (* 2/945 (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 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1/45
(+ 1/45 (* 2/945 (pow x 2)))
(+ 1/45 (* 2/945 (pow x 2)))
(+ 1/45 (* 2/945 (pow x 2)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 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)))))
(/ 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))
(* -1/5 (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 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 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)))))
(/ 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 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 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)))))
(* 1/2025 (pow x 5))
(* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* 1/2025 (pow x 4))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* 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))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 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 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)))))
(/ 945/2 (pow x 5))
(/ (- 945/2 (* 19845/4 (/ 1 (pow x 2)))) (pow x 5))
(/ (+ 945/2 (* -1 (/ (+ 19845/4 (* 178605/8 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 5))
(/ (- (+ 945/2 (* 16253055/16 (/ 1 (pow x 6)))) (+ (* 19845/4 (/ 1 (pow x 2))) (/ 178605/8 (pow x 4)))) (pow x 5))
(* 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))))))
(* -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)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 2/945 (pow x 2))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 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)))))
(/ 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))
(* -1/5 (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 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 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)))))
(/ 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 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 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)))))
(* 1/2025 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))
(* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))
(* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))
(* 1/2025 (pow x 4))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* 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 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 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 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)))))
(/ 945/2 (pow x 5))
(* -1 (/ (- (* 19845/4 (/ 1 (pow x 2))) 945/2) (pow x 5)))
(* -1 (/ (- (+ (* 19845/4 (/ 1 (pow x 2))) (/ 178605/8 (pow x 4))) 945/2) (pow x 5)))
(* -1 (/ (- (+ (* 19845/4 (/ 1 (pow x 2))) (/ 178605/8 (pow x 4))) (+ 945/2 (* 16253055/16 (/ 1 (pow x 6))))) (pow x 5)))
(* 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 (/ (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)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 2/945 (pow x 2))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))

Outputs
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x)
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) x)
(* 1/3 x)
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(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(/ 945/2 (pow x 5))
(/.f64 #s(literal 945/2 binary64) (pow.f64 x #s(literal 5 binary64)))
(/ (- 945/2 (* 19845/4 (/ 1 (pow x 2)))) (pow x 5))
(/.f64 (-.f64 #s(literal 945/2 binary64) (/.f64 #s(literal 19845/4 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(/ (+ 945/2 (* -1 (/ (+ 19845/4 (* 178605/8 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 5))
(/.f64 (-.f64 (-.f64 #s(literal 945/2 binary64) (/.f64 #s(literal 178605/8 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 19845/4 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(/ (- (+ 945/2 (* 16253055/16 (/ 1 (pow x 6)))) (+ (* 19845/4 (/ 1 (pow x 2))) (/ 178605/8 (pow x 4)))) (pow x 5))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 16253055/16 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal -945/2 binary64)) (-.f64 (/.f64 #s(literal 178605/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -19845/4 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 5 binary64)))
(* 2/945 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/945 binary64))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 1/45 binary64) (.f64 x x)) #s(literal 2/945 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 2/945 binary64)) (/.f64 #s(literal 1/45 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 2/945 binary64)) (/.f64 #s(literal 1/45 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (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)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 2/945 (pow x 2))
(.f64 #s(literal 2/945 binary64) (.f64 x x))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 45 binary64) (/.f64 #s(literal 675 binary64) (*.f64 x x))) x) x)
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 10125 binary64) (pow.f64 x #s(literal 4 binary64))) #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))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (/.f64 (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 10125 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 45 binary64)) (/.f64 #s(literal 675 binary64) (*.f64 x x))) (/.f64 #s(literal 151875 binary64) (pow.f64 x #s(literal 6 binary64)))) x) x)
(* -1/5 (pow x 2))
(.f64 #s(literal -1/5 binary64) (.f64 x x))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 45 binary64) (/.f64 #s(literal 675 binary64) (*.f64 x x))) x) x)
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 10125 binary64) (pow.f64 x #s(literal 4 binary64))) #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))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (/.f64 (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 10125 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 45 binary64)) (/.f64 #s(literal 675 binary64) (*.f64 x x))) (/.f64 #s(literal 151875 binary64) (pow.f64 x #s(literal 6 binary64)))) x) x)
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
(* 1/2025 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/2025 binary64))
(* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))
(*.f64 (-.f64 #s(literal 1/2025 binary64) (/.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))
(*.f64 (-.f64 #s(literal 1/2025 binary64) (/.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))
(*.f64 (-.f64 #s(literal 1/2025 binary64) (/.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 5 binary64)))
(* 1/2025 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))
(* 2/945 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/945 binary64))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 1/45 binary64) (.f64 x x)) #s(literal 2/945 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.f64 (-.f64 (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (.f64 x x)) #s(literal 1/45 binary64)) x) x) #s(literal -2/945 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.f64 (-.f64 (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (.f64 x x)) #s(literal 1/45 binary64)) x) x) #s(literal -2/945 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* 2/945 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/945 binary64))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64)) x) x)
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64))
(* 2/945 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 2/945 binary64))
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(/ 945/2 (pow x 5))
(/.f64 #s(literal 945/2 binary64) (pow.f64 x #s(literal 5 binary64)))
(* -1 (/ (- (* 19845/4 (/ 1 (pow x 2))) 945/2) (pow x 5)))
(/.f64 (-.f64 #s(literal 945/2 binary64) (/.f64 #s(literal 19845/4 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (/ (- (+ (* 19845/4 (/ 1 (pow x 2))) (/ 178605/8 (pow x 4))) 945/2) (pow x 5)))
(/.f64 (-.f64 (-.f64 #s(literal 945/2 binary64) (/.f64 #s(literal 178605/8 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 19845/4 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (/ (- (+ (* 19845/4 (/ 1 (pow x 2))) (/ 178605/8 (pow x 4))) (+ 945/2 (* 16253055/16 (/ 1 (pow x 6))))) (pow x 5)))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 16253055/16 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal -945/2 binary64)) (-.f64 (/.f64 #s(literal 178605/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -19845/4 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 5 binary64)))
(* 2/945 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 2/945 binary64))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 1/45 binary64) (.f64 x x)) #s(literal 2/945 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.f64 (-.f64 (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (.f64 x x)) #s(literal 1/45 binary64)) x) x) #s(literal -2/945 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.f64 (-.f64 (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (.f64 x x)) #s(literal 1/45 binary64)) x) x) #s(literal -2/945 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* -1 (/ (cos x) (sin x)))
(/.f64 (neg.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) (/ (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)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 2/945 (pow x 2))
(.f64 #s(literal 2/945 binary64) (.f64 x x))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
(* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))

rewrite267.0ms (1.6%)

Memory

-25.6MiB live, 269.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	308
0	67	306
1	274	294
2	1857	294
0	8287	284

Stop Event

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

Counts

21 → 547

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))))
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))
(fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))))
(/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)))
(.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x)
#s(approx (+ (* (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64))
(/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x)))
(fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))
(.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x)
(/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))))
(pow.f64 x #s(literal -1 binary64))
(*.f64 x x)
(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))

Outputs
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eval159.0ms (1%)

Memory: 14.4MiB live, 288.6MiB allocated
Compiler: Compiled 22 448 to 2 568 computations (88.6% saved)

prune22.0ms (0.1%)

Memory

10.2MiB live, 87.8MiB allocated

Pruning

10 alts after pruning (1 fresh and 9 done)

	Pruned	Kept	Total
New	993	1	994
Fresh	0	0	0
Picked	1	4	5
Done	0	5	5
Total	994	10	1 004

Accuracy

100.0%

Counts

1 004 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x)))
✓	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
✓	99.4%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))))
✓	99.4%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x)))
✓	99.9%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
✓	99.2%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1 binary64) #s(approx (/ (pow x -1) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/175 binary64) (.f64 x x) #s(literal -1/5 binary64)) (.f64 x x) #s(literal 3 binary64)) x))))
✓	99.4%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
✓	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
✓	98.7%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))

Compiler

Compiled 323 to 166 computations (48.6% saved)

regimes11.0ms (0.1%)

Memory

-10.6MiB live, 27.7MiB allocated

Counts

16 → 1

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) x) (*.f64 #s(literal 1/3 binary64) x)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 #s(approx (+ ( (pow x 4) 1/2025) -1/9) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) (.f64 x x) (.f64 #s(literal 1/3 binary64) x)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1 binary64) #s(approx (/ (pow x -1) (+ (* (* (+ (* 2/945 (* x x)) 1/45) x) x) 1/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/175 binary64) (.f64 x x) #s(literal -1/5 binary64)) (.f64 x x) #s(literal 3 binary64)) x))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64))) (/.f64 #s(literal -1 binary64) x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) x) (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal -1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) (.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal 2/945 binary64) (.f64 x x) #s(literal 1/45 binary64)) x) x #s(literal 1/3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 (fma.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2/945 binary64))) x))

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

Calls

2 calls:

6.0ms	x
4.0ms	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes4.0ms (0%)

Memory

17.0MiB live, 17.0MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes4.0ms (0%)

Memory

15.1MiB live, 15.1MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

2 calls:

2.0ms	x
1.0ms	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes10.0ms (0.1%)

Memory

-40.6MiB live, 11.4MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

8.0ms	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
2.0ms	x

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes3.0ms (0%)

Memory

6.4MiB live, 6.4MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

1.0ms	x
1.0ms	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

Accuracy	Segments	Branch
98.7%	1	`x`
98.7%	1	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify27.0ms (0.2%)

Memory

10.8MiB live, 50.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	97
1	37	97

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness639.0ms (3.8%)

Memory

21.8MiB live, 404.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	119	2018
1	334	2014
2	840	2014
3	1991	2010
4	4659	2010
0	8108	1866
0	19	101
0	29	101
1	123	101
2	933	101
0	8742	101
0	67	324
1	179	324
2	458	318
3	1332	318
4	2094	318
5	3093	318
6	3682	318
7	3949	318
8	5089	318
9	7269	318
0	8431	300

Stop Event

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

Compiler

Compiled 105 to 74 computations (29.5% saved)

preprocess77.0ms (0.5%)

Memory: 0.1MiB live, 119.8MiB allocated
Remove: (negabs x)
Compiler: Compiled 182 to 120 computations (34.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	21
1	21	19
2	54	16
3	131	16
4	204	16
5	228	16
6	230	16
0	6	8
0	10	8
1	14	8
2	22	8
3	31	8
4	43	8
5	63	8
6	102	8
7	134	8
8	192	8
9	225	8
10	247	8
0	247	8

Iter	Nodes	Cost
0	6	19
0	10	19
1	14	19
2	22	19
3	31	19
4	43	19
5	63	19
6	102	19
7	134	19
8	192	19
9	225	19
10	247	19
0	247	19

Iter	Nodes	Cost
0	8	21
1	21	19
2	54	16
3	131	16
4	204	16
5	228	16
6	230	16
0	6	8
0	10	8
1	14	8
2	22	8
3	31	8
4	43	8
5	63	8
6	102	8
7	134	8
8	192	8
9	225	8
10	247	8
0	247	8

Iter	Nodes	Cost
0	6	19
0	10	19
1	14	19
2	22	19
3	31	19
4	43	19
5	63	19
6	102	19
7	134	19
8	192	19
9	225	19
10	247	19
0	247	19

start0.0ms (0%)

analyze5.0ms (0%)

sample10.3s (62%)

explain494.0ms (3%)

preprocess21.0ms (0.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify8.0ms (0%)

localize225.0ms (1.4%)

series5.0ms (0%)

simplify300.0ms (1.8%)

rewrite102.0ms (0.6%)

eval47.0ms (0.3%)

prune5.0ms (0%)

simplify74.0ms (0.4%)

localize606.0ms (3.7%)

series9.0ms (0.1%)

simplify155.0ms (0.9%)

rewrite142.0ms (0.9%)

eval62.0ms (0.4%)

prune72.0ms (0.4%)

simplify160.0ms (1%)

localize483.0ms (2.9%)

series26.0ms (0.2%)

simplify146.0ms (0.9%)

rewrite177.0ms (1.1%)

eval150.0ms (0.9%)

prune84.0ms (0.5%)

simplify97.0ms (0.6%)

localize1.3s (7.7%)

series19.0ms (0.1%)

simplify129.0ms (0.8%)

rewrite267.0ms (1.6%)

eval159.0ms (1%)

prune22.0ms (0.1%)

regimes11.0ms (0.1%)

regimes4.0ms (0%)

regimes4.0ms (0%)

regimes10.0ms (0.1%)

regimes3.0ms (0%)

simplify27.0ms (0.2%)

soundness639.0ms (3.8%)

preprocess77.0ms (0.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	21
1	21	19
2	54	16
3	131	16
4	204	16
5	228	16
6	230	16
0	6	8
0	10	8
1	14	8
2	22	8
3	31	8
4	43	8
5	63	8
6	102	8
7	134	8
8	192	8
9	225	8
10	247	8
0	247	8

Iter	Nodes	Cost
0	6	19
0	10	19
1	14	19
2	22	19
3	31	19
4	43	19
5	63	19
6	102	19
7	134	19
8	192	19
9	225	19
10	247	19
0	247	19