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)

sample9.7s (64.2%)

Memory

-31.5MiB live, 8 700.3MiB allocated

Samples

7.4s	3 876×	2	valid
1.8s	4 281×	1	valid
10.0ms	99×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 8.8s

ival-tan: 7.3s (83.2% of total)

ival-div: 654.0ms (7.4% of total)

const: 316.0ms (3.6% of total)

adjust: 224.0ms (2.5% of total)

ival-<: 139.0ms (1.6% of total)

ival-sub: 133.0ms (1.5% of total)

ival-and: 12.0ms (0.1% of total)

exact: 5.0ms (0.1% of total)

ival-assert: 3.0ms (0% of total)

Bogosity

explain746.0ms (4.9%)

Memory

-23.0MiB live, 419.5MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	256	0
-	0	0

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	256	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
1	256

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

557.0ms	248×	2	valid
53.0ms	254×	1	valid
1.0ms	10×	0	valid

Compiler

Compiled 50 to 22 computations (56% saved)

Precisions

Click to see histograms. Total time spent on operations: 588.0ms

ival-tan: 493.0ms (83.8% of total)

ival-sub: 63.0ms (10.7% of total)

ival-div: 19.0ms (3.2% of total)

adjust: 11.0ms (1.9% 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

30.1MiB live, 30.1MiB 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)

prune18.0ms (0.1%)

Memory

-35.5MiB live, 2.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.1%	(-.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 (0.1%)

Memory

9.8MiB live, 9.8MiB 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)

localize374.0ms (2.5%)

Memory

1.0MiB live, 238.6MiB 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	59.43358214330527	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Samples

281.0ms	124×	2	valid
85.0ms	127×	1	valid
0.0ms	5×	0	valid

Compiler

Compiled 21 to 8 computations (61.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 355.0ms

ival-tan: 285.0ms (80.2% of total)

ival-div: 60.0ms (16.9% of total)

adjust: 6.0ms (1.7% 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)

series5.0ms (0%)

Memory

6.4MiB live, 6.4MiB 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))

simplify177.0ms (1.2%)

Memory

26.9MiB live, 255.8MiB 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))

rewrite101.0ms (0.7%)

Memory

4.9MiB live, 203.7MiB 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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eval48.0ms (0.3%)

Memory: -25.8MiB live, 132.4MiB allocated
Compiler: Compiled 5 442 to 762 computations (86% saved)

prune6.0ms (0%)

Memory

26.9MiB live, 26.9MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	320	4	324
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	321	4	325

Accuracy

99.5%

Counts

325 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.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))
▶	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))
▶	98.6%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))

Compiler

Compiled 46 to 31 computations (32.6% saved)

simplify371.0ms (2.4%)

Memory

-32.9MiB live, 215.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(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))
cost-diff	0	(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))
cost-diff	0	(.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)
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.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))
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	25	199
0	42	199
1	74	199
2	136	199
3	290	199
4	637	199
5	953	199
6	1011	199
7	1045	199
8	1535	199
9	4653	199
10	6564	199
11	7012	199
12	7037	199
13	7037	199
14	7261	199
15	7281	199
16	7281	199
17	7299	199
18	7299	199
19	7305	199
0	7305	199

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

localize329.0ms (2.2%)

Memory

12.4MiB live, 484.0MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 binary64))
accuracy	0.01171875	(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))
accuracy	0.01171875	(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))
accuracy	0.33984375	(.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)
accuracy	0.0078125	(fma.f64 #s(literal 2/945 binary64) (*.f64 x x) #s(literal 1/45 binary64))
accuracy	0.01171875	(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	0.018361092648988643	#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	0.33984375	(.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	0.01171875	(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
accuracy	0.14290976226923474	#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	0.33984375	(.f64 (fma.f64 (.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64)) x)
accuracy	0.3359375	(*.f64 x #s(literal 1/3 binary64))
accuracy	0.5865157576709189	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))

Samples

233.0ms	124×	2	valid
73.0ms	127×	1	valid
1.0ms	5×	0	valid

Compiler

Compiled 171 to 29 computations (83% saved)

Precisions

Click to see histograms. Total time spent on operations: 277.0ms

ival-tan: 173.0ms (62.4% of total)

ival-mult: 28.0ms (10.1% of total)

const: 26.0ms (9.4% of total)

adjust: 20.0ms (7.2% of total)

ival-div: 12.0ms (4.3% of total)

ival-add: 12.0ms (4.3% of total)

ival-sub: 6.0ms (2.2% of total)

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

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

exact: 0.0ms (0% of total)

series15.0ms (0.1%)

Memory

19.3MiB live, 19.3MiB allocated

Counts

15 → 180

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>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.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)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.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)) #<representation binary64>) () ())
#s(alt (.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) (patch (.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) #<representation binary64>) () ())
#s(alt (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)) (patch (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)) #<representation binary64>) () ())
#s(alt (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)) (patch (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)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (patch (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 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>) () ())) ())
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#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>) () ())) ())
#s(alt (* -1 (/ (cos x) (sin x))) (taylor -inf x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.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)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.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)) #<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 (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)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.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)) #<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 (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)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.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)) #<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 (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)) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.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)) #<representation binary64>) () ())) ())
#s(alt (* 1/4725 (pow x 7)) (taylor -inf x) (#s(alt (.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) (patch (.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) #<representation binary64>) () ())) ())
#s(alt (* (pow x 7) (+ 1/4725 (* 2/945 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.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) (patch (.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) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (pow x 2))) 1/4725))) (taylor -inf x) (#s(alt (.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) (patch (.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) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/4725 (* 2/945 (/ 1 (pow x 2))))))) (taylor -inf x) (#s(alt (.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) (patch (.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) #<representation binary64>) () ())) ())
#s(alt (* 1/4725 (pow x 6)) (taylor -inf x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (+ 1/4725 (* 2/945 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (+ (* 2/945 (/ 1 (pow x 2))) (* 1/3 (/ 1 (pow x 6))))))) (taylor -inf x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (* 1/4725 (pow x 4)) (taylor -inf x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/4725 (* 2/945 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (* 1/4725 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (patch (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/4725 (* 2/945 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (patch (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/4725 (* 2/945 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (patch (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/4725 (* 2/945 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) (patch (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	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) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (+ (* (+ (* 1/4725 (* x x)) 2/945) (* x x)) 1/45) (* x x)) 1/3) x) (+ (* (+ (* (+ (* 1/4725 (* x x)) 2/945) (* x x)) 1/45) (* x x)) 1/3) (+ (* (+ (* 1/4725 (* x x)) 2/945) (* x x)) 1/45) (+ (* 1/4725 (* x x)) 2/945))
3.0ms	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) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (+ (* (+ (* 1/4725 (* x x)) 2/945) (* x x)) 1/45) (* x x)) 1/3) x) (+ (* (+ (* (+ (* 1/4725 (* x x)) 2/945) (* x x)) 1/45) (* x x)) 1/3) (+ (* (+ (* 1/4725 (* x x)) 2/945) (* x x)) 1/45) (+ (* 1/4725 (* x x)) 2/945))
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) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (+ (* (+ (* 1/4725 (* x x)) 2/945) (* x x)) 1/45) (* x x)) 1/3) x) (+ (* (+ (* (+ (* 1/4725 (* x x)) 2/945) (* x x)) 1/45) (* x x)) 1/3) (+ (* (+ (* 1/4725 (* x x)) 2/945) (* x x)) 1/45) (+ (* 1/4725 (* x x)) 2/945))

Time

Variable

Point

Expression

3.0ms

-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) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (+ (* (+ (* 1/4725 (* x x)) 2/945) (* x x)) 1/45) (* x x)) 1/3) x) (+ (* (+ (* (+ (* 1/4725 (* x x)) 2/945) (* x x)) 1/45) (* x x)) 1/3) (+ (* (+ (* 1/4725 (* x x)) 2/945) (* x x)) 1/45) (+ (* 1/4725 (* x x)) 2/945))

3.0ms

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) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (+ (* (+ (* 1/4725 (* x x)) 2/945) (* x x)) 1/45) (* x x)) 1/3) x) (+ (* (+ (* (+ (* 1/4725 (* x x)) 2/945) (* x x)) 1/45) (* x x)) 1/3) (+ (* (+ (* 1/4725 (* x x)) 2/945) (* x x)) 1/45) (+ (* 1/4725 (* x x)) 2/945))

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) (- (/ 1 x) (/ 1 (tan x))) (* (+ (* (+ (* (+ (* 1/4725 (* x x)) 2/945) (* x x)) 1/45) (* x x)) 1/3) x) (+ (* (+ (* (+ (* 1/4725 (* x x)) 2/945) (* x x)) 1/45) (* x x)) 1/3) (+ (* (+ (* 1/4725 (* x x)) 2/945) (* x x)) 1/45) (+ (* 1/4725 (* x x)) 2/945))

simplify132.0ms (0.9%)

Memory

6.3MiB live, 121.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	96	1520
1	316	1520
2	841	1518
3	2205	1518
4	4798	1518
0	8023	1389

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (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)))
(* 1/3 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 (* (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 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))
1/45
(+ 1/45 (* 2/945 (pow x 2)))
(+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))
(+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))
2/945
(+ 2/945 (* 1/4725 (pow x 2)))
(+ 2/945 (* 1/4725 (pow x 2)))
(+ 2/945 (* 1/4725 (pow x 2)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/3 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)))
(* 1/4725 (pow x 7))
(* (pow x 7) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (+ (* 2/945 (/ 1 (pow x 2))) (* 1/3 (/ 1 (pow x 6)))))))
(* 1/4725 (pow x 6))
(* (pow x 6) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (+ (* 2/945 (/ 1 (pow x 2))) (* 1/3 (/ 1 (pow x 6)))))))
(* 1/4725 (pow x 4))
(* (pow x 4) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* 1/4725 (pow x 2))
(* (pow x 2) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/4725 (* 2/945 (/ 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)))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/4725 (pow x 7))
(* (pow x 7) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (pow x 2))) 1/4725)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))))
(* 1/4725 (pow x 6))
(* (pow x 6) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (+ (* 2/945 (/ 1 (pow x 2))) (* 1/3 (/ 1 (pow x 6)))))))
(* 1/4725 (pow x 4))
(* (pow x 4) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* 1/4725 (pow x 2))
(* (pow x 2) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/4725 (* 2/945 (/ 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))
(* 1/3 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 (* (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 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))
(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))
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 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))
(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))
(+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))
(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))
2/945
#s(literal 2/945 binary64)
(+ 2/945 (* 1/4725 (pow x 2)))
(fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 binary64))
(+ 2/945 (* 1/4725 (pow x 2)))
(fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 binary64))
(+ 2/945 (* 1/4725 (pow x 2)))
(fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 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)))))
(.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))))))
(.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)
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(.f64 #s(literal 2/945 binary64) (.f64 x x))
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(* (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)))))
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(* 1/4725 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4725 binary64))
(* (pow x 4) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 binary64)) x) x)
(* (pow x 4) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(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))
(* (pow x 4) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(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))
(* 1/4725 (pow x 2))
(.f64 #s(literal 1/4725 binary64) (.f64 x x))
(* (pow x 2) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 binary64))
(* (pow x 2) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 binary64))
(* (pow x 2) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 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)))))
(.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 (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))
(* -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)))
(* 1/4725 (pow x 7))
(*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 1/4725 binary64))
(* (pow x 7) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(.f64 (-.f64 (/.f64 #s(literal 2/945 binary64) (.f64 x x)) #s(literal -1/4725 binary64)) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (pow x 2))) 1/4725)))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/45 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4725 binary64)) (/.f64 #s(literal -2/945 binary64) (.f64 x x))) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))))
(.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (.f64 x x)) #s(literal 1/45 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal -1/4725 binary64) (/.f64 #s(literal 2/945 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 7 binary64)))
(* 1/4725 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/4725 binary64))
(* (pow x 6) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/4725 binary64) (.f64 x x) #s(literal 2/945 binary64)))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(.f64 (.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)) x) x)
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (+ (* 2/945 (/ 1 (pow x 2))) (* 1/3 (/ 1 (pow x 6)))))))
(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))
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(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4725 binary64))
(* (pow x 4) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 binary64)) x) x)
(* (pow x 4) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(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))
(* (pow x 4) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(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))
(* 1/4725 (pow x 2))
(.f64 #s(literal 1/4725 binary64) (.f64 x x))
(* (pow x 2) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 binary64))
(* (pow x 2) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 binary64))
(* (pow x 2) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 binary64))

rewrite151.0ms (1%)

Memory

6.6MiB live, 159.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	179
0	42	179
1	183	179
2	1397	179
0	8314	179

Stop Event

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

Counts

15 → 358

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))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.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))
(.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)
(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))
(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))
(fma.f64 #s(literal 1/4725 binary64) (*.f64 x x) #s(literal 2/945 binary64))

Outputs
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eval79.0ms (0.5%)

Memory: 10.3MiB live, 123.0MiB allocated
Compiler: Compiled 16 209 to 1 932 computations (88.1% saved)

prune27.0ms (0.2%)

Memory

-30.3MiB live, 51.2MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	640	3	643
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	640	7	647

Accuracy

100.0%

Counts

647 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (.f64 (.f64 #s(literal 1/45 binary64) (*.f64 x x)) x)))
▶	99.2%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 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)))))
✓	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.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))
✓	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))
✓	98.6%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))

Compiler

Compiled 79 to 57 computations (27.8% saved)

simplify69.0ms (0.5%)

Memory

12.5MiB live, 48.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(.f64 #s(literal 1/45 binary64) (.f64 x x))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (.f64 (.f64 #s(literal 1/45 binary64) (*.f64 x x)) x)))
cost-diff	6144	(fma.f64 x #s(literal 1/3 binary64) (.f64 (.f64 #s(literal 1/45 binary64) (*.f64 x x)) x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(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 (fma.f64 #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 #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 #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: 2 (0.0ms)

Iter	Nodes	Cost
0	21	142
0	31	142
1	47	130
2	69	128
3	92	128
4	112	128
5	136	128
6	171	128
7	203	128
8	385	128
9	944	128
10	1184	128
11	1542	128
12	1784	128
13	1954	128
14	2027	128
15	2111	128
16	2115	128
17	2115	128
0	2115	128

Stop Event

1×	iter limit
1×	saturated
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))) (/.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))))
(/.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #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)
x
#s(literal 1/3 binary64)
(pow.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (.f64 (.f64 #s(literal 1/45 binary64) (*.f64 x x)) x)))
(fma.f64 x #s(literal 1/3 binary64) (.f64 (.f64 #s(literal 1/45 binary64) (*.f64 x x)) x))
x
#s(literal 1/3 binary64)
(.f64 (.f64 #s(literal 1/45 binary64) (*.f64 x x)) x)
(.f64 #s(literal 1/45 binary64) (.f64 x x))
#s(literal 1/45 binary64)
(*.f64 x x)

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

localize409.0ms (2.7%)

Memory

10.1MiB live, 254.9MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.11328125	(.f64 (.f64 #s(literal 1/45 binary64) (*.f64 x x)) x)
accuracy	0.14290976226923474	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (.f64 (.f64 #s(literal 1/45 binary64) (*.f64 x x)) x)))
accuracy	0.1484375	(.f64 #s(literal 1/45 binary64) (.f64 x x))
accuracy	0.3359375	(fma.f64 x #s(literal 1/3 binary64) (.f64 (.f64 #s(literal 1/45 binary64) (*.f64 x x)) x))
accuracy	0	(*.f64 x x)
accuracy	0.01171875	(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
accuracy	0.14290976226923474	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64))))
accuracy	0.390625	(/.f64 (fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (pow.f64 x #s(literal -1 binary64)))
accuracy	0.00390625	(/.f64 #s(literal 1 binary64) (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	0.01171875	(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
accuracy	0.14290976226923474	#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

341.0ms	124×	2	valid
50.0ms	127×	1	valid
1.0ms	5×	0	valid

Compiler

Compiled 117 to 21 computations (82.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 366.0ms

ival-tan: 286.0ms (78.1% of total)

adjust: 27.0ms (7.4% of total)

ival-div: 26.0ms (7.1% of total)

const: 10.0ms (2.7% of total)

ival-mult: 7.0ms (1.9% of total)

ival-add: 4.0ms (1.1% of total)

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

ival-pow: 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)

series12.0ms (0.1%)

Memory

-20.3MiB live, 17.7MiB allocated

Counts

11 → 132

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

Calls

3 calls:

Time

Variable

Point

Expression

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) (/ (+ (* 1/45 (* x x)) 1/3) (pow x -1)) (- (/ 1 x) (/ 1 (tan x))) (* x x) (+ (* x 1/3) (* (* 1/45 (* x x)) x)) (- (/ 1 x) (/ 1 (tan x))) (* 1/45 (* x x)) (* (* 1/45 (* x x)) x))

2.0ms

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) (/ (+ (* 1/45 (* x x)) 1/3) (pow x -1)) (- (/ 1 x) (/ 1 (tan x))) (* x x) (+ (* x 1/3) (* (* 1/45 (* x x)) x)) (- (/ 1 x) (/ 1 (tan x))) (* 1/45 (* x x)) (* (* 1/45 (* x x)) x))

1.0ms

((/ 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) (/ (+ (* 1/45 (* x x)) 1/3) (pow x -1)) (- (/ 1 x) (/ 1 (tan x))) (* x x) (+ (* x 1/3) (* (* 1/45 (* x x)) x)) (- (/ 1 x) (/ 1 (tan x))) (* 1/45 (* x x)) (* (* 1/45 (* x x)) x))

simplify156.0ms (1%)

Memory

18.8MiB live, 135.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	1006
1	196	1006
2	494	1006
3	1171	1006
4	2438	1006
5	5321	1006
0	8370	946

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

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)
(* 1/3 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))))))))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* (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 (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)))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* (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 (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)))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))
(* 1/45 (pow x 3))

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)
(* 1/3 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)
(* 1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(* 1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(* 1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(* 1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 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 #s(literal 10125 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 675 binary64) (.f64 x x)) #s(literal 45 binary64))) (.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 #s(literal 10125 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 675 binary64) (.f64 x x)) #s(literal 45 binary64))) (/.f64 #s(literal 151875 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 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 (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)))
(* 1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(* 1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(* 1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(* 1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 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 #s(literal 10125 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 675 binary64) (.f64 x x)) #s(literal 45 binary64))) (.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 #s(literal 10125 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 675 binary64) (.f64 x x)) #s(literal 45 binary64))) (/.f64 #s(literal 151875 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 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 (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)))
(* 1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(* 1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(* 1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(* 1/45 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))
(* 1/45 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/45 binary64))

rewrite438.0ms (2.9%)

Memory

-28.0MiB live, 175.8MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	116
0	31	116
1	132	102
2	994	102
0	8953	102

Stop Event

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

Counts

11 → 725

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

Outputs
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eval139.0ms (0.9%)

Memory: -27.0MiB live, 163.6MiB allocated
Compiler: Compiled 19 200 to 1 747 computations (90.9% saved)

prune19.0ms (0.1%)

Memory

20.5MiB live, 57.7MiB allocated

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	1 007	3	1 010
Fresh	0	0	0
Picked	2	1	3
Done	0	4	4
Total	1 009	8	1 017

Accuracy

100.0%

Counts

1 017 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (.f64 (.f64 #s(literal 1/45 binary64) (*.f64 x x)) x)))
▶	99.2%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x)))
▶	99.8%	#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)))))
▶	99.1%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
✓	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.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))
✓	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))
✓	98.6%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))

Compiler

Compiled 83 to 61 computations (26.5% saved)

simplify79.0ms (0.5%)

Memory

8.5MiB live, 47.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(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 (fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x)))
cost-diff	1088	(/.f64 (fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x))
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)))))
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))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	166
0	38	166
1	56	166
2	75	166
3	88	166
4	110	166
5	147	166
6	211	164
7	292	164
8	642	164
9	1500	158
10	1991	158
11	2577	158
12	2874	158
13	3243	158
14	3772	158
15	4267	158
16	4267	158
0	4267	156

Stop Event

1×	iter limit
1×	saturated
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)) #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 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 (fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x)))
(/.f64 (fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 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)
x
#s(literal -1/3 binary64)
(/.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)

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

localize306.0ms (2%)

Memory

-14.3MiB live, 345.2MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.01171875	(fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64))
accuracy	0.14290976226923474	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x)))
accuracy	0.390625	(/.f64 (fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x))
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	0.14150355884781568	#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) (fma.f64 #s(literal -1/5 binary64) (*.f64 x x) #s(literal 3 binary64)))
accuracy	0.14290976226923474	#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)))))
accuracy	0.0078125	(/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64)))
accuracy	0.14290976226923474	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
accuracy	0.592973282115828	#s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))

Samples

214.0ms	124×	2	valid
69.0ms	127×	1	valid
1.0ms	5×	0	valid

Compiler

Compiled 109 to 26 computations (76.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 262.0ms

ival-tan: 186.0ms (71.1% of total)

ival-div: 27.0ms (10.3% of total)

const: 20.0ms (7.6% of total)

adjust: 13.0ms (5% of total)

ival-mult: 6.0ms (2.3% of total)

ival-add: 5.0ms (1.9% of total)

ival-sub: 3.0ms (1.1% of total)

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

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

exact: 0.0ms (0% of total)

series8.0ms (0.1%)

Memory

12.5MiB live, 12.5MiB allocated

Counts

11 → 132

Calls

Call 1

Inputs
#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 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 (/.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x)) (patch (/.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 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 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 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>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<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)) #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 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 (/.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x)) (patch (/.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x)) (patch (/.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x)) (patch (/.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x)) (patch (/.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x))) #<representation binary64>) () ())) ())
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#s(alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf 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 (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf 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 (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2)) (taylor -inf 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 (/ (cos x) (sin x))) (taylor -inf 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 x) (/ (cos x) (sin x))) (taylor -inf 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 x) (/ (cos x) (sin x))) (taylor -inf 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 x) (/ (cos x) (sin x))) (taylor -inf 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 (* 1/45 (pow x 3)) (taylor -inf 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 (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf 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 (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf 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 (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf 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 (/ 45 (pow x 2)) (taylor -inf 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 (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf 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 (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf 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 (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2)) (taylor -inf 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 (* -1/5 (pow x 2)) (taylor -inf 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 (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) (taylor -inf 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 (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) (taylor -inf 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 (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) (taylor -inf 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 (* 1/45 (pow x 3)) (taylor -inf x) (#s(alt (/.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x)) (patch (/.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 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 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x)) (patch (/.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 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 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x)) (patch (/.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 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 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x)) (patch (/.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) 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 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 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 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 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 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 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 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 #s(literal -1/45 binary64) (.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 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 (* -1 (* (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 (* -1 (* (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 (* -1 (* (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) (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>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

((- (/ 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))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* -1/5 (* x x)) 3) (/ (+ (* -1/45 (* x x)) -1/3) (/ -1 x)) (- (/ 1 x) (/ 1 (tan x))) (+ (* -1/45 (* x x)) -1/3) (* x x))

1.0ms

-inf

((- (/ 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))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* -1/5 (* x x)) 3) (/ (+ (* -1/45 (* x x)) -1/3) (/ -1 x)) (- (/ 1 x) (/ 1 (tan x))) (+ (* -1/45 (* x x)) -1/3) (* x x))

1.0ms

inf

((- (/ 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))) (/ x (/ 1 (+ (* 1/45 (* x x)) 1/3))) (/ 1 (+ (* 1/45 (* x x)) 1/3)) (+ (* -1/5 (* x x)) 3) (/ (+ (* -1/45 (* x x)) -1/3) (/ -1 x)) (- (/ 1 x) (/ 1 (tan x))) (+ (* -1/45 (* x x)) -1/3) (* x x))

simplify108.0ms (0.7%)

Memory

23.7MiB live, 95.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	84	1112
1	216	1112
2	567	1112
3	1415	1112
4	2870	1112
5	6579	1112
0	8121	1037

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

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

rewrite168.0ms (1.1%)

Memory

-24.1MiB live, 131.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	151
0	38	151
1	162	149
2	1150	143
0	8785	141

Stop Event

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

Counts

11 → 317

Calls

Call 1

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

Outputs
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eval73.0ms (0.5%)

Memory: -5.1MiB live, 112.1MiB allocated
Compiler: Compiled 7 571 to 1 369 computations (81.9% saved)

prune13.0ms (0.1%)

Memory

-1.1MiB live, 37.7MiB allocated

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	478	0	478
Fresh	0	0	0
Picked	0	3	3
Done	0	5	5
Total	478	8	486

Accuracy

100.0%

Counts

486 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (.f64 (.f64 #s(literal 1/45 binary64) (*.f64 x x)) x)))
✓	99.2%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (fma.f64 #s(literal -1/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) (/.f64 #s(literal -1 binary64) x)))
✓	99.8%	#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)))))
✓	99.1%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 1/45 (* x x)) 1/3)) #s(literal 3 binary64))))
✓	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.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))
✓	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))
✓	98.6%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))

Compiler

Compiled 196 to 113 computations (42.3% saved)

regimes7.0ms (0%)

Memory

9.5MiB live, 9.5MiB allocated

Counts

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

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

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	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

5.3MiB live, 5.3MiB 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 x #s(literal 1/3 binary64) (.f64 (.f64 #s(literal 1/45 binary64) (*.f64 x x)) x)))

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

regimes3.0ms (0%)

Memory

4.6MiB live, 4.6MiB 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)

regimes3.0ms (0%)

Memory

4.1MiB live, 4.1MiB 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:

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

Results

Accuracy	Segments	Branch
99.1%	1	`x`
99.1%	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)

regimes2.0ms (0%)

Memory

3.7MiB live, 3.7MiB 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
98.6%	1	`x`
98.6%	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)

simplify50.0ms (0.3%)

Memory

-1.9MiB live, 36.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	97
1	38	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 x #s(literal 1/3 binary64) (.f64 (.f64 #s(literal 1/45 binary64) (*.f64 x x)) 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 x #s(literal 1/3 binary64) (.f64 (.f64 #s(literal 1/45 binary64) (*.f64 x x)) x)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 x #s(literal 1/3 binary64) (.f64 (.f64 (*.f64 x x) #s(literal 1/45 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))

soundness641.0ms (4.2%)

Memory

-9.8MiB live, 422.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	179
0	42	179
1	183	179
2	1397	179
0	8314	179
0	76	1006
1	196	1006
2	494	1006
3	1171	1006
4	2438	1006
5	5321	1006
0	8370	946
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×	done
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 105 to 75 computations (28.6% saved)

preprocess108.0ms (0.7%)

Memory: 33.6MiB live, 72.0MiB allocated
Remove: (negabs x)
Compiler: Compiled 202 to 138 computations (31.7% 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%)

sample9.7s (64.2%)

explain746.0ms (4.9%)

preprocess21.0ms (0.1%)

eval0.0ms (0%)

prune18.0ms (0.1%)

simplify8.0ms (0.1%)

localize374.0ms (2.5%)

series5.0ms (0%)

simplify177.0ms (1.2%)

rewrite101.0ms (0.7%)

eval48.0ms (0.3%)

prune6.0ms (0%)

simplify371.0ms (2.4%)

localize329.0ms (2.2%)

series15.0ms (0.1%)

simplify132.0ms (0.9%)

rewrite151.0ms (1%)

eval79.0ms (0.5%)

prune27.0ms (0.2%)

simplify69.0ms (0.5%)

localize409.0ms (2.7%)

series12.0ms (0.1%)

simplify156.0ms (1%)

rewrite438.0ms (2.9%)

eval139.0ms (0.9%)

prune19.0ms (0.1%)

simplify79.0ms (0.5%)

localize306.0ms (2%)

series8.0ms (0.1%)

simplify108.0ms (0.7%)

rewrite168.0ms (1.1%)

eval73.0ms (0.5%)

prune13.0ms (0.1%)

regimes7.0ms (0%)

regimes4.0ms (0%)

regimes3.0ms (0%)

regimes3.0ms (0%)

regimes2.0ms (0%)

simplify50.0ms (0.3%)

soundness641.0ms (4.2%)

preprocess108.0ms (0.7%)

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