Metrics for invcot (example 3.9)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze7.0ms (0%)

Memory

-31.2MiB live, 7.4MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 16 to 12 computations (25% saved)

sample10.0s (61%)

Memory

42.2MiB live, 9 320.6MiB allocated

Samples

7.9s	3 844×	2	valid
1.5s	4 319×	1	valid
8.0ms	93×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 9.1s

ival-tan: 7.9s (86.5% of total)

ival-div: 417.0ms (4.6% of total)

const: 355.0ms (3.9% of total)

adjust: 211.0ms (2.3% of total)

ival-sub: 166.0ms (1.8% of total)

ival-<: 62.0ms (0.7% 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

explain824.0ms (5%)

Memory

-1.5MiB live, 750.9MiB 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

663.0ms	260×	2	valid
106.0ms	252×	1	valid

Compiler

Compiled 51 to 22 computations (56.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 713.0ms

ival-tan: 672.0ms (94.3% of total)

ival-div: 23.0ms (3.2% of total)

adjust: 11.0ms (1.5% of total)

ival-sub: 6.0ms (0.8% of total)

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

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

exact: 0.0ms (0% of total)

preprocess25.0ms (0.2%)

Memory

6.6MiB live, 44.7MiB allocated

Algorithm

1×	egg-herbie

Rules

112×	`lower-fma.f64`
112×	`lower-fma.f32`
80×	`lower-*.f64`
80×	`lower-*.f32`
48×	`lower-+.f64`

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

Symmetry

(negabs x)

Compiler

Compiled 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	5.8%	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify14.0ms (0.1%)

Memory

-21.8MiB live, 17.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

112×	`lower-fma.f64`
112×	`lower-fma.f32`
80×	`lower-*.f64`
80×	`lower-*.f32`
48×	`lower-+.f64`

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) 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)

localize252.0ms (1.5%)

Memory

32.9MiB live, 343.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	0	(tan.f64 x)
accuracy	0.00390625	(/.f64 #s(literal 1 binary64) (tan.f64 x))
accuracy	60.300821351156515	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Samples

211.0ms	130×	2	valid
31.0ms	126×	1	valid

Compiler

Compiled 21 to 8 computations (61.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 230.0ms

ival-tan: 210.0ms (91.3% of total)

ival-div: 9.0ms (3.9% of total)

adjust: 7.0ms (3% of total)

ival-sub: 3.0ms (1.3% of total)

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

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

exact: 0.0ms (0% of total)

series10.0ms (0.1%)

Memory

-32.4MiB live, 6.3MiB 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 (/ (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 (/ (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 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 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 (/ 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 (/ 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 (/ (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 (/ (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 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 (/ (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 (/ (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

12 calls:

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

simplify285.0ms (1.7%)

Memory

19.1MiB live, 337.7MiB allocated

Algorithm

1×	egg-herbie

Rules

18 970×	`lower-fma.f64`
18 970×	`lower-fma.f32`
3 656×	`lower-*.f64`
3 656×	`lower-*.f32`
3 436×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	324
1	179	324
2	458	318
3	1321	318
4	2085	318
5	3083	318
6	3670	318
7	3941	318
8	5080	318
9	7268	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 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ (+ 1 (* -1/3 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))

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

rewrite277.0ms (1.7%)

Memory

-6.0MiB live, 151.4MiB allocated

Rules

3 072×	`lower-fma.f64`
3 072×	`lower-fma.f32`
2 002×	`lower-*.f64`
2 002×	`lower-*.f32`
1 374×	`frac-times`

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

eval37.0ms (0.2%)

Memory: 22.1MiB live, 58.6MiB allocated
Compiler: Compiled 6 028 to 755 computations (87.5% saved)

prune41.0ms (0.3%)

Memory

11.0MiB live, 86.3MiB allocated

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	322	2	324
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	323	2	325

Accuracy

99.5%

Counts

325 → 2

Alt Table

Click to see full alt table

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

Compiler

Compiled 15 to 9 computations (40% saved)

simplify27.0ms (0.2%)

Memory

-29.0MiB live, 16.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

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

Rules

536×	`lower-fma.f32`
534×	`lower-fma.f64`
360×	`lower-*.f32`
354×	`lower-*.f64`
170×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	54
0	19	54
1	35	54
2	50	54
3	63	54
4	76	54
5	96	54
6	135	54
7	165	54
8	295	54
9	693	54
10	914	54
11	927	54
0	927	54

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize317.0ms (1.9%)

Memory

29.3MiB live, 297.4MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
accuracy	0.00390625	(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
accuracy	0.26171875	(*.f64 x #s(literal 1/45 binary64))
accuracy	0.30859375	(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
accuracy	0.1394590524387257	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
accuracy	0.3046875	(*.f64 #s(literal 1/3 binary64) x)

Samples

225.0ms	130×	2	valid
77.0ms	126×	1	valid

Compiler

Compiled 45 to 15 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 254.0ms

ival-tan: 211.0ms (83% of total)

ival-div: 11.0ms (4.3% of total)

adjust: 9.0ms (3.5% of total)

const: 9.0ms (3.5% of total)

ival-mult: 9.0ms (3.5% of total)

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

ival-add: 2.0ms (0.8% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0%)

Memory

7.8MiB live, 7.8MiB allocated

Counts

6 → 72

Calls

Call 1

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

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

Calls

18 calls:

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

simplify164.0ms (1%)

Memory

4.8MiB live, 158.8MiB allocated

Algorithm

1×	egg-herbie

Rules

4 348×	`lower-*.f64`
4 348×	`lower-*.f32`
4 316×	`lower-fma.f64`
4 316×	`lower-fma.f32`
2 366×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	468
1	114	468
2	282	468
3	644	468
4	1219	468
5	2796	468
6	3279	468
7	4012	468
8	7328	468
0	8840	438

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

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

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

rewrite248.0ms (1.5%)

Memory

1.8MiB live, 199.9MiB allocated

Rules

5 010×	`lower-fma.f32`
5 008×	`lower-fma.f64`
3 848×	`lower-*.f32`
3 842×	`lower-*.f64`
3 116×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	49
0	19	49
1	84	49
2	641	49
3	7572	49
0	8055	49

Stop Event

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

Counts

6 → 181

Calls

Call 1

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

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal 1 binary64))
(/.f64 (*.f64 (neg.f64 x) #s(literal 1/3 binary64)) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 1/3 binary64) (neg.f64 x)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/3 binary64)))
(*.f64 x #s(literal 1/3 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(.f64 (.f64 x #s(literal 1/3 binary64)) #s(literal 1 binary64))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(+.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 x #s(literal 1/3 binary64)))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) (.f64 x x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))) (/.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/3 binary64)) (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 x #s(literal 1/3 binary64)))
(fma.f64 x #s(literal 1/3 binary64) (.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64))) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 #s(literal 1/3 binary64) x (.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 (.f64 x #s(literal 1/3 binary64)) #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))))
(fma.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 (.f64 x #s(literal 1/45 binary64)) (.f64 x x) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) x (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) #s(literal 1 binary64) (.f64 x #s(literal 1/3 binary64)))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/45 binary64)) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) (.f64 x x) (.f64 #s(literal 1/9 binary64) (.f64 x x))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/135 binary64))))) (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64))) (.f64 x (.f64 x x)) (.f64 #s(literal 1/27 binary64) (.f64 x (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))))
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(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/8303765625 binary64) #s(literal -1/729 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal -1/27 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/8303765625 binary64) #s(literal -1/729 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))) (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/4100625 binary64) (fma.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/18225 binary64) #s(literal 1/81 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/4100625 binary64) #s(literal -1/81 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64) #s(literal 1/9 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))))
(.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal 1/3 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))) (fma.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)))
(.f64 (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64))))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64) #s(literal -1/9 binary64))) (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64)) (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) (fma.f64 (.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64))) (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/8303765625 binary64)))) (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) (-.f64 (fma.f64 (.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/4100625 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64)) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)) (+.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) (.f64 x (.f64 x #s(literal 1/135 binary64)))))) (+.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) (.f64 x (.f64 x #s(literal 1/135 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64) #s(literal -1/9 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal -1/27 binary64))) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64)) (fma.f64 x (*.f64 x #s(literal 1/135 binary64)) #s(literal 1/9 binary64))))
(/.f64 #s(literal 1/45 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 x #s(literal 1/45 binary64)) #s(literal 1 binary64))
(/.f64 (*.f64 #s(literal 1/45 binary64) (neg.f64 x)) #s(literal -1 binary64))
(/.f64 (*.f64 (neg.f64 x) #s(literal 1/45 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/45 binary64)))
(*.f64 x #s(literal 1/45 binary64))
(*.f64 #s(literal 1/45 binary64) x)
(.f64 (.f64 x #s(literal 1/45 binary64)) #s(literal 1 binary64))

eval28.0ms (0.2%)

Memory: -23.6MiB live, 51.5MiB allocated
Compiler: Compiled 5 627 to 527 computations (90.6% saved)

prune31.0ms (0.2%)

Memory

23.5MiB live, 61.8MiB allocated

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	249	4	253
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	249	6	255

Accuracy

100.0%

Counts

255 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
▶	99.6%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))))
▶	100.0%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
▶	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
✓	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
✓	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Compiler

Compiled 77 to 44 computations (42.9% saved)

simplify520.0ms (3.2%)

Memory

7.5MiB live, 393.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(.f64 x (.f64 x x))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
cost-diff	320	(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))
cost-diff	0	(.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64)))
cost-diff	0	(/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))))
cost-diff	128	(-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64))
cost-diff	0	(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
cost-diff	1088	(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
cost-diff	0	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
cost-diff	1088	(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))

Rules

36 396×	`lower-fma.f32`
36 388×	`lower-fma.f64`
3 646×	`lower-*.f32`
3 632×	`lower-*.f64`
2 368×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	260
0	55	234
1	102	214
2	189	214
3	352	214
4	408	214
5	518	214
6	827	214
7	878	214
8	1272	214
9	3955	214
10	5919	214
11	6408	214
12	6665	214
13	6930	214
14	7053	214
15	7537	214
16	7660	214
17	7671	214
18	7671	214
19	7671	214
20	7695	214
0	8641	206

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
#s(literal 1/3 binary64)
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
x
(/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
#s(literal 1 binary64)
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(*.f64 x #s(literal 1/45 binary64))
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))))
(/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)))
(.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64)))
x
(fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64))
(.f64 x (.f64 x x))
(*.f64 x x)
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/91125 binary64))
#s(literal 1/91125 binary64)
#s(literal 1/27 binary64)
(fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))
(-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
#s(literal 1/2025 binary64)
#s(literal 1/135 binary64)
#s(literal 1/9 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))
(.f64 x (.f64 x x))
x
(*.f64 x x)
#s(literal 1/45 binary64)
(*.f64 x #s(literal 1/3 binary64))
#s(literal 1/3 binary64)

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 x #s(literal 1/3 binary64)))
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 x #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))))
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
x
(/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #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)))
#s(literal 1 binary64)
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(*.f64 x #s(literal 1/45 binary64))
#s(literal 1/45 binary64)
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64))) #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) #s(literal 1/9 binary64))))
(/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)))
(/.f64 (.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64))) #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) #s(literal 1/9 binary64)))
(.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64)))
(.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64))) #s(literal 1/27 binary64)))
x
(fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64))
(fma.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (*.f64 x x)) #s(literal 1/91125 binary64))) #s(literal 1/27 binary64))
(.f64 x (.f64 x x))
(*.f64 x x)
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/91125 binary64))
#s(literal 1/91125 binary64)
#s(literal 1/27 binary64)
(fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) #s(literal 1/9 binary64))
(-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
#s(literal 1/2025 binary64)
#s(literal 1/135 binary64)
#s(literal 1/9 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64))))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(.f64 x (.f64 x x))
x
(*.f64 x x)
#s(literal 1/45 binary64)
(*.f64 x #s(literal 1/3 binary64))
#s(literal 1/3 binary64)

localize796.0ms (4.9%)

Memory

-56.8MiB live, 542.5MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
accuracy	0.00390625	(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))
accuracy	0.09375	(.f64 x (.f64 x x))
accuracy	0.3046875	(*.f64 x #s(literal 1/3 binary64))
accuracy	0.09375	(.f64 x (.f64 x x))
accuracy	0.12890625	(.f64 (.f64 x x) #s(literal 1/2025 binary64))
accuracy	0.375	(.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64)))
accuracy	0.4192262816206538	(/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)))
accuracy	0.00390625	(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
accuracy	0.00390625	(/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
accuracy	0.0078125	(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
accuracy	0.26171875	(*.f64 x #s(literal 1/45 binary64))
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	0.1394590524387257	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
accuracy	0.34765625	(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))

Samples

644.0ms	130×	2	valid
109.0ms	126×	1	valid

Compiler

Compiled 213 to 35 computations (83.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 673.0ms

ival-add: 325.0ms (48.3% of total)

ival-tan: 223.0ms (33.1% of total)

ival-div: 51.0ms (7.6% of total)

const: 29.0ms (4.3% of total)

adjust: 20.0ms (3% of total)

ival-mult: 19.0ms (2.8% of total)

ival-sub: 5.0ms (0.7% 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

24.1MiB live, 24.1MiB allocated

Counts

18 → 216

Calls

Call 1

Inputs
#s(alt (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #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 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) (patch (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) (patch (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64))) (patch (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (.f64 x #s(literal 1/3 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (.f64 x #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (.f64 x #s(literal 1/3 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 1/45 binary64)) (patch (.f64 x #s(literal 1/45 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 x x) #s(literal 1/2025 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 1/3 binary64)) (patch (.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())

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

Calls

54 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/ (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (+ (* (* x x) (- (* (* x x) 1/2025) 1/135)) 1/9))
1.0ms	x	@	-inf	(- (* (* x x) 1/2025) 1/135)
1.0ms	x	@	0	(/ (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (+ (* (* x x) (- (* (* x x) 1/2025) 1/135)) 1/9))
1.0ms	x	@	inf	(* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27))
0.0ms	x	@	inf	(+ (* (* x (* x x)) 1/45) (* x 1/3))

simplify189.0ms (1.2%)

Memory

14.0MiB live, 211.7MiB allocated

Algorithm

1×	egg-herbie

Rules

9 012×	`lower-fma.f64`
9 012×	`lower-fma.f32`
3 634×	`lower-*.f64`
3 634×	`lower-*.f32`
1 764×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	97	1408
1	249	1408
2	593	1408
3	1339	1408
4	2768	1408
5	6058	1408
0	8127	1324

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

Inputs
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
-1/135
(- (* 1/2025 (pow x 2)) 1/135)
(- (* 1/2025 (pow x 2)) 1/135)
(- (* 1/2025 (pow x 2)) 1/135)
(* 1/2025 (pow x 2))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* 1/2025 (pow x 2))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/27 x)
(* x (+ 1/27 (* 1/91125 (pow x 6))))
(* x (+ 1/27 (* 1/91125 (pow x 6))))
(* x (+ 1/27 (* 1/91125 (pow x 6))))
(* 1/91125 (pow x 7))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(* 1/91125 (pow x 7))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/45 x)
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)

Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) #s(literal 1/45 binary64))) #s(literal 1/3 binary64)))
(* -1 (/ (cos x) (sin x)))
(neg.f64 (/.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 (/ (cos x) (sin x)))
(neg.f64 (/.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)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) #s(literal 1/45 binary64))) #s(literal 1/3 binary64)))
(* -1 (/ (cos x) (sin x)))
(neg.f64 (/.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 (/ (cos x) (sin x)))
(neg.f64 (/.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)))
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/75 binary64)) #s(literal -1/5 binary64)) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/1125 binary64) #s(literal 1/75 binary64)) #s(literal -1/5 binary64)) #s(literal 3 binary64))
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (.f64 x x))) (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.f64 x x))))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (+.f64 (+.f64 (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -675 binary64) (.f64 x x))) (/.f64 #s(literal -151875 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 x x))
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (.f64 x x))) (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.f64 x x))))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (+.f64 (+.f64 (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -675 binary64) (.f64 x x))) (/.f64 #s(literal -151875 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 x x))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(+ 1/3 (* 1/45 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* 1/45 (pow x 2))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
-1/135
#s(literal -1/135 binary64)
(- (* 1/2025 (pow x 2)) 1/135)
(fma.f64 x (*.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))
(- (* 1/2025 (pow x 2)) 1/135)
(fma.f64 x (*.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))
(- (* 1/2025 (pow x 2)) 1/135)
(fma.f64 x (*.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) #s(literal 1/45 binary64))) #s(literal 1/3 binary64)))
(* -1 (/ (cos x) (sin x)))
(neg.f64 (/.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 (/ (cos x) (sin x)))
(neg.f64 (/.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 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/27 x)
(*.f64 x #s(literal 1/27 binary64))
(* x (+ 1/27 (* 1/91125 (pow x 6))))
(.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))
(* x (+ 1/27 (* 1/91125 (pow x 6))))
(.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))
(* x (+ 1/27 (* 1/91125 (pow x 6))))
(.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))
(* 1/91125 (pow x 7))
(.f64 x (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1/91125 binary64)))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))
(* 1/91125 (pow x 7))
(.f64 x (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1/91125 binary64)))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 2/945 binary64) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) #s(literal 1/45 binary64))) #s(literal 1/3 binary64)))
(* -1 (/ (cos x) (sin x)))
(neg.f64 (/.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 (/ (cos x) (sin x)))
(neg.f64 (/.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 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/45 x)
(*.f64 x #s(literal 1/45 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)

rewrite252.0ms (1.5%)

Memory

12.1MiB live, 274.6MiB allocated

Rules

5 058×	`lower-fma.f32`
5 050×	`lower-fma.f64`
4 762×	`lower-/.f32`
4 752×	`lower-/.f64`
4 428×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	203
0	55	185
1	229	168
2	1662	168
0	8458	162

Stop Event

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

Counts

18 → 470

Calls

Call 1

Inputs
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) x)
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
(/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))))
(/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)))
(.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
(.f64 x (.f64 x x))
(*.f64 x x)
(*.f64 x #s(literal 1/45 binary64))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(*.f64 x #s(literal 1/3 binary64))

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) x))) #s(literal -1 binary64)))
(neg.f64 (*.f64 #s(literal -1/3 binary64) x))
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x))))
(/.f64 #s(literal -1/3 binary64) (/.f64 #s(literal -1 binary64) x))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x)) #s(literal -1 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) x))
(*.f64 x #s(literal 1/3 binary64))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) x)))))
(*.f64 #s(literal -1/3 binary64) (neg.f64 x))
(.f64 #s(literal -1/3 binary64) (.f64 x #s(literal -1 binary64)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
(exp.f64 (neg.f64 (log.f64 x)))
(neg.f64 (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 x)))
(/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 x))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64))
(pow.f64 x #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
(pow.f64 (neg.f64 (neg.f64 x)) #s(literal -1 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))) #s(literal -1 binary64)))
(+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 #s(literal 1/45 binary64) (.f64 x x))))
(+.f64 (.f64 x (.f64 #s(literal 1/45 binary64) (.f64 x x))) (.f64 #s(literal 1/3 binary64) x))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))) #s(literal 1 binary64)) (/.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (.f64 (neg.f64 x) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) (-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 #s(literal 1/45 binary64) (.f64 x x))))) (/.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 x (.f64 x x))))) (-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 #s(literal 1/45 binary64) (.f64 x x))))))
(fma.f64 #s(literal 1/3 binary64) x (.f64 x (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 #s(literal 1/45 binary64) (.f64 x x))))
(fma.f64 x #s(literal 1/3 binary64) (.f64 x (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(fma.f64 x (.f64 #s(literal 1/45 binary64) (.f64 x x)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x x)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x #s(literal 1/45 binary64)) (.f64 x x) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/45 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 #s(literal 1/45 binary64) (.f64 x x)) x (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) x)))) (.f64 x (.f64 #s(literal 1/45 binary64) (.f64 x x))))
(fma.f64 #s(literal -1/3 binary64) (neg.f64 x) (.f64 x (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(fma.f64 #s(literal -1/3 binary64) (.f64 x #s(literal -1 binary64)) (.f64 x (.f64 #s(literal 1/45 binary64) (.f64 x x))))
(neg.f64 (.f64 (neg.f64 x) (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) #s(literal 1/135 binary64)))) (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64)))))
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(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x))))
(/.f64 #s(literal -1/3 binary64) (/.f64 #s(literal -1 binary64) x))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) x)) #s(literal -1 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) x))
(*.f64 x #s(literal 1/3 binary64))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) x)))))
(*.f64 #s(literal -1/3 binary64) (neg.f64 x))
(.f64 #s(literal -1/3 binary64) (.f64 x #s(literal -1 binary64)))

eval110.0ms (0.7%)

Memory: 3.9MiB live, 166.1MiB allocated
Compiler: Compiled 22 160 to 1 412 computations (93.6% saved)

prune73.0ms (0.4%)

Memory

-24.4MiB live, 127.0MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	826	2	828
Fresh	0	0	0
Picked	3	1	4
Done	0	2	2
Total	829	5	834

Accuracy

100.0%

Counts

834 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
▶	99.6%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))))
▶	99.8%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
✓	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
✓	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Compiler

Compiled 52 to 30 computations (42.3% saved)

simplify210.0ms (1.3%)

Memory

17.9MiB live, 104.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64)))
cost-diff	0	(/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))))
cost-diff	128	(-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64))
cost-diff	0	#s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))
cost-diff	0	(/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))

Rules

2 632×	`lower-fma.f32`
2 630×	`lower-fma.f64`
1 672×	`lower-*.f32`
1 666×	`lower-*.f64`
592×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	181
0	43	169
1	79	157
2	154	157
3	309	157
4	334	157
5	355	157
6	394	157
7	427	157
8	741	157
9	2247	157
10	3259	157
11	3425	157
12	3543	157
13	3639	157
14	3767	157
15	3874	157
16	3940	157
17	3971	157
18	3988	157
19	4004	157
20	4022	157
21	4022	157
22	4022	157
23	4040	157
0	4040	147

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 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))
x
#s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))
#s(literal 3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))))
(/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)))
#s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64)))
(*.f64 x #s(literal 1/27 binary64))
x
#s(literal 1/27 binary64)
(fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))
(*.f64 x x)
(-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
#s(literal 1/2025 binary64)
#s(literal 1/135 binary64)
#s(literal 1/9 binary64)

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))
x
#s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))
#s(literal 3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)) #s(literal 1/9 binary64))))
(/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)))
(/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)) #s(literal 1/9 binary64)))
#s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64)))
(*.f64 x #s(literal 1/27 binary64))
x
#s(literal 1/27 binary64)
(fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)) #s(literal 1/9 binary64))
(*.f64 x x)
(-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64))
(fma.f64 x (*.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(.f64 x (.f64 x #s(literal 1/2025 binary64)))
#s(literal 1/2025 binary64)
#s(literal 1/135 binary64)
#s(literal 1/9 binary64)

localize420.0ms (2.6%)

Memory

39.3MiB live, 567.1MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64))
accuracy	0.12890625	(.f64 (.f64 x x) #s(literal 1/2025 binary64))
accuracy	0.375	(*.f64 x #s(literal 1/27 binary64))
accuracy	0.4192262816206538	(/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)))
accuracy	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
accuracy	0.0078125	(/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))
accuracy	0.13841774067722493	#s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))

Samples

303.0ms	130×	2	valid
76.0ms	126×	1	valid

Compiler

Compiled 124 to 33 computations (73.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 358.0ms

ival-tan: 232.0ms (64.9% of total)

const: 52.0ms (14.5% of total)

ival-div: 27.0ms (7.6% of total)

ival-mult: 18.0ms (5% of total)

adjust: 17.0ms (4.8% of total)

ival-add: 6.0ms (1.7% of total)

ival-sub: 5.0ms (1.4% of total)

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

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

exact: 0.0ms (0% of total)

series16.0ms (0.1%)

Memory

-29.6MiB live, 13.0MiB allocated

Counts

9 → 108

Calls

Call 1

Inputs
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)) (patch #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) (patch (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (patch #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 1/27 binary64)) (patch (.f64 x #s(literal 1/27 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 x x) #s(literal 1/2025 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 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 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 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 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 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 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 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 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #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 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #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 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #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 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 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 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #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 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #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 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #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 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 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 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 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 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 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 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/45 (pow x 3)) (taylor inf x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #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 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #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 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #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 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/45 (pow x 3)) (taylor -inf x) (#s(alt (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #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 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #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 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) (patch (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* 1/45 (pow x 3)) (taylor -inf x) (#s(alt (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))) (patch (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/27 x) (taylor 0 x) (#s(alt #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (patch #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/27 (* 1/91125 (pow x 6)))) (taylor 0 x) (#s(alt #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (patch #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/27 (* 1/91125 (pow x 6)))) (taylor 0 x) (#s(alt #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (patch #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/27 (* 1/91125 (pow x 6)))) (taylor 0 x) (#s(alt #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (patch #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/91125 (pow x 7)) (taylor inf x) (#s(alt #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (patch #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6))))) (taylor inf x) (#s(alt #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (patch #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6))))) (taylor inf x) (#s(alt #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (patch #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6))))) (taylor inf x) (#s(alt #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (patch #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/91125 (pow x 7)) (taylor -inf x) (#s(alt #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (patch #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6))))) (taylor -inf x) (#s(alt #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (patch #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6))))) (taylor -inf x) (#s(alt #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (patch #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6))))) (taylor -inf x) (#s(alt #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (patch #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/27 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/27 binary64)) (patch (.f64 x #s(literal 1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/27 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/27 binary64)) (patch (.f64 x #s(literal 1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/27 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/27 binary64)) (patch (.f64 x #s(literal 1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/27 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/27 binary64)) (patch (.f64 x #s(literal 1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/27 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/27 binary64)) (patch (.f64 x #s(literal 1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/27 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/27 binary64)) (patch (.f64 x #s(literal 1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/27 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/27 binary64)) (patch (.f64 x #s(literal 1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/27 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/27 binary64)) (patch (.f64 x #s(literal 1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/27 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/27 binary64)) (patch (.f64 x #s(literal 1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/27 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/27 binary64)) (patch (.f64 x #s(literal 1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/27 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/27 binary64)) (patch (.f64 x #s(literal 1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/27 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/27 binary64)) (patch (.f64 x #s(literal 1/27 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2025 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2025 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2025 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2025 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2025 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2025 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2025 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2025 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2025 (pow x 2)) (taylor inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2025 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2025 (pow x 2)) (taylor inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2025 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2025 (pow x 2)) (taylor inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2025 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2025 (pow x 2)) (taylor inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2025 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2025 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2025 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2025 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2025 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2025 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2025 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2025 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2025 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #<representation binary64>) () ())) ())

Calls

27 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(* x 1/27)
0.0ms	x	@	inf	(* x 1/27)
0.0ms	x	@	0	(* x 1/27)
0.0ms	x	@	inf	(* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27))
0.0ms	x	@	0	(- (/ 1 x) (/ 1 (tan x)))

simplify213.0ms (1.3%)

Memory

-8.9MiB live, 322.6MiB allocated

Algorithm

1×	egg-herbie

Rules

11 290×	`lower-fma.f64`
11 290×	`lower-fma.f32`
3 726×	`lower-*.f64`
3 726×	`lower-*.f32`
1 914×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	95	832
1	240	832
2	574	832
3	1309	832
4	2622	832
5	4461	832
6	7451	832
0	8152	778

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
-1/135
(- (* 1/2025 (pow x 2)) 1/135)
(- (* 1/2025 (pow x 2)) 1/135)
(- (* 1/2025 (pow x 2)) 1/135)
(* 1/2025 (pow x 2))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* 1/2025 (pow x 2))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/27 x)
(* x (+ 1/27 (* 1/91125 (pow x 6))))
(* x (+ 1/27 (* 1/91125 (pow x 6))))
(* x (+ 1/27 (* 1/91125 (pow x 6))))
(* 1/91125 (pow x 7))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(* 1/91125 (pow x 7))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(* 1/27 x)
(* 1/27 x)
(* 1/27 x)
(* 1/27 x)
(* 1/27 x)
(* 1/27 x)
(* 1/27 x)
(* 1/27 x)
(* 1/27 x)
(* 1/27 x)
(* 1/27 x)
(* 1/27 x)
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))

Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/4725 binary64) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #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 (/ (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 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/75 binary64) #s(literal -1/5 binary64)) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/1125 binary64)) #s(literal 1/75 binary64)) #s(literal -1/5 binary64)) #s(literal 3 binary64))
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (+.f64 (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -675 binary64) (.f64 x x)))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (+.f64 (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (/.f64 #s(literal -675 binary64) (.f64 x x)) (/.f64 #s(literal -151875 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))) (.f64 x x))
(/ 45 (pow x 2))
(/.f64 #s(literal 45 binary64) (*.f64 x x))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (/.f64 #s(literal -675 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (+.f64 (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -675 binary64) (.f64 x x)))) (*.f64 x x))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 #s(literal 45 binary64) (+.f64 (/.f64 #s(literal 10125 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (/.f64 #s(literal -675 binary64) (.f64 x x)) (/.f64 #s(literal -151875 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))) (.f64 x x))
-1/135
#s(literal -1/135 binary64)
(- (* 1/2025 (pow x 2)) 1/135)
(fma.f64 x (*.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))
(- (* 1/2025 (pow x 2)) 1/135)
(fma.f64 x (*.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))
(- (* 1/2025 (pow x 2)) 1/135)
(fma.f64 x (*.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))
(* 1/2025 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2025 binary64)))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))
(* 1/2025 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2025 binary64)))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))
(* (pow x 2) (- 1/2025 (* 1/135 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/4725 binary64) #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) #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 (/ (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 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(* 1/45 (pow x 3))
(.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 #s(literal 1/45 binary64) (.f64 x x) #s(literal 1/3 binary64)))
(* 1/27 x)
(*.f64 x #s(literal 1/27 binary64))
(* x (+ 1/27 (* 1/91125 (pow x 6))))
(.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))
(* x (+ 1/27 (* 1/91125 (pow x 6))))
(.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))
(* x (+ 1/27 (* 1/91125 (pow x 6))))
(.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))
(* 1/91125 (pow x 7))
(.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (*.f64 x #s(literal 1/91125 binary64)))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))
(* 1/91125 (pow x 7))
(.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (*.f64 x #s(literal 1/91125 binary64)))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))
(* (pow x 7) (+ 1/91125 (* 1/27 (/ 1 (pow x 6)))))
(.f64 x (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/91125 binary64) #s(literal 1/27 binary64)))
(* 1/27 x)
(*.f64 x #s(literal 1/27 binary64))
(* 1/27 x)
(*.f64 x #s(literal 1/27 binary64))
(* 1/27 x)
(*.f64 x #s(literal 1/27 binary64))
(* 1/27 x)
(*.f64 x #s(literal 1/27 binary64))
(* 1/27 x)
(*.f64 x #s(literal 1/27 binary64))
(* 1/27 x)
(*.f64 x #s(literal 1/27 binary64))
(* 1/27 x)
(*.f64 x #s(literal 1/27 binary64))
(* 1/27 x)
(*.f64 x #s(literal 1/27 binary64))
(* 1/27 x)
(*.f64 x #s(literal 1/27 binary64))
(* 1/27 x)
(*.f64 x #s(literal 1/27 binary64))
(* 1/27 x)
(*.f64 x #s(literal 1/27 binary64))
(* 1/27 x)
(*.f64 x #s(literal 1/27 binary64))
(* 1/2025 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2025 binary64)))
(* 1/2025 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2025 binary64)))
(* 1/2025 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2025 binary64)))
(* 1/2025 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2025 binary64)))
(* 1/2025 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2025 binary64)))
(* 1/2025 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2025 binary64)))
(* 1/2025 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2025 binary64)))
(* 1/2025 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2025 binary64)))
(* 1/2025 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2025 binary64)))
(* 1/2025 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2025 binary64)))
(* 1/2025 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2025 binary64)))
(* 1/2025 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2025 binary64)))

rewrite248.0ms (1.5%)

Memory

21.4MiB live, 285.6MiB allocated

Rules

6 364×	`lower-fma.f32`
6 362×	`lower-fma.f64`
4 038×	`lower-*.f32`
4 032×	`lower-*.f64`
3 578×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	159
0	43	147
1	187	135
2	1324	135
0	8654	126

Stop Event

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

Counts

9 → 119

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))
#s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))
(-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))))
(/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)))
#s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64)))
(*.f64 x #s(literal 1/27 binary64))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))

Outputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) #s(literal 3 binary64)) x)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))) (neg.f64 (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))))
(neg.f64 (neg.f64 (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))))
(neg.f64 (.f64 #s(literal 1 binary64) (neg.f64 (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) #s(literal 3 binary64))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)) x))
(/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)) (neg.f64 x)))
(/.f64 (neg.f64 x) (neg.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) x))
(pow.f64 (/.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)) x) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(.f64 x (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) #s(literal 3 binary64)))))
(.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) #s(literal 3 binary64))) x)
(.f64 (pow.f64 (/.f64 #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) #s(literal 3 binary64)) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)) x) #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(neg.f64 (neg.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(/.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)) #s(literal 1 binary64))
(/.f64 (neg.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) #s(literal -1 binary64))
#s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))
(.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) #s(literal 3 binary64)))
(.f64 #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) #s(literal 3 binary64)) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (neg.f64 #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(+.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))
(+.f64 #s(literal -1/135 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))
(+.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8303765625 binary64))) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4100625 binary64)) (fma.f64 (.f64 x x) #s(literal 1/273375 binary64) #s(literal 1/18225 binary64)))) (neg.f64 (/.f64 #s(literal 1/2460375 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4100625 binary64)) (fma.f64 (.f64 x x) #s(literal 1/273375 binary64) #s(literal 1/18225 binary64))))))
(+.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4100625 binary64))) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal 1/135 binary64))) (neg.f64 (/.f64 #s(literal 1/18225 binary64) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal 1/135 binary64)))))
(-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8303765625 binary64))) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4100625 binary64)) (fma.f64 (.f64 x x) #s(literal 1/273375 binary64) #s(literal 1/18225 binary64)))) (/.f64 #s(literal 1/2460375 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4100625 binary64)) (fma.f64 (.f64 x x) #s(literal 1/273375 binary64) #s(literal 1/18225 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4100625 binary64))) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal 1/135 binary64))) (/.f64 #s(literal 1/18225 binary64) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal 1/135 binary64))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8303765625 binary64))) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4100625 binary64)) (-.f64 #s(literal 1/18225 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))) (/.f64 #s(literal 1/2460375 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4100625 binary64)) (-.f64 #s(literal 1/18225 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))))
(fma.f64 x (*.f64 x #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))
(fma.f64 (.f64 x #s(literal 1/45 binary64)) (.f64 x #s(literal 1/45 binary64)) #s(literal -1/135 binary64))
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(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (.f64 x (neg.f64 x)) #s(literal -1/9 binary64))) (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (*.f64 x (neg.f64 x)) #s(literal -1/9 binary64))))
(fma.f64 (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64))))) #s(literal 1/729 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64))))) (.f64 (/.f64 #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64))))) #s(literal 1/729 binary64))) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64))) #s(literal -1/9 binary64)))))
(fma.f64 (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64))))) #s(literal 1/729 binary64))) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64))) #s(literal -1/9 binary64))) (.f64 (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64))))) #s(literal 1/729 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)))))))
(fma.f64 (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 x (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64))) (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)))) #s(literal -1/81 binary64))) (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64))) (.f64 (/.f64 #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 x (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64))) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)))) #s(literal -1/81 binary64))) #s(literal -1/9 binary64)))
(neg.f64 (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (*.f64 x (neg.f64 x)) #s(literal -1/9 binary64))))
(neg.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (*.f64 x (neg.f64 x)) #s(literal -1/9 binary64)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) #s(literal 1/9 binary64)) #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) #s(literal 1/9 binary64)) #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64)))))
(/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) #s(literal 1/9 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (.f64 x (neg.f64 x)) #s(literal -1/9 binary64)) #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64)))))
(/.f64 (neg.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64)))) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (*.f64 x (neg.f64 x)) #s(literal -1/9 binary64)))
(pow.f64 (/.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) #s(literal 1/9 binary64)) #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64)))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) #s(literal 1/9 binary64))))
(.f64 #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) #s(literal 1/9 binary64))))
(.f64 #s(literal -1 binary64) (/.f64 #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (*.f64 x (neg.f64 x)) #s(literal -1/9 binary64))))
(.f64 (neg.f64 #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) #s(literal 1/9 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) #s(literal 1/9 binary64))) #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) #s(literal 1/9 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64))))) #s(literal 1/729 binary64))) (+.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)))) #s(literal 1/81 binary64)) (.f64 (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64))) #s(literal -1/9 binary64))))
(.f64 (/.f64 #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64))))) #s(literal 1/729 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)))) #s(literal 1/81 binary64)) (.f64 (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64))) #s(literal -1/9 binary64))))))
(.f64 (/.f64 #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 x (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64))) (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)))) #s(literal -1/81 binary64))) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) #s(literal -1/9 binary64)))
(.f64 (/.f64 #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 x (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64))) (.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)))) #s(literal -1/81 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) #s(literal -1/9 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) #s(literal 1/9 binary64)) #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/2025 binary64) #s(literal -1/135 binary64)) #s(literal 1/9 binary64)) #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64)))) #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64)))))
(neg.f64 (neg.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64)))))
#s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64)))
(.f64 #s(literal 1 binary64) #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64))))
(.f64 #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64))) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (neg.f64 #s(approx ( x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (*.f64 x #s(literal 1/27 binary64)))))
(/.f64 #s(literal 1/27 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 x #s(literal 1/27 binary64))
(*.f64 #s(literal 1/27 binary64) x)
(/.f64 (*.f64 x #s(literal 1/2025 binary64)) (/.f64 #s(literal 1 binary64) x))
(pow.f64 (*.f64 x #s(literal 1/45 binary64)) #s(literal 2 binary64))
(.f64 x (.f64 x #s(literal 1/2025 binary64)))
(.f64 (.f64 x #s(literal 1/45 binary64)) (*.f64 x #s(literal 1/45 binary64)))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(.f64 #s(literal 1/2025 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 1/2025 binary64)) x)

eval27.0ms (0.2%)

Memory: -0.2MiB live, 47.1MiB allocated
Compiler: Compiled 5 549 to 467 computations (91.6% saved)

prune21.0ms (0.1%)

Memory

7.9MiB live, 46.2MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	0	0	0
Picked	1	1	2
Done	0	3	3
Total	227	5	232

Accuracy

100.0%

Counts

232 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
	99.6%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) #s(approx (- (* (* x x) 1/2025) 1/135) #s(literal -1/135 binary64)) #s(literal 1/9 binary64))))
✓	99.8%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
✓	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
✓	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Compiler

Compiled 163 to 65 computations (60.1% saved)

regimes10.0ms (0.1%)

Memory

-23.1MiB live, 14.0MiB allocated

Counts

10 → 1

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) #s(approx (- (* (* x x) 1/2025) 1/135) #s(literal -1/135 binary64)) #s(literal 1/9 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

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

Calls

2 calls:

7.0ms	x
3.0ms	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes5.0ms (0%)

Memory

10.1MiB live, 10.1MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(approx (* x (+ (* (* x (* x x)) (* (* x (* x x)) 1/91125)) 1/27)) (.f64 x #s(literal 1/27 binary64))) (fma.f64 (.f64 x x) #s(approx (- (* (* x x) 1/2025) 1/135) #s(literal -1/135 binary64)) #s(literal 1/9 binary64))))

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

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
99.8%	1	`x`
99.8%	1	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes2.0ms (0%)

Memory

5.9MiB live, 5.9MiB 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 #s(literal 1/3 binary64) x))

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

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify6.0ms (0%)

Memory

9.9MiB live, 9.9MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	53
1	28	53

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

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

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

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

soundness567.0ms (3.5%)

Memory

-8.2MiB live, 312.7MiB allocated

Rules

18 970×	`lower-fma.f64`
18 970×	`lower-fma.f32`
9 012×	`lower-fma.f64`
9 012×	`lower-fma.f32`
5 010×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	49
0	19	49
1	84	49
2	641	49
3	7572	49
0	8055	49
0	97	1408
1	249	1408
2	593	1408
3	1339	1408
4	2768	1408
5	6058	1408
0	8127	1324
0	67	324
1	179	324
2	458	318
3	1321	318
4	2085	318
5	3083	318
6	3670	318
7	3941	318
8	5080	318
9	7268	318
0	8431	300

Stop Event

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

Compiler

Compiled 68 to 41 computations (39.7% saved)

preprocess74.0ms (0.5%)

Memory: -12.2MiB live, 107.8MiB allocated
Remove: (negabs x)
Compiler: Compiled 158 to 100 computations (36.7% 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	14	54
0	19	54
1	35	54
2	50	54
3	63	54
4	76	54
5	96	54
6	135	54
7	165	54
8	295	54
9	693	54
10	914	54
11	927	54
0	927	54

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	14	54
0	19	54
1	35	54
2	50	54
3	63	54
4	76	54
5	96	54
6	135	54
7	165	54
8	295	54
9	693	54
10	914	54
11	927	54
0	927	54

start0.0ms (0%)

analyze7.0ms (0%)

sample10.0s (61%)

explain824.0ms (5%)

preprocess25.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify14.0ms (0.1%)

localize252.0ms (1.5%)

series10.0ms (0.1%)

simplify285.0ms (1.7%)

rewrite277.0ms (1.7%)

eval37.0ms (0.2%)

prune41.0ms (0.3%)

simplify27.0ms (0.2%)

localize317.0ms (1.9%)

series6.0ms (0%)

simplify164.0ms (1%)

rewrite248.0ms (1.5%)

eval28.0ms (0.2%)

prune31.0ms (0.2%)

simplify520.0ms (3.2%)

localize796.0ms (4.9%)

series15.0ms (0.1%)

simplify189.0ms (1.2%)

rewrite252.0ms (1.5%)

eval110.0ms (0.7%)

prune73.0ms (0.4%)

simplify210.0ms (1.3%)

localize420.0ms (2.6%)

series16.0ms (0.1%)

simplify213.0ms (1.3%)

rewrite248.0ms (1.5%)

eval27.0ms (0.2%)

prune21.0ms (0.1%)

regimes10.0ms (0.1%)

regimes5.0ms (0%)

regimes2.0ms (0%)

simplify6.0ms (0%)

soundness567.0ms (3.5%)

preprocess74.0ms (0.5%)

end0.0ms (0%)

Profiling

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

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

Iter	Nodes	Cost
0	14	54
0	19	54
1	35	54
2	50	54
3	63	54
4	76	54
5	96	54
6	135	54
7	165	54
8	295	54
9	693	54
10	914	54
11	927	54
0	927	54