Metrics for invcot (example 3.9)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze8.0ms (0.1%)

Memory

-33.4MiB live, 10.8MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 16 to 12 computations (25% saved)

sample9.2s (56.9%)

Memory

34.1MiB live, 9 750.1MiB allocated

Samples

7.1s	3 855×	2	valid
1.7s	4 306×	1	valid
11.0ms	95×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 8.3s

ival-tan: 7.1s (85.2% of total)

ival-div: 487.0ms (5.9% of total)

const: 277.0ms (3.3% of total)

adjust: 243.0ms (2.9% of total)

ival-sub: 126.0ms (1.5% of total)

ival-<: 76.0ms (0.9% of total)

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

exact: 6.0ms (0.1% of total)

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

Bogosity

explain930.0ms (5.8%)

Memory

-3.3MiB live, 437.2MiB 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

693.0ms	252×	2	valid
127.0ms	254×	1	valid
0.0ms	6×	0	valid

Compiler

Compiled 51 to 22 computations (56.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 798.0ms

ival-tan: 681.0ms (85.4% of total)

ival-sub: 68.0ms (8.5% of total)

ival-div: 36.0ms (4.5% of total)

adjust: 11.0ms (1.4% of total)

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

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

exact: 0.0ms (0% of total)

preprocess23.0ms (0.1%)

Memory

16.4MiB live, 16.4MiB 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: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify44.0ms (0.3%)

Memory

-30.5MiB live, 7.1MiB 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)

localize261.0ms (1.6%)

Memory

17.5MiB live, 95.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 1 binary64) (tan.f64 x))
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	0	(tan.f64 x)
accuracy	59.68212772619532	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Samples

219.0ms	126×	2	valid
32.0ms	127×	1	valid
0.0ms	3×	0	valid

Compiler

Compiled 21 to 8 computations (61.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 210.0ms

ival-tan: 191.0ms (90.8% of total)

ival-div: 10.0ms (4.8% of total)

adjust: 6.0ms (2.9% of total)

ival-sub: 3.0ms (1.4% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0%)

Memory

3.5MiB live, 3.5MiB 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))

simplify464.0ms (2.9%)

Memory

-7.3MiB live, 263.6MiB 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))

rewrite256.0ms (1.6%)

Memory

-5.3MiB live, 317.1MiB 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))))))
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eval37.0ms (0.2%)

Memory: 28.2MiB live, 103.9MiB allocated
Compiler: Compiled 6 028 to 755 computations (87.5% saved)

prune44.0ms (0.3%)

Memory

14.8MiB live, 134.1MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

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

Accuracy

99.6%

Counts

325 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.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))))
▶	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.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))))
▶	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
▶	98.9%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Compiler

Compiled 50 to 29 computations (42% saved)

simplify351.0ms (2.2%)

Memory

-2.1MiB live, 315.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

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

9 704×	`lower-fma.f32`
9 692×	`lower-fma.f64`
2 552×	`lower-*.f32`
2 536×	`lower-*.f64`
992×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	205
0	48	205
1	112	205
2	269	205
3	524	205
4	738	205
5	817	205
6	860	205
7	890	205
8	1379	205
9	4469	205
10	6388	205
11	6824	205
12	6849	205
13	6849	205
14	7073	205
15	7093	205
16	7093	205
17	7111	205
18	7111	205
19	7117	205
0	7117	205

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

localize370.0ms (2.3%)

Memory

-19.0MiB live, 690.9MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(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))
accuracy	0.01171875	(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))
accuracy	0.26171875	(*.f64 x #s(literal 1/4725 binary64))
accuracy	0.26953125	(.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)))
accuracy	0.0078125	(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))
accuracy	0.04139136623493911	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.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))))
accuracy	0.265625	(.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)))
accuracy	0.41796875	(*.f64 x #s(literal 2/945 binary64))
accuracy	0.0078125	(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
accuracy	0.1621354006212276	#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	0.26953125	(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
accuracy	0.296875	(*.f64 x #s(literal 1/45 binary64))
accuracy	0.27734375	(*.f64 #s(literal 1/3 binary64) x)
accuracy	0.4661806728055334	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Samples

234.0ms	126×	2	valid
96.0ms	127×	1	valid
1.0ms	3×	0	valid

Compiler

Compiled 177 to 32 computations (81.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 300.0ms

ival-tan: 167.0ms (55.6% of total)

ival-mult: 53.0ms (17.6% of total)

adjust: 26.0ms (8.7% of total)

const: 24.0ms (8% of total)

ival-add: 15.0ms (5% of total)

ival-div: 12.0ms (4% of total)

ival-sub: 3.0ms (1% 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

33.7MiB live, 33.7MiB allocated

Counts

16 → 192

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

Calls

48 calls:

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

simplify205.0ms (1.3%)

Memory

-16.2MiB live, 374.8MiB allocated

Algorithm

1×	egg-herbie

Rules

13 634×	`lower-fma.f64`
13 634×	`lower-fma.f32`
4 376×	`lower-*.f64`
4 376×	`lower-*.f32`
1 912×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	97	1480
1	308	1480
2	796	1478
3	2034	1478
4	4552	1478
0	8303	1367

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

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)
(* 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 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(* 2/945 (pow x 4))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* 2/945 (pow x 4))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (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 (* (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))))))))
(* 1/4725 (pow x 7))
(* (pow x 7) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (+ (* 2/945 (/ 1 (pow x 2))) (* 1/3 (/ 1 (pow x 6)))))))
(* 1/4725 (pow x 7))
(* (pow x 7) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (pow x 2))) 1/4725)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))
(* 1/4725 (pow x 6))
(* (pow x 6) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (+ (* 2/945 (/ 1 (pow x 2))) (* 1/3 (/ 1 (pow x 6)))))))
(* 1/4725 (pow x 6))
(* (pow x 6) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (+ (* 2/945 (/ 1 (pow x 2))) (* 1/3 (/ 1 (pow x 6)))))))
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 1/4725 x)
(* 1/4725 x)
(* 1/4725 x)
(* 1/4725 x)
(* 1/4725 x)
(* 1/4725 x)
(* 1/4725 x)
(* 1/4725 x)
(* 1/4725 x)
(* 1/4725 x)
(* 1/4725 x)
(* 1/4725 x)
1/45
(+ 1/45 (* 2/945 (pow x 2)))
(+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))
(+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))
(* 1/4725 (pow x 4))
(* (pow x 4) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* 1/4725 (pow x 4))
(* (pow x 4) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))

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)))
(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)
(* 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 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)))
(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 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))
(* 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)))
(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 (* (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 (* 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)))
(* 2/945 (pow x 5))
(.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 2/945 binary64))))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (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)))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (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)))
(* 2/945 (pow x 5))
(.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 2/945 binary64))))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.f64 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)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.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)))
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 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(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))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(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))
(* 2/945 (pow x 4))
(.f64 x (.f64 x (.f64 x (.f64 x #s(literal 2/945 binary64)))))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(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))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(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))
(* 2/945 (pow x 4))
(.f64 x (.f64 x (.f64 x (.f64 x #s(literal 2/945 binary64)))))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(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))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(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))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (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)))
(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 (* (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)))
(* 1/4725 (pow x 7))
(*.f64 #s(literal 1/4725 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/4725 binary64) (/.f64 #s(literal 2/945 binary64) (.f64 x x))))
(* (pow x 7) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/4725 binary64) (/.f64 (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/45 binary64) (.f64 x x))) (*.f64 x x))))
(* (pow x 7) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (+ (* 2/945 (/ 1 (pow x 2))) (* 1/3 (/ 1 (pow x 6)))))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/4725 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x x))))) (/.f64 (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/45 binary64) (.f64 x x))) (.f64 x x)))))
(* 1/4725 (pow x 7))
(*.f64 #s(literal 1/4725 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/4725 binary64) (/.f64 #s(literal 2/945 binary64) (.f64 x x))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (pow x 2))) 1/4725)))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/4725 binary64) (/.f64 (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/45 binary64) (.f64 x x))) (*.f64 x x))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (fma.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (/.f64 (+.f64 #s(literal -1/45 binary64) (/.f64 #s(literal -1/3 binary64) (.f64 x x))) (.f64 x x)) #s(literal -2/945 binary64)) #s(literal 1/4725 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 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(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))
(+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))
(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))
(* 1/4725 (pow x 6))
(.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4725 binary64))))
(* (pow x 6) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(.f64 (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(.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)))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (+ (* 2/945 (/ 1 (pow x 2))) (* 1/3 (/ 1 (pow x 6)))))))
(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))
(* 1/4725 (pow x 6))
(.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4725 binary64))))
(* (pow x 6) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(.f64 (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(.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)))
(* (pow x 6) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (+ (* 2/945 (/ 1 (pow x 2))) (* 1/3 (/ 1 (pow x 6)))))))
(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))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 1/4725 x)
(*.f64 x #s(literal 1/4725 binary64))
(* 1/4725 x)
(*.f64 x #s(literal 1/4725 binary64))
(* 1/4725 x)
(*.f64 x #s(literal 1/4725 binary64))
(* 1/4725 x)
(*.f64 x #s(literal 1/4725 binary64))
(* 1/4725 x)
(*.f64 x #s(literal 1/4725 binary64))
(* 1/4725 x)
(*.f64 x #s(literal 1/4725 binary64))
(* 1/4725 x)
(*.f64 x #s(literal 1/4725 binary64))
(* 1/4725 x)
(*.f64 x #s(literal 1/4725 binary64))
(* 1/4725 x)
(*.f64 x #s(literal 1/4725 binary64))
(* 1/4725 x)
(*.f64 x #s(literal 1/4725 binary64))
(* 1/4725 x)
(*.f64 x #s(literal 1/4725 binary64))
(* 1/4725 x)
(*.f64 x #s(literal 1/4725 binary64))
1/45
#s(literal 1/45 binary64)
(+ 1/45 (* 2/945 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))
(+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))
(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))
(+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))
(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))
(* 1/4725 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4725 binary64)))
(* (pow x 4) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))
(* (pow x 4) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(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))
(* (pow x 4) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(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))
(* 1/4725 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4725 binary64)))
(* (pow x 4) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))
(* (pow x 4) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(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))
(* (pow x 4) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(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))

rewrite263.0ms (1.6%)

Memory

20.9MiB live, 491.5MiB allocated

Rules

5 660×	`lower-fma.f32`
5 648×	`lower-fma.f64`
4 274×	`lower-/.f64`
4 274×	`lower-/.f32`
4 098×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	176
0	48	176
1	221	176
2	1738	176
0	8331	176

Stop Event

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

Counts

16 → 340

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

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 x #s(literal 1/3 binary64))
(*.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 (.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 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64))))) (-.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 x #s(literal 1/3 binary64)))) (/.f64 (.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 x #s(literal 1/3 binary64))) (-.f64 (.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 1/45 binary64)) (.f64 x x) (*.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 #s(literal 1/45 binary64))) x (*.f64 x #s(literal 1/3 binary64)))
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(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))))) (-.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))))) #s(literal 1/91125 binary64)) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))))) #s(literal 1/2025 binary64)) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))))) #s(literal 1/91125 binary64)) (+.f64 #s(literal 1/2025 binary64) (-.f64 (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))))) (.f64 x (.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64))))))
(/.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))))) #s(literal -1/2025 binary64)) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal -1/45 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))))) #s(literal 1/91125 binary64))) (neg.f64 (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))))) #s(literal 1/2025 binary64)) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))))) #s(literal 1/91125 binary64))) (neg.f64 (+.f64 #s(literal 1/2025 binary64) (-.f64 (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))))) (.f64 x (.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)))))))
(/.f64 (neg.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))))) #s(literal -1/2025 binary64))) (neg.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal -1/45 binary64))))
(/.f64 (-.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))))))) (-.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))))) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal -1/45 binary64))) (.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal -1/45 binary64)) #s(literal 1/2025 binary64))) (.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal -1/45 binary64)) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal -1/45 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))))) #s(literal 1/91125 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))))) #s(literal 1/2025 binary64)) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))))) #s(literal -1/2025 binary64)))) (neg.f64 (neg.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal -1/45 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))))))) (neg.f64 (-.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))))))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/105488578125 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (fma.f64 x (.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) (fma.f64 x (.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))))) (fma.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/4725 binary64)))) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/4725 binary64)))) (-.f64 (.f64 (fma.f64 x (.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64)) (fma.f64 x (.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))) (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/4725 binary64)))) (fma.f64 x (*.f64 x #s(literal 2/945 binary64)) #s(literal 1/45 binary64))))))
(/.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/4725 binary64))))) #s(literal 3 binary64)) (.f64 #s(literal 8/843908625 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (fma.f64 (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/4725 binary64))))) (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/4725 binary64))))) (-.f64 (.f64 #s(literal 4/893025 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/4725 binary64))))) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))))) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal -1/45 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/2025 binary64) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal -1/45 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))))) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal -1/45 binary64))) (/.f64 (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))))) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal -1/45 binary64))) (fma.f64 (/.f64 #s(literal 1/2025 binary64) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal -1/45 binary64))) (/.f64 #s(literal 1/2025 binary64) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal -1/45 binary64))) (.f64 (/.f64 (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))))) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal -1/45 binary64))) (/.f64 #s(literal 1/2025 binary64) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal -1/45 binary64)))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)))
(.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))))) #s(literal 1/91125 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))))) #s(literal 1/2025 binary64)) (.f64 x (.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64))))))
(.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))))) #s(literal 1/91125 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2025 binary64) (-.f64 (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)))))))
(.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))))) #s(literal -1/2025 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal -1/45 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))))) #s(literal 1/91125 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))))) #s(literal 1/2025 binary64)) (.f64 x (.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)))))))
(.f64 (neg.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))))) #s(literal -1/2025 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal -1/45 binary64)))))
(.f64 (-.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))))))

eval76.0ms (0.5%)

Memory: -1.3MiB live, 154.9MiB allocated
Compiler: Compiled 18 198 to 1 163 computations (93.6% saved)

prune263.0ms (1.6%)

Memory

-6.9MiB live, 165.7MiB allocated

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	569	5	574
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	569	9	578

Accuracy

100.0%

Counts

578 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/3 binary64))))
▶	99.3%	#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))))
▶	99.7%	#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)))))
▶	98.7%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
✓	99.6%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.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))))
✓	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.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))))
✓	99.3%	#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 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (*.f64 x x))))))))
✓	98.9%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Compiler

Compiled 206 to 127 computations (38.3% saved)

simplify179.0ms (1.1%)

Memory

-3.2MiB live, 227.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (*.f64 x x))))))))
cost-diff	128	(-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x))))
cost-diff	128	(-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x))))))
cost-diff	0	(.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))
cost-diff	0	(fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64))
cost-diff	0	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/3 binary64))))
cost-diff	320	(fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) (.f64 x (.f64 x x)) (*.f64 x #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))
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	(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))))

Rules

8 654×	`lower-fma.f32`
8 644×	`lower-fma.f64`
3 234×	`lower-*.f32`
3 214×	`lower-*.f64`
1 574×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	357
0	67	331
1	129	305
2	274	303
3	828	303
4	1762	303
5	3426	303
6	6617	303
0	8030	293

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 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))) (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)
#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))) (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/3 binary64))))
(fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64))
x
(.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))
(fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))
(*.f64 x #s(literal 1/4725 binary64))
#s(literal 1/4725 binary64)
#s(literal 2/945 binary64)
#s(literal 1/45 binary64)
(.f64 x (.f64 x x))
(*.f64 x x)
(*.f64 x #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (*.f64 x x))))))))
(.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (*.f64 x x)))))))
x
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x))))))
#s(literal 1 binary64)
(/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))))
(-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
#s(literal 1/3 binary64)
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(*.f64 x #s(literal 1/45 binary64))
#s(literal 1/45 binary64)
(-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x))))
#s(literal 1/9 binary64)
(.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))
#s(literal 1/2025 binary64)
(.f64 (.f64 x x) (*.f64 x x))
(*.f64 x 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 (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))))
(.f64 x (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))) (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 x (.f64 x #s(literal 1/45 binary64)) #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 x (.f64 x #s(literal 1/45 binary64)) #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)
#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))) (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.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))))
(fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/3 binary64)))
(.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)))
(fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64))
(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))
x
(.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))
(fma.f64 x (*.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))
(*.f64 x #s(literal 1/4725 binary64))
#s(literal 1/4725 binary64)
#s(literal 2/945 binary64)
#s(literal 1/45 binary64)
(.f64 x (.f64 x x))
(*.f64 x x)
(*.f64 x #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (*.f64 x x))))))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 (.f64 x (fma.f64 x (.f64 x (.f64 (.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 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (*.f64 x x)))))))
(/.f64 (.f64 x (fma.f64 x (.f64 x (.f64 (.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)))
x
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x))))))
(/.f64 (fma.f64 x (.f64 x (.f64 (.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)))
#s(literal 1 binary64)
(/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))))
(/.f64 (fma.f64 x (.f64 x #s(literal -1/45 binary64)) #s(literal 1/3 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1/2025 binary64))) #s(literal 1/9 binary64)))
(-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(fma.f64 x (*.f64 x #s(literal -1/45 binary64)) #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(*.f64 x #s(literal 1/45 binary64))
#s(literal 1/45 binary64)
(-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x))))
(fma.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal -1/2025 binary64))) #s(literal 1/9 binary64))
#s(literal 1/9 binary64)
(.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))))
#s(literal 1/2025 binary64)
(.f64 (.f64 x x) (*.f64 x x))
(.f64 x (.f64 x (*.f64 x x)))
(*.f64 x x)

localize453.0ms (2.8%)

Memory

23.1MiB live, 494.5MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.16015625	(.f64 x (.f64 x #s(literal 1/45 binary64)))
accuracy	0.1621354006212276	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (*.f64 x x))))))))
accuracy	0.26953125	(.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (*.f64 x x)))))))
accuracy	0.296875	(*.f64 x #s(literal 1/45 binary64))
accuracy	0.0859375	(.f64 x (.f64 x x))
accuracy	0.26171875	(*.f64 x #s(literal 1/4725 binary64))
accuracy	0.27734375	(*.f64 x #s(literal 1/3 binary64))
accuracy	0.421875	(.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	0.3671875	(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
accuracy	0.4661806728055334	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x)))
accuracy	0.00390625	(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))
accuracy	0.0859375	(.f64 x (.f64 x x))
accuracy	0.1621354006212276	#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	0.27734375	(*.f64 x #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	(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
accuracy	0.1621354006212276	#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)))))
accuracy	0.296875	(*.f64 x #s(literal 1/45 binary64))

Samples

286.0ms	126×	2	valid
110.0ms	127×	1	valid
1.0ms	3×	0	valid

Compiler

Compiled 297 to 40 computations (86.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 349.0ms

ival-tan: 176.0ms (50.4% of total)

ival-mult: 45.0ms (12.9% of total)

ival-add: 42.0ms (12% of total)

const: 27.0ms (7.7% of total)

ival-div: 25.0ms (7.2% of total)

adjust: 25.0ms (7.2% of total)

ival-sub: 7.0ms (2% of total)

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

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

exact: 0.0ms (0% of total)

series22.0ms (0.1%)

Memory

-17.9MiB live, 22.3MiB allocated

Counts

24 → 288

Calls

Call 1

Inputs
#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 (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 #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 (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/3 binary64))) (patch (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/3 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/3 binary64)))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/3 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) (patch (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) (patch (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (patch (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))) (patch (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.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 x #s(literal 1/3 binary64)) (patch (.f64 x #s(literal 1/3 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 1/4725 binary64)) (patch (.f64 x #s(literal 1/4725 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x))))))) (patch (.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x))))))) #<representation binary64>) () ())
#s(alt (.f64 x (.f64 x #s(literal 1/45 binary64))) (patch (.f64 x (.f64 x #s(literal 1/45 binary64))) #<representation binary64>) () ())

Outputs
#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>) () ())) ())
#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 (* 1/3 x) (taylor 0 x) (#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 (* x (+ 1/3 (* 1/45 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 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 (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 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 (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 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 (* -1 (/ (cos x) (sin x))) (taylor inf x) (#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 (- (/ 1 x) (/ (cos x) (sin x))) (taylor inf x) (#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 (- (/ 1 x) (/ (cos x) (sin x))) (taylor inf x) (#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 (- (/ 1 x) (/ (cos x) (sin x))) (taylor inf x) (#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 (* -1 (/ (cos x) (sin x))) (taylor -inf x) (#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 (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#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 (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#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 (- (/ 1 x) (/ (cos x) (sin x))) (taylor -inf x) (#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 3 (taylor 0 x) (#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 (+ 3 (* -1/5 (pow x 2))) (taylor 0 x) (#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 (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5))) (taylor 0 x) (#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 (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 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 (/ 45 (pow x 2)) (taylor inf x) (#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 (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2)) (taylor inf x) (#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 (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2)) (taylor inf x) (#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 (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2)) (taylor inf x) (#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 (/ 45 (pow x 2)) (taylor -inf x) (#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 (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf x) (#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 (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf x) (#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 (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2)) (taylor -inf x) (#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 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 (* 1/3 x) (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>) () ())) ())
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#s(alt (* 1/45 (pow x 2)) (taylor inf x) (#s(alt (.f64 x (.f64 x #s(literal 1/45 binary64))) (patch (.f64 x (.f64 x #s(literal 1/45 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/45 (pow x 2)) (taylor inf x) (#s(alt (.f64 x (.f64 x #s(literal 1/45 binary64))) (patch (.f64 x (.f64 x #s(literal 1/45 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/45 (pow x 2)) (taylor -inf x) (#s(alt (.f64 x (.f64 x #s(literal 1/45 binary64))) (patch (.f64 x (.f64 x #s(literal 1/45 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/45 (pow x 2)) (taylor -inf x) (#s(alt (.f64 x (.f64 x #s(literal 1/45 binary64))) (patch (.f64 x (.f64 x #s(literal 1/45 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/45 (pow x 2)) (taylor -inf x) (#s(alt (.f64 x (.f64 x #s(literal 1/45 binary64))) (patch (.f64 x (.f64 x #s(literal 1/45 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/45 (pow x 2)) (taylor -inf x) (#s(alt (.f64 x (.f64 x #s(literal 1/45 binary64))) (patch (.f64 x (.f64 x #s(literal 1/45 binary64))) #<representation binary64>) () ())) ())

Calls

72 calls:

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

simplify226.0ms (1.4%)

Memory

28.5MiB live, 250.2MiB allocated

Algorithm

1×	egg-herbie

Rules

12 032×	`lower-fma.f64`
12 032×	`lower-fma.f32`
4 016×	`lower-*.f64`
4 016×	`lower-*.f32`
2 824×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	126	1988
1	350	1988
2	882	1985
3	2156	1984
4	5123	1984
0	8296	1855

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 288

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/3 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)))))
(* 1/3 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)
(* 1/3 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 (* (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))))))))
(* 1/4725 (pow x 7))
(* (pow x 7) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (+ (* 2/945 (/ 1 (pow x 2))) (* 1/3 (/ 1 (pow x 6)))))))
(* 1/4725 (pow x 7))
(* (pow x 7) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 2/945 (* 1/45 (/ 1 (pow x 2)))) (pow x 2))) 1/4725)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))))
(* 1/3 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)))
1/45
(+ 1/45 (* 2/945 (pow x 2)))
(+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))
(+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2)))))
(* 1/4725 (pow x 4))
(* (pow x 4) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* 1/4725 (pow x 4))
(* (pow x 4) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 1/4725 (+ (/ 1/45 (pow x 4)) (* 2/945 (/ 1 (pow x 2))))))
(* 2/945 x)
(* x (+ 2/945 (* 1/4725 (pow x 2))))
(* x (+ 2/945 (* 1/4725 (pow x 2))))
(* x (+ 2/945 (* 1/4725 (pow x 2))))
(* 1/4725 (pow x 3))
(* (pow x 3) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* 1/4725 (pow x 3))
(* (pow x 3) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/4725 (* 2/945 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/4725 (* 2/945 (/ 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)))))
1/3
(+ 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) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(* -1/45 (pow x 2))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
(* (pow x 2) (- (* 1/3 (/ 1 (pow x 2))) 1/45))
1/9
(+ 1/9 (* -1/2025 (pow x 4)))
(+ 1/9 (* -1/2025 (pow x 4)))
(+ 1/9 (* -1/2025 (pow x 4)))
(* -1/2025 (pow x 4))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* -1/2025 (pow x 4))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* (pow x 4) (- (* 1/9 (/ 1 (pow x 4))) 1/2025))
(* 1/3 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)))
(* 1/45 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)
(* 1/3 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)
(* 1/4725 x)
(* 1/4725 x)
(* 1/4725 x)
(* 1/4725 x)
(* 1/4725 x)
(* 1/4725 x)
(* 1/4725 x)
(* 1/4725 x)
(* 1/4725 x)
(* 1/4725 x)
(* 1/4725 x)
(* 1/4725 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)))))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))
(* 1/45 (pow x 2))

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

rewrite333.0ms (2.1%)

Memory

19.0MiB live, 416.6MiB allocated

Rules

5 698×	`lower-/.f32`
5 686×	`lower-/.f64`
5 150×	`lower-*.f32`
5 130×	`lower-*.f64`
3 674×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	278
0	67	225
1	281	211
2	2154	211
0	9173	209

Stop Event

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

Counts

24 → 1 009

Calls

Call 1

Inputs
(/.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))
(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 #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)
(fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/3 binary64)))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/3 binary64))))
(fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x))))))
(-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (*.f64 x x))))))))
(*.f64 x #s(literal 1/45 binary64))
(*.f64 x #s(literal 1/3 binary64))
(*.f64 x #s(literal 1/4725 binary64))
(.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (*.f64 x x)))))))
(.f64 x (.f64 x #s(literal 1/45 binary64)))

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

eval372.0ms (2.3%)

Memory: -34.6MiB live, 349.3MiB allocated
Compiler: Compiled 45 259 to 2 727 computations (94% saved)

prune168.0ms (1%)

Memory

-5.2MiB live, 303.4MiB allocated

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	1 434	2	1 436
Fresh	0	0	0
Picked	3	2	5
Done	0	4	4
Total	1 437	8	1 445

Accuracy

100.0%

Counts

1 445 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/3 binary64))))
✓	99.3%	#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))))
▶	99.8%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))))
▶	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
✓	99.6%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.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))))
✓	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.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))))
✓	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
✓	98.9%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Compiler

Compiled 101 to 58 computations (42.6% saved)

simplify61.0ms (0.4%)

Memory

9.2MiB live, 76.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))
cost-diff	0	#s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))
cost-diff	0	(/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 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

568×	`lower-fma.f32`
566×	`lower-fma.f64`
440×	`lower-*.f32`
438×	`lower-*.f64`
176×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	121
0	27	121
1	39	121
2	51	121
3	60	121
4	73	121
5	93	121
6	132	121
7	162	121
8	279	121
9	587	121
10	805	121
11	1007	121
12	1217	121
13	1281	121
14	1333	121
15	1357	121
16	1362	121
17	1363	121
0	1363	115

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

localize280.0ms (1.7%)

Memory

10.9MiB live, 391.6MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))
accuracy	0.15688377102770049	#s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))
accuracy	0.1621354006212276	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))))
accuracy	0.00390625	(/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))
accuracy	0.1621354006212276	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
accuracy	0.4606430713482149	#s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))

Samples

205.0ms	126×	2	valid
54.0ms	127×	1	valid
2.0ms	3×	0	valid

Compiler

Compiled 73 to 20 computations (72.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 243.0ms

ival-tan: 189.0ms (77.7% of total)

ival-div: 18.0ms (7.4% of total)

const: 12.0ms (4.9% of total)

adjust: 11.0ms (4.5% of total)

ival-mult: 6.0ms (2.5% of total)

ival-add: 4.0ms (1.6% of total)

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

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

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

exact: 0.0ms (0% of total)

series6.0ms (0%)

Memory

-30.1MiB live, 8.5MiB allocated

Counts

8 → 96

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 #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())

Outputs
#s(alt (* 1/3 x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* 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>) () ())) ())
#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 3 (taylor 0 x) (#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 (+ 3 (* -1/5 (pow x 2))) (taylor 0 x) (#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 (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5))) (taylor 0 x) (#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 (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5))) (taylor 0 x) (#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 (/ 45 (pow x 2)) (taylor inf x) (#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 (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2)) (taylor inf x) (#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 (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2)) (taylor inf x) (#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 (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2)) (taylor inf x) (#s(alt #s(approx (/ 1 (+ (* 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 (/ 45 (pow x 2)) (taylor -inf x) (#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 (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf x) (#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 (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf x) (#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 (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (* 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 (* 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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))))) (patch #s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #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)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))) (patch (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))) #<representation binary64>) () ())) ())
#s(alt 3 (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -1/5 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5))) (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5))) (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 45 (pow x 2)) (taylor inf x) (#s(alt #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2)) (taylor inf x) (#s(alt #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2)) (taylor inf x) (#s(alt #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2)) (taylor inf x) (#s(alt #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 45 (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) (patch #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt 3 (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -1/5 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -1/5 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 3 (* -1/5 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/5 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (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>) () ())) ())

Calls

24 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(+ (* (* x x) -1/5) 3)
0.0ms	x	@	0	(+ (* (* x x) -1/5) 3)
0.0ms	x	@	inf	(/ 1 (+ (* x (* x 1/45)) 1/3))
0.0ms	x	@	0	(- (/ 1 x) (/ 1 (tan x)))
0.0ms	x	@	-inf	(+ (* (* x x) -1/5) 3)

simplify213.0ms (1.3%)

Memory

21.9MiB live, 251.3MiB allocated

Algorithm

1×	egg-herbie

Rules

12 352×	`lower-fma.f64`
12 352×	`lower-fma.f32`
3 826×	`lower-*.f64`
3 826×	`lower-*.f32`
2 020×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	830
1	197	830
2	496	830
3	1186	830
4	2297	830
5	3916	830
6	6491	830
0	8114	779

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

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))
(* 1/3 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))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* -1/5 (pow x 2)))
(* -1/5 (pow x 2))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* -1/5 (pow x 2))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

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

rewrite184.0ms (1.1%)

Memory

-3.6MiB live, 231.2MiB allocated

Rules

6 178×	`lower-fma.f32`
6 176×	`lower-fma.f64`
4 388×	`lower-*.f32`
4 386×	`lower-*.f64`
3 458×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	116
0	27	116
1	121	116
2	862	116
0	8623	110

Stop Event

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

Counts

8 → 147

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

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 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) 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)))
(/.f64 x (.f64 (neg.f64 #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) #s(literal 3 binary64))) #s(literal -1 binary64)))
(/.f64 (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)) x)))
(/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) (neg.f64 #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) #s(literal 3 binary64)))))
(/.f64 (neg.f64 x) (neg.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
(/.f64 (neg.f64 x) (.f64 #s(literal 1 binary64) (neg.f64 #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) #s(literal 3 binary64)))))
(/.f64 (neg.f64 x) (.f64 #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) #s(literal 3 binary64)) #s(literal -1 binary64)))
(/.f64 (neg.f64 x) (.f64 (neg.f64 #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) #s(literal 3 binary64))) #s(literal 1 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))
(/.f64 (neg.f64 (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) #s(literal 3 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) #s(literal 3 binary64))) (neg.f64 x)) #s(literal -1 binary64))
(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 (/.f64 x #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) #s(literal 3 binary64))) #s(literal 1 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 (.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))) #s(literal 1 binary64)) x)
(-.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))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) x)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 x) #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 x (.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))))) (/.f64 (neg.f64 x) #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))))
(neg.f64 (/.f64 (neg.f64 x) #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64)))))
(neg.f64 (.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) #s(approx (/ 1 (+ ( x (* x 1/45)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal 3 binary64))) x)))
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(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64)) #s(literal 27 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal 9 binary64)) (.f64 (*.f64 x x) #s(literal 3/5 binary64)))))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64)) #s(literal 27 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -3/5 binary64))))))
(.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -9 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/5 binary64)) #s(literal -3 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/125 binary64)) #s(literal 27 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal 9 binary64)) (.f64 (*.f64 x x) #s(literal 3/5 binary64))))))
(.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/25 binary64)) #s(literal -9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/5 binary64) #s(literal 3 binary64))))
(.f64 (-.f64 #s(literal 9 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/25 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3 binary64) (.f64 (*.f64 x x) #s(literal 1/5 binary64)))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(neg.f64 (*.f64 x (neg.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 x (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 x x) #s(literal 1 binary64))
(/.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) x))
(/.f64 (*.f64 x (neg.f64 x)) #s(literal -1 binary64))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 x x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (.f64 x (neg.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))

eval26.0ms (0.2%)

Memory: 12.1MiB live, 50.1MiB allocated
Compiler: Compiled 3 991 to 458 computations (88.5% saved)

prune25.0ms (0.2%)

Memory

7.3MiB live, 46.0MiB allocated

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	243	0	243
Fresh	0	0	0
Picked	0	2	2
Done	0	6	6
Total	243	8	251

Accuracy

100.0%

Counts

251 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/3 binary64))))
✓	99.3%	#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))))
✓	99.8%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))))
✓	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (/.f64 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) #s(literal 3 binary64))))
✓	99.6%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.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))))
✓	99.5%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.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))))
✓	99.3%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
✓	98.9%	#s(approx (- (/ 1 x) (/ 1 (tan x))) (*.f64 #s(literal 1/3 binary64) x))

Compiler

Compiled 244 to 106 computations (56.6% saved)

regimes8.0ms (0%)

Memory

11.5MiB live, 11.5MiB allocated

Counts

12 → 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 x #s(approx (/ 1 (+ (* x (* x 1/45)) 1/3)) (fma.f64 (*.f64 x x) #s(literal -1/5 binary64) #s(literal 3 binary64)))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.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))))
#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 (.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))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/4725 binary64)) #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/3 binary64))))
#s(approx (- (/ 1 x) (/ 1 (tan x))) (.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (*.f64 x x))))))))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes13.0ms (0.1%)

Memory

-41.1MiB live, 7.4MiB allocated

Counts

5 → 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)))

Outputs
#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))))

Calls

2 calls:

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

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes29.0ms (0.2%)

Memory

22.6MiB live, 22.6MiB allocated

Counts

3 → 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))))

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.3%	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)

regimes3.0ms (0%)

Memory

5.2MiB live, 5.2MiB allocated

Counts

2 → 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))))

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:

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)

regimes2.0ms (0%)

Memory

4.6MiB live, 4.6MiB 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
98.9%	1	`x`
98.9%	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)

simplify7.0ms (0%)

Memory

-28.8MiB live, 9.4MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	97
1	39	97

Stop Event

1×

saturated

Calls

Call 1

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

soundness645.0ms (4%)

Memory

33.2MiB live, 373.6MiB allocated

Rules

18 970×	`lower-fma.f64`
18 970×	`lower-fma.f32`
12 032×	`lower-fma.f64`
12 032×	`lower-fma.f32`
5 660×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	176
0	48	176
1	221	176
2	1738	176
0	8331	176
0	126	1988
1	350	1988
2	882	1985
3	2156	1984
4	5123	1984
0	8296	1855
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×	done
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 116 to 64 computations (44.8% saved)

preprocess77.0ms (0.5%)

Memory: -12.1MiB live, 104.8MiB allocated
Remove: (negabs x)
Compiler: Compiled 192 to 100 computations (47.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

start0.0ms (0%)

analyze8.0ms (0.1%)

sample9.2s (56.9%)

explain930.0ms (5.8%)

preprocess23.0ms (0.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify44.0ms (0.3%)

localize261.0ms (1.6%)

series5.0ms (0%)

simplify464.0ms (2.9%)

rewrite256.0ms (1.6%)

eval37.0ms (0.2%)

prune44.0ms (0.3%)

simplify351.0ms (2.2%)

localize370.0ms (2.3%)

series15.0ms (0.1%)

simplify205.0ms (1.3%)

rewrite263.0ms (1.6%)

eval76.0ms (0.5%)

prune263.0ms (1.6%)

simplify179.0ms (1.1%)

localize453.0ms (2.8%)

series22.0ms (0.1%)

simplify226.0ms (1.4%)

rewrite333.0ms (2.1%)

eval372.0ms (2.3%)

prune168.0ms (1%)

simplify61.0ms (0.4%)

localize280.0ms (1.7%)

series6.0ms (0%)

simplify213.0ms (1.3%)

rewrite184.0ms (1.1%)

eval26.0ms (0.2%)

prune25.0ms (0.2%)

regimes8.0ms (0%)

regimes13.0ms (0.1%)

regimes29.0ms (0.2%)

regimes3.0ms (0%)

regimes2.0ms (0%)

simplify7.0ms (0%)

soundness645.0ms (4%)

preprocess77.0ms (0.5%)

end0.0ms (0%)

Profiling

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

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