Metrics for tanhf (example 3.4)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze109.0ms (2%)

Memory

28.3MiB live, 141.6MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
25%	25%	75%	0%	0%	0%	0%	3
37.5%	37.5%	62.5%	0%	0%	0%	0%	4
43.8%	43.7%	56.2%	0%	0%	0%	0%	5
46.9%	46.9%	53.1%	0%	0%	0%	0%	6
48.4%	48.4%	51.5%	0%	0%	0%	0%	7
49.2%	49.2%	50.8%	0%	0%	0%	0%	8
49.6%	49.6%	50.4%	0%	0%	0%	0%	9
49.8%	49.8%	50.2%	0%	0%	0%	0%	10
49.9%	49.9%	50.1%	0%	0%	0%	0%	11
50%	49.9%	50%	0%	0%	0%	0%	12

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample1.9s (34%)

Memory

6.1MiB live, 1 645.0MiB allocated

Samples

647.0ms	2 257×	2	valid
592.0ms	4 208×	0	valid
189.0ms	569×	3	valid
128.0ms	1 215×	1	valid
8.0ms	7×	4	valid

Precisions

Click to see histograms. Total time spent on operations: 1.2s

ival-cos: 730.0ms (59.6% of total)

ival-sin: 180.0ms (14.7% of total)

adjust: 122.0ms (10% of total)

ival-div: 97.0ms (7.9% of total)

ival-sub: 82.0ms (6.7% of total)

ival-true: 6.0ms (0.5% of total)

exact: 5.0ms (0.4% of total)

ival-assert: 3.0ms (0.2% of total)

Bogosity

explain254.0ms (4.7%)

Memory

26.2MiB live, 149.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
71	-	1	(3.8973132795588845e+154)	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
65	-	3	(-1.3440810208745528e-158)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(cos.f64 x)`
0	-	0	-	`(sin.f64 x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	70	4
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`	u/n	62	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	62

Confusion

	Predicted +	Predicted -
+	132	1
-	0	123

Precision

1.0

Recall

0.9924812030075187

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	132	1	0
-	0	3	120

Precision?

0.9779411764705882

Recall?

1.0

Freqs

test

number	freq
0	124
1	132

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

114.0ms	130×	2	valid
27.0ms	256×	0	valid
11.0ms	96×	1	valid
10.0ms	30×	3	valid

Compiler

Compiled 45 to 22 computations (51.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 119.0ms

ival-cos: 90.0ms (75.5% of total)

ival-sin: 11.0ms (9.2% of total)

adjust: 7.0ms (5.9% of total)

ival-div: 6.0ms (5% of total)

ival-sub: 5.0ms (4.2% of total)

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

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

exact: 0.0ms (0% of total)

preprocess44.0ms (0.8%)

Memory

5.9MiB live, 43.4MiB allocated

Algorithm

1×	egg-herbie

Rules

204×	`lower-fma.f64`
204×	`lower-fma.f32`
140×	`lower-*.f64`
140×	`lower-*.f32`
98×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	4

Stop Event

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

Calls

Call 1

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

Outputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))

Symmetry

(negabs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.0%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify27.0ms (0.5%)

Memory

-26.1MiB live, 10.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f64 x)
cost-diff	0	(cos.f64 x)
cost-diff	0	(-.f64 #s(literal 1 binary64) (cos.f64 x))
cost-diff	6592	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Rules

204×	`lower-fma.f64`
204×	`lower-fma.f32`
140×	`lower-*.f64`
140×	`lower-*.f32`
82×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

Outputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(sin.f64 x)

localize54.0ms (1%)

Memory

-5.9MiB live, 39.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(sin.f64 x)
accuracy	0	(cos.f64 x)
accuracy	14.871107673648089	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
accuracy	15.681067201600388	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Samples

19.0ms	128×	0	valid
18.0ms	65×	2	valid
5.0ms	48×	1	valid
5.0ms	15×	3	valid

Compiler

Compiled 19 to 8 computations (57.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-cos: 19.0ms (49.1% of total)

ival-sin: 11.0ms (28.4% of total)

adjust: 3.0ms (7.8% of total)

ival-div: 3.0ms (7.8% of total)

ival-sub: 2.0ms (5.2% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

1.6MiB live, 1.6MiB allocated

Counts

4 → 48

Calls

Call 1

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

Outputs
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/6 (pow x 2)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())

Calls

3 calls:

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

simplify279.0ms (5.1%)

Memory

35.1MiB live, 190.0MiB allocated

Algorithm

1×	egg-herbie

Rules

19 148×	`lower-fma.f64`
19 148×	`lower-fma.f32`
3 796×	`lower-*.f64`
3 796×	`lower-*.f32`
3 232×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	286
1	224	286
2	555	280
3	1661	280
4	3000	280
5	4254	280
6	4606	280
7	5336	280
8	6824	280
0	8376	256

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 47

Calls

Call 1

Inputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(sin x)
(sin x)
(sin x)
(sin x)
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(sin x)
(sin x)
(sin x)
(sin x)

Outputs
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) (.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) x)
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)

rewrite144.0ms (2.7%)

Memory

-12.0MiB live, 148.4MiB allocated

Rules

4 606×	`lower-*.f64`
4 606×	`lower-*.f32`
3 722×	`lower-/.f32`
3 720×	`lower-/.f64`
2 028×	`lower--.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	10	12
1	39	12
2	245	12
3	2355	11
0	8885	11

Stop Event

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

Counts

4 → 615

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval103.0ms (1.9%)

Memory: 10.0MiB live, 168.6MiB allocated
Compiler: Compiled 13 164 to 1 644 computations (87.5% saved)

prune16.0ms (0.3%)

Memory

9.7MiB live, 45.5MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	656	6	662
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	657	6	663

Accuracy

100.0%

Counts

663 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
	6.7%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
▶	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
▶	51.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
▶	51.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
▶	51.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
▶	51.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))

Compiler

Compiled 106 to 78 computations (26.4% saved)

simplify66.0ms (1.2%)

Memory

-1.6MiB live, 73.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
cost-diff	0	(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
cost-diff	0	(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
cost-diff	0	(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
cost-diff	0	(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
cost-diff	0	(*.f64 x #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))

Rules

1 918×	`lower-fma.f32`
1 906×	`lower-fma.f64`
788×	`distribute-lft-in`
552×	`lower-+.f64`
552×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	204
0	46	192
1	84	192
2	144	192
3	296	192
4	653	192
5	949	192
6	999	192
7	1077	192
8	1200	192
9	1410	192
10	1452	192
11	1455	192
12	1463	192
13	1469	192
14	1473	192
15	1480	192
16	1655	192
17	1905	192
18	1911	192
0	1911	192

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal 1/240 binary64)
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
#s(literal 17/40320 binary64)
(*.f64 x x)
x
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)

Outputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal 1/240 binary64)
(*.f64 x x)
x
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
#s(literal 17/40320 binary64)
(*.f64 x x)
x
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)

localize181.0ms (3.3%)

Memory

-8.2MiB live, 154.6MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.0390625	(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
accuracy	0.046875	(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
accuracy	0.31100143025645166	(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
accuracy	31.37875180515255	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
accuracy	0.037441259768442016	(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
accuracy	0.04296875	(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
accuracy	0.29798805030693365	(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
accuracy	31.373095023632263	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
accuracy	0	(*.f64 x x)
accuracy	0.046875	(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
accuracy	0.29558851795670427	(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
accuracy	31.33590837736428	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
accuracy	0	(*.f64 x #s(literal 1/2 binary64))
accuracy	31.162441164189012	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))

Samples

81.0ms	65×	2	valid
41.0ms	128×	0	valid
20.0ms	48×	1	valid
15.0ms	15×	3	valid

Compiler

Compiled 176 to 31 computations (82.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 133.0ms

ival-cos: 58.0ms (43.7% of total)

ival-mult: 26.0ms (19.6% of total)

adjust: 12.0ms (9% of total)

const: 12.0ms (9% of total)

ival-add: 9.0ms (6.8% of total)

ival-tan: 5.0ms (3.8% of total)

ival-sin: 5.0ms (3.8% of total)

ival-div: 3.0ms (2.3% of total)

ival-sub: 3.0ms (2.3% of total)

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

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

exact: 0.0ms (0% of total)

series23.0ms (0.4%)

Memory

-24.9MiB live, 19.6MiB allocated

Counts

17 → 204

Calls

Call 1

Inputs
#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())
#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (patch (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))) (taylor 0 x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))) (taylor 0 x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/24 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/24 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/24 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/24 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt 1/24 (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/24 (* 1/240 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/24 (* 1/240 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/24 (* 1/240 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor 0 x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/24 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt 1/24 (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/24 (* 1/240 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt 1/240 (taylor 0 x) (#s(alt (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (patch (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/240 (* 17/40320 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (patch (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/240 (* 17/40320 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (patch (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/240 (* 17/40320 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (patch (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor inf x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor inf x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor inf x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor inf x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 3)) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/240 (pow x 5)) (taylor inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 1/240 (pow x 4)) (taylor inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/240 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 17/40320 (pow x 7)) (taylor inf x) (#s(alt (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6))))))) (taylor inf x) (#s(alt (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 17/40320 (pow x 6)) (taylor inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6))))))) (taylor inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 17/40320 (pow x 4)) (taylor inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 17/40320 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (patch (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (patch (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (patch (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (patch (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor -inf x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor -inf x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor -inf x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor -inf x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 3)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/240 (pow x 5)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 1/240 (pow x 4)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/240 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 17/40320 (pow x 7)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2))))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 17/40320 (pow x 6)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6))))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 17/40320 (pow x 4)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 17/40320 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (patch (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (patch (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (patch (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (patch (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

11.0ms

-inf

((tan (* 1/2 x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (* x 1/2) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (+ (* 17/40320 (* x x)) 1/240))

3.0ms

inf

((tan (* 1/2 x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (* x 1/2) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (+ (* 17/40320 (* x x)) 1/240))

2.0ms

((tan (* 1/2 x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (* x 1/2) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (* x x)) 1/2) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (+ (* 17/40320 (* x x)) 1/240))

simplify149.0ms (2.7%)

Memory

28.8MiB live, 102.1MiB allocated

Algorithm

1×	egg-herbie

Rules

14 174×	`lower-fma.f64`
14 174×	`lower-fma.f32`
4 532×	`lower-*.f64`
4 532×	`lower-*.f32`
2 884×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	97	1554
1	319	1554
2	843	1549
3	2202	1546
4	4802	1546
0	8092	1417

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* 1/24 (pow x 2))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* 1/24 (pow x 2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
1/24
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/24 (* 1/240 (pow x 2)))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
1/24
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
1/240
(+ 1/240 (* 17/40320 (pow x 2)))
(+ 1/240 (* 17/40320 (pow x 2)))
(+ 1/240 (* 17/40320 (pow x 2)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/240 (pow x 5))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 4))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 2))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 17/40320 (pow x 7))
(* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(* 17/40320 (pow x 6))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(* 17/40320 (pow x 4))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* 17/40320 (pow x 2))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/240 (pow x 5))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(* 1/240 (pow x 4))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 2))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 17/40320 (pow x 7))
(* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
(* 17/40320 (pow x 6))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(* 17/40320 (pow x 4))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* 17/40320 (pow x 2))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))

Outputs
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
1/24
#s(literal 1/24 binary64)
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
1/24
#s(literal 1/24 binary64)
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
1/240
#s(literal 1/240 binary64)
(+ 1/240 (* 17/40320 (pow x 2)))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(+ 1/240 (* 17/40320 (pow x 2)))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(+ 1/240 (* 17/40320 (pow x 2)))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(* 1/24 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(* 1/240 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/240 binary64))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/240 binary64)) (pow.f64 x #s(literal 5 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/240 binary64)) (pow.f64 x #s(literal 5 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)))
(* 1/240 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/240 binary64))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x)
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(* 1/240 (pow x 2))
(.f64 #s(literal 1/240 binary64) (.f64 x x))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(* 17/40320 (pow x 7))
(*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 17/40320 binary64))
(* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (-.f64 (/.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal -17/40320 binary64)) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 17/40320 binary64)) (/.f64 #s(literal -1/240 binary64) (.f64 x x))) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 17/40320 binary64)) (-.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1/240 binary64) (.f64 x x)))) (pow.f64 x #s(literal 7 binary64)))
(* 17/40320 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 17/40320 binary64))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) x) x)
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(* 17/40320 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 17/40320 binary64))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) x) x)
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(* 17/40320 (pow x 2))
(.f64 #s(literal 17/40320 binary64) (.f64 x x))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(* 1/24 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(* 1/240 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/240 binary64))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(.f64 (-.f64 (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)) x) x) #s(literal -1/240 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(.f64 (-.f64 (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)) x) x) #s(literal -1/240 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* 1/240 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/240 binary64))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x)
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(* 1/240 (pow x 2))
(.f64 #s(literal 1/240 binary64) (.f64 x x))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(* 17/40320 (pow x 7))
(*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 17/40320 binary64))
(* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (-.f64 (/.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal -17/40320 binary64)) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))
(.f64 (-.f64 (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/240 binary64)) x) x) #s(literal -17/40320 binary64)) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
(.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal -17/40320 binary64) (/.f64 #s(literal 1/240 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 7 binary64)))
(* 17/40320 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 17/40320 binary64))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) x) x)
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(* 17/40320 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 17/40320 binary64))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) x) x)
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(* 17/40320 (pow x 2))
(.f64 #s(literal 17/40320 binary64) (.f64 x x))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))

rewrite215.0ms (3.9%)

Memory

-11.2MiB live, 178.7MiB allocated

Rules

6 308×	`lower-fma.f32`
6 296×	`lower-fma.f64`
4 758×	`lower-*.f32`
4 746×	`lower-*.f64`
4 410×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	182
0	46	170
1	179	170
2	1220	170
0	8510	170

Stop Event

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

Counts

17 → 514

Calls

Call 1

Inputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(*.f64 x x)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval114.0ms (2.1%)

Memory: 27.6MiB live, 149.7MiB allocated
Compiler: Compiled 19 313 to 2 439 computations (87.4% saved)

prune39.0ms (0.7%)

Memory

-15.6MiB live, 68.1MiB allocated

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	806	2	808
Fresh	0	1	1
Picked	0	5	5
Done	0	0	0
Total	806	8	814

Accuracy

100.0%

Counts

814 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.7%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
✓	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
▶	51.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))))
▶	51.2%	#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
✓	51.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
✓	51.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
✓	51.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	51.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))

Compiler

Compiled 70 to 53 computations (24.3% saved)

simplify28.0ms (0.5%)

Memory

-14.3MiB live, 24.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	6464	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
cost-diff	0	(*.f64 x x)
cost-diff	0	(.f64 #s(literal 1/24 binary64) (.f64 x x))
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))))
cost-diff	320	(fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64)))
cost-diff	0	(/.f64 #s(literal 2 binary64) x)
cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
cost-diff	1088	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))

Rules

266×	`lower-fma.f32`
264×	`lower-fma.f64`
178×	`lower-*.f32`
172×	`lower-*.f64`
120×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	71
0	27	59
1	46	57
2	66	57
3	80	57
4	101	57
5	125	57
6	158	57
7	232	57
8	356	57
9	564	57
10	606	57
11	609	57
12	617	57
13	622	57
14	626	57
15	633	57
16	666	57
17	690	57
18	692	57
0	692	55

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
#s(literal 1 binary64)
(/.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64)))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
#s(literal 1/24 binary64)
(*.f64 x x)
x
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
#s(literal 1 binary64)
#s(literal -1/2 binary64)

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1 binary64)
(/.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x))
(fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64)))
(.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x)
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
(*.f64 x x)
x
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
#s(literal 1 binary64)
#s(literal 1 binary64)
#s(literal -1/2 binary64)

localize91.0ms (1.7%)

Memory

15.4MiB live, 167.5MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
accuracy	0	(*.f64 x #s(literal 1/2 binary64))
accuracy	0.04296875	(fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64)))
accuracy	0.38543226795670427	(.f64 #s(literal 1/24 binary64) (.f64 x x))
accuracy	31.33590837736428	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))))
accuracy	0	(/.f64 #s(literal 2 binary64) x)
accuracy	0.20703125	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
accuracy	31.162441164189012	#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))

Samples

34.0ms	65×	2	valid
23.0ms	128×	0	valid
13.0ms	48×	1	valid
9.0ms	15×	3	valid

Compiler

Compiled 57 to 20 computations (64.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

ival-cos: 26.0ms (43.4% of total)

adjust: 8.0ms (13.4% of total)

ival-div: 6.0ms (10% of total)

ival-mult: 6.0ms (10% of total)

ival-sin: 5.0ms (8.3% of total)

const: 3.0ms (5% of total)

ival-sub: 2.0ms (3.3% of total)

ival-pow: 2.0ms (3.3% of total)

ival-add: 1.0ms (1.7% of total)

exact: 1.0ms (1.7% of total)

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

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

series7.0ms (0.1%)

Memory

8.7MiB live, 8.7MiB allocated

Counts

9 → 96

Calls

Call 1

Inputs
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 2 binary64) x) (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/24 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/24 binary64) (.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (patch (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 2 binary64) x) (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 2 binary64) x) (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 2 binary64) x) (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 2 binary64) x) (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/24 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/24 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/24 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/24 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/24 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/24 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/24 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/24 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor inf x) (#s(alt (/.f64 #s(literal 2 binary64) x) (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor inf x) (#s(alt (/.f64 #s(literal 2 binary64) x) (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor inf x) (#s(alt (/.f64 #s(literal 2 binary64) x) (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor inf x) (#s(alt (/.f64 #s(literal 2 binary64) x) (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 3)) (taylor inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal 1/24 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/24 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal 1/24 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/24 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal 1/24 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/24 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal 1/24 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/24 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 2 binary64) x) (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 2 binary64) x) (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 2 binary64) x) (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 2 binary64) x) (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 3)) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/24 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/24 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/24 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/24 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/24 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/24 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/24 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/24 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

inf

((/ 1 (/ 2 x)) (/ (- 1 (cos x)) (sin x)) (/ 2 x) (+ (* (* 1/24 (* x x)) x) (* x 1/2)) (/ (- 1 (cos x)) (sin x)) (* 1/24 (* x x)) (* x x) (pow 1 -1/2) (* x 1/2))

1.0ms

-inf

((/ 1 (/ 2 x)) (/ (- 1 (cos x)) (sin x)) (/ 2 x) (+ (* (* 1/24 (* x x)) x) (* x 1/2)) (/ (- 1 (cos x)) (sin x)) (* 1/24 (* x x)) (* x x) (pow 1 -1/2) (* x 1/2))

1.0ms

((/ 1 (/ 2 x)) (/ (- 1 (cos x)) (sin x)) (/ 2 x) (+ (* (* 1/24 (* x x)) x) (* x 1/2)) (/ (- 1 (cos x)) (sin x)) (* 1/24 (* x x)) (* x x) (pow 1 -1/2) (* x 1/2))

simplify219.0ms (4%)

Memory

-28.5MiB live, 115.0MiB allocated

Algorithm

1×	egg-herbie

Rules

6 696×	`lower-fma.f64`
6 696×	`lower-fma.f32`
5 206×	`lower-*.f64`
5 206×	`lower-*.f32`
1 982×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	458
1	105	458
2	263	458
3	611	458
4	1006	458
5	1723	458
6	3066	458
7	4239	458
8	5187	458
9	5889	458
10	6770	458
11	7195	458
12	7976	458
0	8012	437

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

Inputs
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)

Outputs
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* 1/24 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* 1/24 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))

rewrite158.0ms (2.9%)

Memory

17.6MiB live, 168.2MiB allocated

Rules

7 420×	`lower-fma.f32`
7 418×	`lower-fma.f64`
4 532×	`lower-*.f32`
4 526×	`lower-*.f64`
2 658×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	63
0	27	51
1	100	49
2	618	49
3	6439	49
0	8220	47

Stop Event

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

Counts

9 → 213

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
(/.f64 #s(literal 2 binary64) x)
(fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(*.f64 x x)
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
(*.f64 x #s(literal 1/2 binary64))

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval46.0ms (0.9%)

Memory: 1.0MiB live, 104.6MiB allocated
Compiler: Compiled 4 983 to 721 computations (85.5% saved)

prune35.0ms (0.6%)

Memory

-18.3MiB live, 28.5MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	308	1	309
Fresh	0	0	0
Picked	2	1	3
Done	0	5	5
Total	310	7	317

Accuracy

100.0%

Counts

317 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
✓	51.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))))
✓	51.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
✓	51.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
✓	51.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	51.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))
▶	6.7%	#s(literal 1 binary64)

Compiler

Compiled 62 to 45 computations (27.4% saved)

simplify3.0ms (0.1%)

Memory

3.5MiB live, 3.5MiB allocated

Algorithm

1×	egg-herbie

Rules

2× 1-exp

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
0	1	1
1	3	1
0	3	1

Stop Event

1×	saturated
1×	saturated
1×	saturated

Calls

Call 1

Inputs
#s(literal 1 binary64)

Outputs
#s(literal 1 binary64)

localize6.0ms (0.1%)

Memory

9.1MiB live, 9.1MiB allocated

Samples

3.0ms

256×

valid

Compiler

Compiled 3 to 4 computations (-33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

exact: 0.0ms (0% of total)

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

series0.0ms (0%)

Memory

0.0MiB live, 0.0MiB allocated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

simplify2.0ms (0%)

Memory

4.8MiB live, 4.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

rewrite6.0ms (0.1%)

Memory

12.7MiB live, 12.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

eval0.0ms (0%)

Memory: 0.7MiB live, 0.7MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune27.0ms (0.5%)

Memory

-23.6MiB live, 15.8MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	6	6
Total	7	7

Accuracy

100.0%

Counts

7 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
✓	51.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))))
✓	51.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
✓	51.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
✓	51.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	51.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))
✓	6.7%	#s(literal 1 binary64)

Compiler

Compiled 140 to 81 computations (42.1% saved)

regimes8.0ms (0.1%)

Memory

26.6MiB live, 26.6MiB allocated

Counts

10 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Outputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))

Calls

2 calls:

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

Results

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes9.0ms (0.2%)

Memory

-15.0MiB live, 23.0MiB allocated

Counts

8 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))

Outputs

#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))

#s(literal 1 binary64)

Calls

2 calls:

5.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
3.0ms	x

Results

Accuracy	Segments	Branch
54.0%	2	`x`
53.8%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated

Counts

6 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(literal 1 binary64)

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
54.0%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes5.0ms (0.1%)

Memory

-27.8MiB live, 10.9MiB allocated

Counts

5 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))))
#s(literal 1 binary64)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
54.0%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes2.0ms (0%)

Memory

8.5MiB live, 8.5MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

#s(literal 1 binary64)

#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))

#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(literal 1 binary64)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
54.0%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes2.0ms (0%)

Memory

7.2MiB live, 7.2MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))
#s(literal 1 binary64)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
53.9%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes3.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)

Outputs
#s(literal 1 binary64)

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
6.7%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
6.7%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

bsearch20.0ms (0.4%)

Memory

-14.3MiB live, 26.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	1.2501490516133542	11.32371699071231

Samples

9.0ms

96×

valid

Compiler

Compiled 130 to 100 computations (23.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-cos: 3.0ms (41.8% of total)

ival-sin: 3.0ms (41.8% of total)

ival-div: 1.0ms (13.9% of total)

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

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

2.5MiB live, 2.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	1.2501490516133542	11.32371699071231

Compiler

Compiled 100 to 88 computations (12% saved)

bsearch1.0ms (0%)

Memory

2.1MiB live, 2.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	1.2501490516133542	11.32371699071231

Compiler

Compiled 82 to 82 computations (0% saved)

bsearch1.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	1.2501490516133542	11.32371699071231

Compiler

Compiled 70 to 76 computations (-8.6% saved)

bsearch1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	1.2501490516133542	11.32371699071231

Compiler

Compiled 40 to 58 computations (-45% saved)

simplify23.0ms (0.4%)

Memory

10.1MiB live, 47.9MiB allocated

Algorithm

1×	egg-herbie

Rules

10×	`-commutative-binary64-.f64`
2×	`1-exp-binary32-exp.f32`
2×	`1-exp-binary64-exp.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	122
1	45	122

Stop Event

1×

saturated

Calls

Call 1

Inputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
#s(literal 1 binary64)

Outputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness956.0ms (17.6%)

Memory

-36.3MiB live, 465.7MiB allocated

Rules

19 148×	`lower-fma.f64`
19 148×	`lower-fma.f32`
7 420×	`lower-fma.f32`
7 418×	`lower-fma.f64`
6 308×	`lower-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	63
0	27	51
1	100	49
2	618	49
3	6439	49
0	8220	47
0	6	15
0	10	12
1	39	12
2	245	12
3	2355	11
0	8885	11
0	27	182
0	46	170
1	179	170
2	1220	170
0	8510	170
0	79	286
1	224	286
2	555	280
3	1661	280
4	3000	280
5	4254	280
6	4606	280
7	5336	280
8	6824	280
0	8376	256

Stop Event

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

Compiler

Compiled 181 to 105 computations (42% saved)

preprocess107.0ms (2%)

Memory: -8.2MiB live, 67.9MiB allocated
Remove: (negabs x)
Compiler: Compiled 212 to 100 computations (52.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	4

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14

Iter	Nodes	Cost
0	19	71
0	27	59
1	46	57
2	66	57
3	80	57
4	101	57
5	125	57
6	158	57
7	232	57
8	356	57
9	564	57
10	606	57
11	609	57
12	617	57
13	622	57
14	626	57
15	633	57
16	666	57
17	690	57
18	692	57
0	692	55

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	4

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14

Iter	Nodes	Cost
0	19	71
0	27	59
1	46	57
2	66	57
3	80	57
4	101	57
5	125	57
6	158	57
7	232	57
8	356	57
9	564	57
10	606	57
11	609	57
12	617	57
13	622	57
14	626	57
15	633	57
16	666	57
17	690	57
18	692	57
0	692	55

start0.0ms (0%)

analyze109.0ms (2%)

sample1.9s (34%)

explain254.0ms (4.7%)

preprocess44.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify27.0ms (0.5%)

localize54.0ms (1%)

series3.0ms (0.1%)

simplify279.0ms (5.1%)

rewrite144.0ms (2.7%)

eval103.0ms (1.9%)

prune16.0ms (0.3%)

simplify66.0ms (1.2%)

localize181.0ms (3.3%)

series23.0ms (0.4%)

simplify149.0ms (2.7%)

rewrite215.0ms (3.9%)

eval114.0ms (2.1%)

prune39.0ms (0.7%)

simplify28.0ms (0.5%)

localize91.0ms (1.7%)

series7.0ms (0.1%)

simplify219.0ms (4%)

rewrite158.0ms (2.9%)

eval46.0ms (0.9%)

prune35.0ms (0.6%)

simplify3.0ms (0.1%)

localize6.0ms (0.1%)

series0.0ms (0%)

simplify2.0ms (0%)

rewrite6.0ms (0.1%)

eval0.0ms (0%)

prune27.0ms (0.5%)

regimes8.0ms (0.1%)

regimes9.0ms (0.2%)

regimes3.0ms (0.1%)

regimes5.0ms (0.1%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes3.0ms (0.1%)

bsearch20.0ms (0.4%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

simplify23.0ms (0.4%)

soundness956.0ms (17.6%)

preprocess107.0ms (2%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	4

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14

Iter	Nodes	Cost
0	19	71
0	27	59
1	46	57
2	66	57
3	80	57
4	101	57
5	125	57
6	158	57
7	232	57
8	356	57
9	564	57
10	606	57
11	609	57
12	617	57
13	622	57
14	626	57
15	633	57
16	666	57
17	690	57
18	692	57
0	692	55