Metrics for tanhf (example 3.4)

analyze113.0ms (1.2%)

Memory

15.2MiB live, 132.9MiB 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 (19.9%)

Memory

55.1MiB live, 1 767.6MiB allocated

Samples

684.0ms	2 304×	2	valid
443.0ms	4 147×	0	valid
289.0ms	577×	3	valid
164.0ms	1 226×	1	valid
2.0ms	2×	4	valid

Precisions

Click to see histograms. Total time spent on operations: 1.3s

ival-cos: 871.0ms (64.9% of total)

ival-sin: 167.0ms (12.4% of total)

adjust: 109.0ms (8.1% of total)

ival-div: 102.0ms (7.6% of total)

ival-sub: 79.0ms (5.9% of total)

ival-true: 6.0ms (0.4% of total)

exact: 5.0ms (0.4% of total)

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

Bogosity

preprocess66.0ms (0.7%)

Memory

-5.9MiB live, 32.2MiB 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))
(neg.f64 (tan.f64 (*.f64 x #s(literal -1/2 binary64))))

Symmetry

(negabs x)

explain195.0ms (2%)

Memory

-32.3MiB live, 180.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
74	-	2	(2.6523431052011097e+71)	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
67	-	1	(6.295029718274413e-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	72	6
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`	u/n	66	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	66

Confusion

	Predicted +	Predicted -
+	138	2
-	0	116

Precision

1.0

Recall

0.9857142857142858

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	138	2	0
-	0	4	112

Precision?

0.9722222222222222

Recall?

1.0

Freqs

test

number	freq
0	118
1	138

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

55.0ms	148×	2	valid
26.0ms	250×	0	valid
16.0ms	32×	3	valid
9.0ms	82×	1	valid

Compiler

Compiled 54 to 28 computations (48.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 82.0ms

ival-cos: 54.0ms (65.5% of total)

ival-sin: 10.0ms (12.1% of total)

adjust: 7.0ms (8.5% of total)

ival-div: 6.0ms (7.3% of total)

ival-sub: 5.0ms (6.1% of total)

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.8%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify29.0ms (0.3%)

Memory

1.9MiB live, 38.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	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	6848	(/.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))
(neg.f64 (tan.f64 (*.f64 x #s(literal -1/2 binary64))))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(sin.f64 x)

localize55.0ms (0.6%)

Memory

20.1MiB live, 97.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	75.7%	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	accuracy	75.5%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Samples

23.0ms	74×	2	valid
13.0ms	125×	0	valid
6.0ms	16×	3	valid
4.0ms	41×	1	valid

Compiler

Compiled 19 to 8 computations (57.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-cos: 23.0ms (61.4% of total)

ival-sin: 5.0ms (13.3% of total)

adjust: 4.0ms (10.7% of total)

ival-div: 3.0ms (8% of total)

ival-sub: 2.0ms (5.3% 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%)

Memory

5.6MiB live, 5.6MiB 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 (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)) (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 (* 1/2 (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 (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 (- 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 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 (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 (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 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 (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 (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

12 calls:

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

simplify456.0ms (4.7%)

Memory

-23.6MiB live, 531.0MiB 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	1656	280
4	3000	280
5	4243	280
6	4592	280
7	5323	280
8	6815	280
0	8390	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 (cos 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)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 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 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
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)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
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))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)

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

rewrite302.0ms (3.1%)

Memory

30.3MiB live, 418.7MiB allocated

Algorithm

1×	batch-egg-rewrite

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
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (log.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) #s(literal -1 binary64))))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x))))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x))))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal 1 binary64)))
(+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(+.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(+.f64 (.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)) (.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(+.f64 (.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (*.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)))
(+.f64 (.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (*.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (cos.f64 x)))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x))) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(+.f64 (.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (.f64 (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))
(+.f64 (.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))
(+.f64 (.f64 (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (*.f64 (cos.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))
(-.f64 #s(literal 0 binary64) (neg.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 (/.f64 (+.f64 #s(literal 0 binary64) (sin.f64 (+.f64 x x))) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (neg.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (sin.f64 x)) (neg.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (sin.f64 x)) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (sin.f64 x)))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x)) (/.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))) (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (fma.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(fma.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))
(fma.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(fma.f64 (cos.f64 x) (/.f64 #s(literal -1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x))))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x))))
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal 1 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal 1 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (cos.f64 x) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(fma.f64 (neg.f64 (cos.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(fma.f64 (neg.f64 (cos.f64 x)) (/.f64 #s(literal -1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 x)) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 x)) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x))))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x))))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal 1 binary64)))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(fma.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))
(fma.f64 (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (.f64 (cos.f64 x) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))
(fma.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64) (.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(fma.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)))
(fma.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (cos.f64 x)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x))))
(fma.f64 (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x))))
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eval100.0ms (1%)

Memory: -9.2MiB live, 158.5MiB allocated
Compiler: Compiled 14 450 to 1 633 computations (88.7% saved)

prune96.0ms (1%)

Memory

8.1MiB live, 213.5MiB 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
	8.2%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
▶	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
▶	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
▶	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
▶	53.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
▶	53.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 118 to 74 computations (37.3% saved)

simplify84.0ms (0.9%)

Memory

-13.7MiB live, 64.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	210
0	52	198
1	122	198
2	276	198
3	538	198
4	761	198
5	848	198
6	885	198
7	959	198
8	1081	198
9	1289	198
10	1331	198
11	1334	198
12	1342	198
13	1348	198
14	1352	198
15	1359	198
16	1534	198
17	1790	198
18	1796	198
0	1796	198

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize207.0ms (2.2%)

Memory

2.9MiB live, 193.9MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))
✓	accuracy	99.9%	(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
✓	accuracy	99.5%	(*.f64 x #s(literal 17/40320 binary64))
✓	accuracy	53.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	accuracy	99.9%	(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
✓	accuracy	99.9%	(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
✓	accuracy	99.9%	(*.f64 x #s(literal 1/240 binary64))
✓	accuracy	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	accuracy	99.9%	(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	99.9%	(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
✓	accuracy	99.4%	(*.f64 x #s(literal 1/24 binary64))
✓	accuracy	53.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	accuracy	53.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))

Samples

66.0ms	74×	2	valid
39.0ms	125×	0	valid
34.0ms	16×	3	valid
22.0ms	41×	1	valid

Compiler

Compiled 182 to 34 computations (81.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 135.0ms

ival-cos: 57.0ms (42.3% of total)

ival-mult: 26.0ms (19.3% of total)

const: 14.0ms (10.4% of total)

adjust: 13.0ms (9.6% of total)

ival-add: 9.0ms (6.7% of total)

ival-tan: 5.0ms (3.7% of total)

ival-sin: 5.0ms (3.7% of total)

ival-div: 3.0ms (2.2% of total)

ival-sub: 2.0ms (1.5% of total)

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

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

exact: 0.0ms (0% of total)

series18.0ms (0.2%)

Memory

24.8MiB live, 24.8MiB allocated

Counts

20 → 240

Calls

Call 1

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

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

Calls

60 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(+ (* (* x x) (+ (* x (* x 1/240)) 1/24)) 1/2)
1.0ms	x	@	inf	(* x 1/2)
1.0ms	x	@	inf	(* x (+ (* x (* x 1/24)) 1/2))
0.0ms	x	@	inf	(tan (* x 1/2))
0.0ms	x	@	-inf	(tan (* x 1/2))

simplify379.0ms (3.9%)

Memory

-19.6MiB live, 438.3MiB allocated

Algorithm

1×	egg-herbie

Rules

14 366×	`lower-fma.f64`
14 366×	`lower-fma.f32`
4 532×	`lower-*.f64`
4 532×	`lower-*.f32`
2 914×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	100	1662
1	325	1662
2	842	1657
3	2164	1654
4	4762	1654
0	8122	1525

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

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

rewrite344.0ms (3.6%)

Memory

-9.9MiB live, 463.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 984×	`lower-*.f32`
4 966×	`lower-*.f64`
4 560×	`lower-/.f64`
4 560×	`lower-/.f32`
3 720×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	191
0	52	179
1	217	179
2	1560	179
0	8169	179

Stop Event

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

Counts

20 → 566

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64))))) #s(literal -1 binary64)))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (sin.f64 x)) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (sin.f64 x)))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x)) (/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x))) (tan.f64 (/.f64 (neg.f64 x) #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(-.f64 (/.f64 (.f64 #s(literal 1 binary64) (sin.f64 x)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (/.f64 (.f64 (sin.f64 x) (cos.f64 x)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
(-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sin.f64 x) (tan.f64 x)))))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sin.f64 x) (tan.f64 x)))))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) (/.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 x))) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(neg.f64 (tan.f64 (/.f64 (neg.f64 x) #s(literal 2 binary64))))
(neg.f64 (/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (.f64 (sin.f64 x) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 (sin.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
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(.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))))) #s(literal 1/13824 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))) #s(literal 1/576 binary64)) (.f64 x (.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64))))))
(.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))))) #s(literal 1/13824 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/576 binary64) (-.f64 (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64)))))))
(.f64 (fma.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))) #s(literal -1/576 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal -1/24 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))))) #s(literal 1/13824 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))) #s(literal 1/576 binary64)) (.f64 x (.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64)))))))
(.f64 (neg.f64 (fma.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))) #s(literal -1/576 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal -1/24 binary64)))))
(.f64 (-.f64 #s(literal 1/576 binary64) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))))))
(+.f64 #s(literal 1/240 binary64) (.f64 x (.f64 x #s(literal 17/40320 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal 17/40320 binary64))) #s(literal 1/240 binary64))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64))) (/.f64 #s(literal 1/57600 binary64) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64))))
(-.f64 (/.f64 #s(literal 1/57600 binary64) (-.f64 #s(literal 1/240 binary64) (.f64 x (.f64 x #s(literal 17/40320 binary64))))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64)) (-.f64 #s(literal 1/240 binary64) (.f64 x (.f64 x #s(literal 17/40320 binary64))))))
(fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))
(fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(fma.f64 (*.f64 x #s(literal 17/40320 binary64)) x #s(literal 1/240 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/57600 binary64) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64)) (.f64 (.f64 x x) #s(literal 17/9676800 binary64)))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 4913/65548320768000 binary64)) #s(literal 1/13824000 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/240 binary64) (.f64 x (.f64 x #s(literal 17/40320 binary64)))) (-.f64 #s(literal 1/57600 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64)) #s(literal 1/13824000 binary64)) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64) #s(literal 1/57600 binary64)) (.f64 (.f64 x x) #s(literal 17/9676800 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64)) #s(literal 1/13824000 binary64)) (+.f64 #s(literal 1/57600 binary64) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64)) (.f64 (*.f64 x x) #s(literal 17/9676800 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64) #s(literal -1/57600 binary64)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64)) #s(literal 1/13824000 binary64))) (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64) #s(literal 1/57600 binary64)) (.f64 (.f64 x x) #s(literal 17/9676800 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64)) #s(literal 1/13824000 binary64))) (neg.f64 (+.f64 #s(literal 1/57600 binary64) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64)) (.f64 (*.f64 x x) #s(literal 17/9676800 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64) #s(literal -1/57600 binary64))) (neg.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64))))
(/.f64 (-.f64 #s(literal 1/57600 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64))) (-.f64 #s(literal 1/240 binary64) (.f64 x (.f64 x #s(literal 17/40320 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64)) #s(literal 1/57600 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64)) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64)))) #s(literal 1/2641807540224000000000 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64))) (-.f64 #s(literal 1/191102976000000 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 4913/906139986296832000000 binary64)))) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64) #s(literal 1/57600 binary64)) (.f64 (.f64 x x) #s(literal 17/9676800 binary64)))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64)))) #s(literal 1/191102976000000 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64))) #s(literal 1/13824000 binary64)) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64) #s(literal 1/57600 binary64)) (.f64 (.f64 x x) #s(literal 17/9676800 binary64)))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64)))) #s(literal 1/191102976000000 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64)) (+.f64 #s(literal 1/3317760000 binary64) (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64)) #s(literal 1/57600 binary64)))) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64))) #s(literal 1/3317760000 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64) #s(literal 1/57600 binary64)) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64)) #s(literal 1/13824000 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64) #s(literal 1/57600 binary64)) (.f64 (.f64 x x) #s(literal 17/9676800 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64) #s(literal -1/57600 binary64)))) (neg.f64 (neg.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/57600 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64)))) (neg.f64 (-.f64 #s(literal 1/240 binary64) (.f64 x (.f64 x #s(literal 17/40320 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/57600 binary64) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64))) (fma.f64 (/.f64 #s(literal 1/57600 binary64) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64))) (/.f64 #s(literal 1/57600 binary64) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64))) (.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64))) (/.f64 #s(literal 1/57600 binary64) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64)))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64)) #s(literal 1/13824000 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64) #s(literal 1/57600 binary64)) (.f64 (*.f64 x x) #s(literal 17/9676800 binary64)))))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64)) #s(literal 1/13824000 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/57600 binary64) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64)) (.f64 (.f64 x x) #s(literal 17/9676800 binary64))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64) #s(literal -1/57600 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64)) #s(literal 1/13824000 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64) #s(literal 1/57600 binary64)) (.f64 (*.f64 x x) #s(literal 17/9676800 binary64))))))
(.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64) #s(literal -1/57600 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64)))))
(.f64 (-.f64 #s(literal 1/57600 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/1625702400 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/240 binary64) (.f64 x (*.f64 x #s(literal 17/40320 binary64))))))

eval115.0ms (1.2%)

Memory: 6.8MiB live, 236.9MiB allocated
Compiler: Compiled 25 121 to 1 993 computations (92.1% saved)

prune224.0ms (2.3%)

Memory

-9.0MiB live, 313.8MiB allocated

Pruning

12 alts after pruning (7 fresh and 5 done)

	Pruned	Kept	Total
New	836	6	842
Fresh	0	1	1
Picked	0	5	5
Done	0	0	0
Total	836	12	848

Accuracy

100.0%

Counts

848 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	8.2%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
✓	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
▶	53.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/2 binary64))))
▶	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
▶	53.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
▶	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
▶	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 17/40320 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) #s(literal 1/2 binary64))))
✓	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
	52.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))) #s(literal -1/576 binary64)) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
✓	53.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	53.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 313 to 169 computations (46% saved)

simplify95.0ms (1%)

Memory

6.1MiB live, 116.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 17/40320 binary64) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) #s(literal 1/2 binary64))
✓	cost-diff	0	(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 17/40320 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
✓	cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 17/40320 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) #s(literal 1/2 binary64))))
✓	cost-diff	640	(fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 17/40320 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))
✓	cost-diff	0	(*.f64 x #s(literal 1/240 binary64))
✓	cost-diff	0	(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
✓	cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
✓	cost-diff	320	(fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 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))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 x (.f64 x x))
✓	cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
✓	cost-diff	320	(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	0	(.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))
✓	cost-diff	0	(fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64))
✓	cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/2 binary64))))
✓	cost-diff	320	(fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/2 binary64)))

Rules

1 918×	`lower-fma.f32`
1 902×	`lower-fma.f64`
692×	`distribute-lft-in`
552×	`lower-+.f64`
552×	`lower-+.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	331
0	60	278
1	128	274
2	283	274
3	596	274
4	861	274
5	908	274
6	941	274
7	1015	274
8	1139	274
9	1347	274
10	1389	274
11	1392	274
12	1400	274
13	1406	274
14	1410	274
15	1417	274
16	1592	274
17	1829	274
18	1835	274
0	1835	274

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize471.0ms (4.9%)

Memory

-19.7MiB live, 356.7MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
✓	accuracy	99.9%	(*.f64 x #s(literal 1/240 binary64))
✓	accuracy	99.8%	(.f64 (.f64 x x) (*.f64 x x))
✓	accuracy	53.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 17/40320 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) #s(literal 1/2 binary64))))
✓	accuracy	99.9%	(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
✓	accuracy	99.9%	(*.f64 x #s(literal 1/240 binary64))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(/.f64 #s(literal 2 binary64) x)
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
✓	accuracy	53.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	99.9%	(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	53.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	99.8%	(.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))
✓	accuracy	99.5%	(*.f64 x #s(literal 17/40320 binary64))
✓	accuracy	53.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/2 binary64))))

Samples

273.0ms	41×	1	valid
69.0ms	74×	2	valid
50.0ms	125×	0	valid
15.0ms	16×	3	valid

Compiler

Compiled 276 to 39 computations (85.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 353.0ms

const: 263.0ms (74.5% of total)

ival-mult: 26.0ms (7.4% of total)

ival-cos: 24.0ms (6.8% of total)

adjust: 15.0ms (4.2% of total)

ival-add: 12.0ms (3.4% of total)

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

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

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

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

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

exact: 0.0ms (0% of total)

series14.0ms (0.1%)

Memory

25.1MiB live, 25.1MiB allocated

Counts

22 → 264

Calls

Call 1

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

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

Calls

66 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(+ (* (* x (* x x)) 1/24) (* x 1/2))
0.0ms	x	@	-inf	(* x (* x x))
0.0ms	x	@	0	(/ 2 x)
0.0ms	x	@	-inf	(+ (* (+ (* x (* x 1/240)) 1/24) (* x (* x x))) (* x 1/2))
0.0ms	x	@	inf	(+ (* (+ (* x (* x (+ (* x (* x 17/40320)) 1/240))) 1/24) (* x (* x x))) (* x 1/2))

simplify365.0ms (3.8%)

Memory

18.2MiB live, 487.4MiB allocated

Algorithm

1×	egg-herbie

Rules

15 008×	`lower-fma.f64`
15 008×	`lower-fma.f32`
4 780×	`lower-*.f64`
4 780×	`lower-*.f32`
2 508×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	95	1788
1	307	1788
2	810	1784
3	2085	1784
4	4668	1784
0	8691	1652

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

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

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

rewrite446.0ms (4.6%)

Memory

-30.6MiB live, 567.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

8 344×	`lower-fma.f32`
8 328×	`lower-fma.f64`
4 660×	`lower-*.f32`
4 644×	`lower-*.f64`
3 922×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	271
0	60	222
1	260	218
2	2023	218
0	8853	218

Stop Event

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

Counts

22 → 641

Calls

Call 1

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

Outputs
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(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)))
(*.f64 #s(literal -1/2 binary64) (neg.f64 x))
(*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)))
(exp.f64 (fma.f64 #s(literal 2 binary64) (log.f64 x) (log.f64 (*.f64 x x))))
(pow.f64 x #s(literal 4 binary64))
(pow.f64 (*.f64 x x) #s(literal 2 binary64))
(pow.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1 binary64))
(.f64 x (.f64 x (*.f64 x x)))
(.f64 (.f64 x x) (*.f64 x x))
(.f64 (.f64 x (*.f64 x x)) x)

eval224.0ms (2.3%)

Memory: 35.2MiB live, 310.5MiB allocated
Compiler: Compiled 43 392 to 1 813 computations (95.8% saved)

prune233.0ms (2.4%)

Memory

-18.2MiB live, 298.6MiB allocated

Pruning

12 alts after pruning (3 fresh and 9 done)

	Pruned	Kept	Total
New	1 162	2	1 164
Fresh	1	1	2
Picked	1	4	5
Done	0	5	5
Total	1 164	12	1 176

Accuracy

100.0%

Counts

1 176 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	8.2%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
✓	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	53.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/2 binary64))))
✓	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
✓	53.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
✓	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
✓	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
▶	52.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
▶	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	53.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	53.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 181 to 100 computations (44.8% saved)

simplify361.0ms (3.8%)

Memory

-14.4MiB live, 436.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	6464	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))
✓	cost-diff	0	(.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
✓	cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
✓	cost-diff	0	(fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
✓	cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	cost-diff	128	(+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal 1/24 binary64))

Rules

11 720×	`lower-fma.f32`
11 710×	`lower-fma.f64`
6 908×	`lower-+.f32`
6 906×	`lower-+.f64`
4 440×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	346
0	49	338
1	117	338
2	347	333
3	1297	323
4	3344	323
5	3650	323
6	3709	323
7	3764	323
8	3838	323
9	3972	323
0	8288	314

Stop Event

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

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
x
(fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x x)
(+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal 1/24 binary64))
(.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x))
(fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))
(*.f64 x #s(literal 17/40320 binary64))
#s(literal 17/40320 binary64)
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
x
(fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))
(*.f64 x x)
(/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64)))
(fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64))
(.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))
(.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))
(fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))
(*.f64 x #s(literal 17/40320 binary64))
#s(literal 17/40320 binary64)
#s(literal 1/240 binary64)
#s(literal -1/576 binary64)
(fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))
#s(literal -1/24 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 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
x
(fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x x)
(+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal 1/24 binary64))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))) #s(literal 1/24 binary64))
(.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x))
(.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))))
(fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))
(fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))
(*.f64 x #s(literal 17/40320 binary64))
#s(literal 17/40320 binary64)
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/576 binary64)) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
(.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/576 binary64)) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
x
(fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))
(fma.f64 (.f64 x x) (/.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/576 binary64)) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))
(*.f64 x x)
(/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64)))
(/.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/576 binary64)) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))) #s(literal -1/24 binary64)))
(fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/576 binary64))
(.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))
(.f64 (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))
(.f64 x (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)))
(fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))
(fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))
(*.f64 x #s(literal 17/40320 binary64))
#s(literal 17/40320 binary64)
#s(literal 1/240 binary64)
#s(literal -1/576 binary64)
(fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))) #s(literal -1/24 binary64))
#s(literal -1/24 binary64)
#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)

localize210.0ms (2.2%)

Memory

36.9MiB live, 337.8MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
✓	accuracy	99.8%	(.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))
✓	accuracy	99.5%	(*.f64 x #s(literal 17/40320 binary64))
✓	accuracy	66.6%	(/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64)))
✓	accuracy	53.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
✓	accuracy	99.9%	(fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))
✓	accuracy	99.8%	(.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x))
✓	accuracy	99.5%	(*.f64 x #s(literal 17/40320 binary64))
✓	accuracy	53.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))

Samples

61.0ms	74×	2	valid
45.0ms	125×	0	valid
28.0ms	41×	1	valid
14.0ms	16×	3	valid

Compiler

Compiled 319 to 34 computations (89.3% saved)

Precisions

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

ival-mult: 28.0ms (23.6% of total)

ival-cos: 26.0ms (21.9% of total)

const: 19.0ms (16% of total)

adjust: 13.0ms (11% of total)

ival-div: 12.0ms (10.1% of total)

ival-add: 10.0ms (8.4% of total)

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

ival-sub: 3.0ms (2.5% of total)

ival-pow: 3.0ms (2.5% of total)

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

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

exact: 0.0ms (0% of total)

series13.0ms (0.1%)

Memory

-16.9MiB live, 21.7MiB allocated

Counts

14 → 156

Calls

Call 1

Inputs
#s(alt (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) (patch (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #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 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.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 (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 17/40320 binary64)) (patch (.f64 x #s(literal 17/40320 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) (patch (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #<representation binary64>) () ())
#s(alt (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (patch (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) (patch (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (patch (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #<representation binary64>) () ())

Outputs
#s(alt 1/24 (taylor 0 x) (#s(alt (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) (patch (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #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 (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) (patch (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #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 (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) (patch (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #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 (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) (patch (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 17/40320 (pow x 4)) (taylor inf x) (#s(alt (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) (patch (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #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 (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) (patch (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #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 (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) (patch (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #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 (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) (patch (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 17/40320 (pow x 4)) (taylor -inf x) (#s(alt (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) (patch (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #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 (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) (patch (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #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 (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) (patch (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #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 (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) (patch (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #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 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #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 (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #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 (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #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 (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #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 (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #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 (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #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 (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #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 (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (* 1/57600 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (patch (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/57600 (* 17/4838400 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (patch (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/57600 (* (pow x 2) (+ 17/4838400 (* 289/1625702400 (pow x 2)))))) (taylor 0 x) (#s(alt (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (patch (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/57600 (* (pow x 2) (+ 17/4838400 (* 289/1625702400 (pow x 2)))))) (taylor 0 x) (#s(alt (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (patch (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 289/1625702400 (pow x 6)) (taylor inf x) (#s(alt (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (patch (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (+ 289/1625702400 (* 17/4838400 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (patch (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (+ 289/1625702400 (+ (/ 1/57600 (pow x 4)) (* 17/4838400 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (patch (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (+ 289/1625702400 (+ (/ 1/57600 (pow x 4)) (* 17/4838400 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (patch (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 289/1625702400 (pow x 6)) (taylor -inf x) (#s(alt (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (patch (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (+ 289/1625702400 (* 17/4838400 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (patch (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (+ 289/1625702400 (+ (/ 1/57600 (pow x 4)) (* 17/4838400 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (patch (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (+ 289/1625702400 (+ (/ 1/57600 (pow x 4)) (* 17/4838400 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (patch (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #<representation binary64>) () ())) ())

Calls

39 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(* x (+ (* (* x x) (/ (+ (* (* x x) (* (* x (+ (* x (* x 17/40320)) 1/240)) (* x (+ (* x (* x 17/40320)) 1/240)))) -1/576) (+ (* (+ (* x (* x 17/40320)) 1/240) (* x x)) -1/24))) 1/2))
0.0ms	x	@	0	(* x (+ (* (* x x) (/ (+ (* (* x x) (* (* x (+ (* x (* x 17/40320)) 1/240)) (* x (+ (* x (* x 17/40320)) 1/240)))) -1/576) (+ (* (+ (* x (* x 17/40320)) 1/240) (* x x)) -1/24))) 1/2))
0.0ms	x	@	inf	(/ (+ (* (* x x) (* (* x (+ (* x (* x 17/40320)) 1/240)) (* x (+ (* x (* x 17/40320)) 1/240)))) -1/576) (+ (* (+ (* x (* x 17/40320)) 1/240) (* x x)) -1/24))
0.0ms	x	@	0	(/ (+ (* (* x x) (* (* x (+ (* x (* x 17/40320)) 1/240)) (* x (+ (* x (* x 17/40320)) 1/240)))) -1/576) (+ (* (+ (* x (* x 17/40320)) 1/240) (* x x)) -1/24))
0.0ms	x	@	0	(* (* x (+ (* x (* x 17/40320)) 1/240)) (* x (+ (* x (* x 17/40320)) 1/240)))

simplify341.0ms (3.5%)

Memory

13.0MiB live, 386.6MiB allocated

Algorithm

1×	egg-herbie

Rules

10 320×	`lower-fma.f64`
10 320×	`lower-fma.f32`
3 952×	`lower-*.f64`
3 952×	`lower-*.f32`
1 952×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	93	1418
1	299	1418
2	777	1414
3	1964	1414
4	3889	1414
5	7235	1414
0	8121	1295

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

Calls

Call 1

Inputs
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)))))
(* 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 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))))))
(* 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 (cos 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)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin 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))))))))
(* 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 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)))))))
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)))))))
(* 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 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)))))))
(* 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 (cos 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)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin 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))))))))
(* 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 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)))))))
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)))))))
(* 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 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)))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 17/40320 x)
(* 17/40320 x)
(* 17/40320 x)
(* 17/40320 x)
(* 17/40320 x)
(* 17/40320 x)
(* 17/40320 x)
(* 17/40320 x)
(* 17/40320 x)
(* 17/40320 x)
(* 17/40320 x)
(* 17/40320 x)
(* 1/240 (pow x 2))
(* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))
(* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))
(* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))
(* 17/40320 (pow x 4))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* 17/40320 (pow x 4))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (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)))
(* 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)))))
(* 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)))))
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)))))
(* 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 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))))))
(* 1/57600 (pow x 2))
(* (pow x 2) (+ 1/57600 (* 17/4838400 (pow x 2))))
(* (pow x 2) (+ 1/57600 (* (pow x 2) (+ 17/4838400 (* 289/1625702400 (pow x 2))))))
(* (pow x 2) (+ 1/57600 (* (pow x 2) (+ 17/4838400 (* 289/1625702400 (pow x 2))))))
(* 289/1625702400 (pow x 6))
(* (pow x 6) (+ 289/1625702400 (* 17/4838400 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 289/1625702400 (+ (/ 1/57600 (pow x 4)) (* 17/4838400 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 289/1625702400 (+ (/ 1/57600 (pow x 4)) (* 17/4838400 (/ 1 (pow x 2))))))
(* 289/1625702400 (pow x 6))
(* (pow x 6) (+ 289/1625702400 (* 17/4838400 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 289/1625702400 (+ (/ 1/57600 (pow x 4)) (* 17/4838400 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 289/1625702400 (+ (/ 1/57600 (pow x 4)) (* 17/4838400 (/ 1 (pow x 2))))))

Outputs
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 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* 17/40320 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 17/40320 binary64))))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* 17/40320 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 17/40320 binary64))))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) #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 (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))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
(* 17/40320 (pow x 7))
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(.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 x x) #s(literal 289/1625702400 binary64))))
(* (pow x 6) (+ 289/1625702400 (* 17/4838400 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 x (*.f64 x #s(literal 289/1625702400 binary64)) #s(literal 17/4838400 binary64)))
(* (pow x 6) (+ 289/1625702400 (+ (/ 1/57600 (pow x 4)) (* 17/4838400 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 289/1625702400 binary64)) #s(literal 17/4838400 binary64)))) (/.f64 (.f64 #s(literal 1/57600 binary64) (.f64 x (*.f64 x x))) x))
(* (pow x 6) (+ 289/1625702400 (+ (/ 1/57600 (pow x 4)) (* 17/4838400 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 289/1625702400 binary64)) #s(literal 17/4838400 binary64)))) (/.f64 (.f64 #s(literal 1/57600 binary64) (.f64 x (*.f64 x x))) x))

rewrite379.0ms (3.9%)

Memory

-17.4MiB live, 582.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 218×	`lower-fma.f32`
7 210×	`lower-fma.f64`
4 250×	`lower-/.f32`
4 248×	`lower-/.f64`
4 016×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	280
0	49	177
1	227	177
2	1777	177
0	8443	169

Stop Event

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

Counts

14 → 638

Calls

Call 1

Inputs
(+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal 1/24 binary64))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
(fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))
(*.f64 x x)
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
(*.f64 x #s(literal 17/40320 binary64))
(.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x))
(fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))
(/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64)))
(.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)))) #s(literal -1 binary64)))
(+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal 1/24 binary64))
(+.f64 #s(literal 1/24 binary64) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)))
(+.f64 (/.f64 (.f64 x (.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal -1/24 binary64)))))
(-.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal -1/24 binary64))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1/24 binary64) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x))))
(-.f64 (/.f64 (.f64 x (.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal -1/24 binary64))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x))) #s(literal 1/576 binary64))) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) (/.f64 (/.f64 #s(literal 1/331776 binary64) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x))) #s(literal 1/576 binary64))) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal -1/24 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/24 binary64) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)))) (-.f64 #s(literal -1/24 binary64) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x))))
(-.f64 (/.f64 (.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64)) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x))) #s(literal 1/576 binary64)))) (/.f64 #s(literal 1/331776 binary64) (.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64)) (fma.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x))) #s(literal 1/576 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) (.f64 x (.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))) (fma.f64 x (.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (+.f64 #s(literal 1/576 binary64) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))) (/.f64 #s(literal -1/13824 binary64) (fma.f64 x (.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (+.f64 #s(literal 1/576 binary64) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 (*.f64 x x) #s(literal -1/24 binary64)))))))
(-.f64 (/.f64 #s(literal 1/576 binary64) (-.f64 #s(literal 1/24 binary64) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)))) (/.f64 (.f64 x (.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (-.f64 #s(literal 1/24 binary64) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)))))
(fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64))
(fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(fma.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) x #s(literal 1/24 binary64))
(fma.f64 (.f64 x (.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal -1/24 binary64)))))
(fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64)) #s(literal 1/13824000 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 289/1625702400 binary64)) #s(literal 1/57600 binary64)) (.f64 (.f64 x x) #s(literal 17/9676800 binary64)))) #s(literal 1/24 binary64))
(fma.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 289/1625702400 binary64)) #s(literal -1/57600 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64))) #s(literal 1/24 binary64))
(fma.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/65548320768000 binary64)) #s(literal 1/13824000 binary64)) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 289/1625702400 binary64)) #s(literal 1/57600 binary64)) (.f64 (.f64 x x) #s(literal 17/9676800 binary64)))) #s(literal 1/24 binary64))
(fma.f64 (.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 289/1625702400 binary64)) #s(literal -1/57600 binary64)) (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal -1/240 binary64))) #s(literal 1/24 binary64))
(fma.f64 (/.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) (fma.f64 x (.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal -1/576 binary64))) (/.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (neg.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64)))))
(fma.f64 (/.f64 x (fma.f64 x (.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal -1/576 binary64))) (/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (neg.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64)))))
(fma.f64 (/.f64 x (fma.f64 x (.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal -1/576 binary64))) (/.f64 (.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (neg.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64)))))
(fma.f64 (/.f64 x (fma.f64 x (.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal -1/576 binary64))) (/.f64 (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)))) (neg.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64)))))
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eval189.0ms (2%)

Memory: 18.1MiB live, 165.8MiB allocated
Compiler: Compiled 58 075 to 2 520 computations (95.7% saved)

prune178.0ms (1.9%)

Memory

2.2MiB live, 202.5MiB allocated

Pruning

13 alts after pruning (4 fresh and 9 done)

	Pruned	Kept	Total
New	1 056	4	1 060
Fresh	0	0	0
Picked	2	1	3
Done	1	8	9
Total	1 059	13	1 072

Accuracy

100.0%

Counts

1 072 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	53.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/2 binary64))))
✓	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
✓	53.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
✓	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
	52.9%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x #s(approx (+ ( x (* x 17/40320)) 1/240) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
	52.8%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) #s(approx ( (* x (+ (* x (* x 17/40320)) 1/240)) (* x (+ (* x (* x 17/40320)) 1/240))) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 289/1625702400 binary64)) #s(literal 17/4838400 binary64))) #s(literal 1/57600 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
	52.9%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) #s(approx ( (* x (+ (* x (* x 17/40320)) 1/240)) (* x (+ (* x (* x 17/40320)) 1/240))) (.f64 (.f64 x x) #s(literal 1/57600 binary64))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
✓	53.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	53.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	53.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
	8.2%	#s(literal 1 binary64)

Compiler

Compiled 595 to 214 computations (64% saved)

regimes18.0ms (0.2%)

Memory

-32.1MiB live, 22.1MiB allocated

Counts

19 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.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 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 17/40320 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) #s(approx ( (* x (+ (* x (* x 17/40320)) 1/240)) (* x (+ (* x (* x 17/40320)) 1/240))) (.f64 (.f64 x x) #s(literal 1/57600 binary64))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x #s(approx (+ ( x (* x 17/40320)) 1/240) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) #s(approx ( (* x (+ (* x (* x 17/40320)) 1/240)) (* x (+ (* x (* x 17/40320)) 1/240))) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 289/1625702400 binary64)) #s(literal 17/4838400 binary64))) #s(literal 1/57600 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))) #s(literal -1/576 binary64)) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

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

Calls

2 calls:

11.0ms	x
5.0ms	(/.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 10 to 7 computations (30% saved)

regimes11.0ms (0.1%)

Memory

7.2MiB live, 7.2MiB allocated

Counts

17 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.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 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 17/40320 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) #s(approx ( (* x (+ (* x (* x 17/40320)) 1/240)) (* x (+ (* x (* x 17/40320)) 1/240))) (.f64 (.f64 x x) #s(literal 1/57600 binary64))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x #s(approx (+ ( x (* x 17/40320)) 1/240) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) #s(approx ( (* x (+ (* x (* x 17/40320)) 1/240)) (* x (+ (* x (* x 17/40320)) 1/240))) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 289/1625702400 binary64)) #s(literal 17/4838400 binary64))) #s(literal 1/57600 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))) #s(literal -1/576 binary64)) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))

Outputs

#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x (fma.f64 (*.f64 x x) (/.f64 (fma.f64 (*.f64 x x) (*.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (*.f64 x #s(approx (+ (* x (* x 17/40320)) 1/240) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))

#s(literal 1 binary64)

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
57.6%	2	`x`
57.4%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes5.0ms (0.1%)

Memory

4.3MiB live, 4.3MiB allocated

Counts

12 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.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 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 17/40320 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) #s(approx ( (* x (+ (* x (* x 17/40320)) 1/240)) (* x (+ (* x (* x 17/40320)) 1/240))) (.f64 (.f64 x x) #s(literal 1/57600 binary64))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))

Outputs

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

#s(literal 1 binary64)

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
57.6%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Memory

8.3MiB live, 8.3MiB allocated

Counts

9 → 2

Calls

Call 1

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

Outputs

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

#s(literal 1 binary64)

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
57.6%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Memory

8.7MiB live, 8.7MiB allocated

Counts

8 → 2

Calls

Call 1

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

Outputs

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

#s(literal 1 binary64)

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
57.6%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Memory

8.4MiB live, 8.4MiB allocated

Counts

7 → 2

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
57.5%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0.1%)

Memory

-27.7MiB live, 11.8MiB allocated

Counts

5 → 2

Calls

Call 1

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

Calls

2 calls:

3.0ms	x
2.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Results

Accuracy	Segments	Branch
57.1%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
57.3%	2	`x`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes2.0ms (0%)

Memory

5.2MiB live, 5.2MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

#s(literal 1 binary64)

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

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
57.3%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Memory

8.9MiB live, 8.9MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
56.9%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
57.0%	2	`x`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes3.0ms (0%)

Memory

7.8MiB live, 7.8MiB 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	x
1.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Results

Accuracy	Segments	Branch
8.2%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
8.2%	1	`x`

Compiler

Compiled 10 to 7 computations (30% saved)

bsearch17.0ms (0.2%)

Memory

-6.5MiB live, 32.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	2.4319872440987833	45.688399963628214

Samples

11.0ms

112×

valid

Compiler

Compiled 312 to 157 computations (49.7% saved)

Precisions

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

ival-cos: 4.0ms (43.4% of total)

ival-sin: 4.0ms (43.4% of total)

ival-sub: 1.0ms (10.9% of total)

ival-div: 1.0ms (10.9% 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

2.6MiB live, 2.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	2.4319872440987833	45.688399963628214

Compiler

Compiled 193 to 129 computations (33.2% saved)

bsearch1.0ms (0%)

Memory

2.4MiB live, 2.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	2.4319872440987833	45.688399963628214

Compiler

Compiled 186 to 122 computations (34.4% saved)

bsearch1.0ms (0%)

Memory

2.3MiB live, 2.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	2.4319872440987833	45.688399963628214

Compiler

Compiled 179 to 115 computations (35.8% saved)

bsearch1.0ms (0%)

Memory

2.2MiB live, 2.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	2.4319872440987833	45.688399963628214

Compiler

Compiled 144 to 101 computations (29.9% 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	2.4319872440987833	45.688399963628214

Compiler

Compiled 123 to 87 computations (29.3% saved)

bsearch1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	2.4319872440987833	45.688399963628214

Compiler

Compiled 109 to 80 computations (26.6% saved)

bsearch3.0ms (0%)

Memory

-35.3MiB live, 2.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
3.0ms	2.4319872440987833	45.688399963628214

Compiler

Compiled 74 to 59 computations (20.3% saved)

simplify7.0ms (0.1%)

Memory

20.0MiB live, 20.0MiB allocated

Algorithm

1×	egg-herbie

Rules

28×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	244
1	84	244

Stop Event

1×

saturated

Calls

Call 1

Inputs
(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 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x #s(approx (+ ( x (* x 17/40320)) 1/240) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64)) (.f64 x (.f64 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 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal 1/24 binary64)) #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 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #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 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.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 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #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 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))
#s(literal 1 binary64)

Outputs
(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 x (fma.f64 (.f64 x x) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x #s(approx (+ ( x (* x 17/40320)) 1/240) #s(literal 1/240 binary64)))) #s(literal -1/576 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64)) (.f64 x (.f64 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 x (fma.f64 (.f64 x x) (+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) (*.f64 x x)) #s(literal 1/24 binary64)) #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 x (fma.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) #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 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #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 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.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 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #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 #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)

soundness1.2s (12.9%)

Memory

34.4MiB live, 858.7MiB allocated

Rules

19 148×	`lower-fma.f64`
19 148×	`lower-fma.f32`
10 320×	`lower-fma.f64`
10 320×	`lower-fma.f32`
8 344×	`lower-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	280
0	49	177
1	227	177
2	1777	177
0	8443	169
0	79	286
1	224	286
2	555	280
3	1656	280
4	3000	280
5	4243	280
6	4592	280
7	5323	280
8	6815	280
0	8390	256
0	6	15
0	10	12
1	39	12
2	245	12
3	2355	11
0	8885	11
0	34	271
0	60	222
1	260	218
2	2023	218
0	8853	218
0	93	1418
1	299	1418
2	777	1414
3	1964	1414
4	3889	1414
5	7235	1414
0	8121	1295
0	30	191
0	52	179
1	217	179
2	1560	179
0	8169	179

Stop Event

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

Compiler

Compiled 507 to 241 computations (52.5% saved)

preprocess69.0ms (0.7%)

Memory: -5.6MiB live, 109.9MiB allocated
Remove: (negabs x)
Compiler: Compiled 400 to 124 computations (69% 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	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

analyze113.0ms (1.2%)

sample1.9s (19.9%)

preprocess66.0ms (0.7%)

explain195.0ms (2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify29.0ms (0.3%)

localize55.0ms (0.6%)

series3.0ms (0%)

simplify456.0ms (4.7%)

rewrite302.0ms (3.1%)

eval100.0ms (1%)

prune96.0ms (1%)

simplify84.0ms (0.9%)

localize207.0ms (2.2%)

series18.0ms (0.2%)

simplify379.0ms (3.9%)

rewrite344.0ms (3.6%)

eval115.0ms (1.2%)

prune224.0ms (2.3%)

simplify95.0ms (1%)

localize471.0ms (4.9%)

series14.0ms (0.1%)

simplify365.0ms (3.8%)

rewrite446.0ms (4.6%)

eval224.0ms (2.3%)

prune233.0ms (2.4%)

simplify361.0ms (3.8%)

localize210.0ms (2.2%)

series13.0ms (0.1%)

simplify341.0ms (3.5%)

rewrite379.0ms (3.9%)

eval189.0ms (2%)

prune178.0ms (1.9%)

regimes18.0ms (0.2%)

regimes11.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0%)

regimes4.0ms (0%)

regimes3.0ms (0%)

regimes5.0ms (0.1%)

regimes2.0ms (0%)

regimes3.0ms (0%)

regimes3.0ms (0%)

bsearch17.0ms (0.2%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch3.0ms (0%)

simplify7.0ms (0.1%)

soundness1.2s (12.9%)

preprocess69.0ms (0.7%)

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