Metrics for tanhf (example 3.4)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze122.0ms (1.7%)

Memory

0.2MiB live, 142.6MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample1.9s (26.4%)

Memory

68.4MiB live, 1 660.7MiB allocated

Samples

782.0ms	2 315×	2	valid
465.0ms	4 134×	0	valid
215.0ms	564×	3	valid
126.0ms	1 240×	1	valid
3.0ms	3×	4	valid

Precisions

Click to see histograms. Total time spent on operations: 1.4s

ival-cos: 809.0ms (58% of total)

ival-sin: 197.0ms (14.1% of total)

adjust: 167.0ms (12% of total)

ival-div: 126.0ms (9% of total)

ival-sub: 83.0ms (5.9% of total)

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

exact: 4.0ms (0.3% of total)

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

Bogosity

explain161.0ms (2.3%)

Memory

-11.3MiB live, 147.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
67	0	-	3	(6.430988246087809e-158)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
61	1	(-1.643300117467892e+76)	2	(-9.766544499061171e+99)	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(cos.f64 x)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`	u/n	64	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	64
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	60	6

Confusion

	Predicted +	Predicted -
+	123	1
-	1	131

Precision

0.9919354838709677

Recall

0.9919354838709677

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	123	1	0
-	1	5	126

Precision?

0.9538461538461539

Recall?

1.0

Freqs

test

number	freq
0	132
1	124

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

38.0ms	134×	2	valid
34.0ms	276×	0	valid
33.0ms	28×	3	valid
8.0ms	72×	1	valid
2.0ms	2×	4	valid

Compiler

Compiled 46 to 22 computations (52.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 99.0ms

ival-cos: 69.0ms (69.9% of total)

ival-sin: 12.0ms (12.1% of total)

adjust: 6.0ms (6.1% of total)

ival-div: 6.0ms (6.1% of total)

ival-sub: 5.0ms (5.1% of total)

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

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

exact: 0.0ms (0% of total)

preprocess44.0ms (0.6%)

Memory

22.9MiB live, 22.9MiB 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)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB 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
▶	55.8%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify28.0ms (0.4%)

Memory

-24.0MiB live, 13.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

localize117.0ms (1.7%)

Memory

-9.5MiB live, 49.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(sin.f64 x)
accuracy	0	(cos.f64 x)
accuracy	12.891534963109264	(-.f64 #s(literal 1 binary64) (cos.f64 x))
accuracy	15.255575525459218	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Samples

69.0ms	14×	3	valid
19.0ms	67×	2	valid
15.0ms	138×	0	valid
4.0ms	36×	1	valid
2.0ms	1×	4	valid

Compiler

Compiled 19 to 8 computations (57.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 100.0ms

ival-cos: 85.0ms (84.8% of total)

ival-sin: 5.0ms (5% of total)

adjust: 4.0ms (4% of total)

ival-div: 3.0ms (3% of total)

ival-sub: 2.0ms (2% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0%)

Memory

3.9MiB live, 3.9MiB 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	(/ (- 1 (cos x)) (sin x))
0.0ms	x	@	0	(cos x)
0.0ms	x	@	0	(- 1 (cos x))

simplify307.0ms (4.3%)

Memory

-6.1MiB live, 344.2MiB 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)

rewrite314.0ms (4.4%)

Memory

-2.7MiB live, 315.5MiB allocated

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

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

Counts

4 → 615

Calls

Call 1

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

Outputs
(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))))
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eval88.0ms (1.2%)

Memory: 6.0MiB live, 162.4MiB allocated
Compiler: Compiled 14 450 to 1 633 computations (88.7% saved)

prune149.0ms (2.1%)

Memory

36.1MiB live, 194.7MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	657	5	662
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	658	5	663

Accuracy

100.0%

Counts

663 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.7%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
▶	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
▶	47.6%	#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))))
▶	47.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
▶	47.9%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 78 to 52 computations (33.3% saved)

simplify41.0ms (0.6%)

Memory

-12.7MiB live, 65.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

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

Rules

580×	`lower-fma.f32`
574×	`lower-fma.f64`
284×	`lower-*.f32`
270×	`lower-*.f64`
256×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	127
0	40	116
1	81	116
2	148	116
3	234	116
4	266	116
5	293	116
6	326	116
7	400	116
8	522	116
9	731	116
10	773	116
11	776	116
12	784	116
13	789	116
14	793	116
15	800	116
16	880	116
17	967	116
18	971	116
0	971	116

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

localize166.0ms (2.3%)

Memory

9.1MiB live, 161.0MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
accuracy	0.05078125	(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	0.0703125	(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
accuracy	0.078125	(*.f64 x #s(literal 1/240 binary64))
accuracy	33.55703534378688	#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	0.03515625	(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
accuracy	0.046875	(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
accuracy	0.3046875	(*.f64 x #s(literal 1/24 binary64))
accuracy	33.532980232292616	#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	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	33.37533156142736	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
accuracy	0	(*.f64 x #s(literal 1/2 binary64))
accuracy	0.00390625	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))

Samples

54.0ms	139×	0	valid
48.0ms	67×	2	valid
12.0ms	35×	1	valid
9.0ms	14×	3	valid
2.0ms	1×	4	valid

Compiler

Compiled 109 to 27 computations (75.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 102.0ms

const: 25.0ms (24.5% of total)

ival-mult: 23.0ms (22.5% of total)

ival-cos: 20.0ms (19.6% of total)

adjust: 10.0ms (9.8% of total)

ival-tan: 6.0ms (5.9% of total)

ival-sin: 5.0ms (4.9% of total)

ival-add: 5.0ms (4.9% of total)

ival-div: 3.0ms (2.9% of total)

ival-sub: 2.0ms (2% of total)

ival-pow: 2.0ms (2% of total)

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

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

exact: 0.0ms (0% of total)

series13.0ms (0.2%)

Memory

15.9MiB live, 15.9MiB allocated

Counts

15 → 168

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 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (patch (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 1/240 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>) () ())

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

Calls

42 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	(* x (+ (* (* x x) (+ (* x (* x 1/240)) 1/24)) 1/2))

simplify239.0ms (3.4%)

Memory

-13.3MiB live, 269.9MiB allocated

Algorithm

1×	egg-herbie

Rules

14 916×	`lower-fma.f64`
14 916×	`lower-fma.f32`
3 880×	`lower-*.f64`
3 880×	`lower-*.f32`
2 216×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	1034
1	192	1034
2	479	1034
3	1125	1034
4	2283	1034
5	5525	1034
0	8283	953

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

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)
(* 1/240 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)))))

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)))
(/ (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 (.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 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 (.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 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 (.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 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 (.f64 x 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 (.f64 x 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
#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 (* 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))
(* 1/240 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/240 binary64)))
(* (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 (.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 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (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))
(* 1/240 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/240 binary64)))
(* (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 (.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 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (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))
(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)
(* 1/240 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 (.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))

rewrite290.0ms (4.1%)

Memory

14.8MiB live, 331.0MiB allocated

Rules

8 674×	`lower-fma.f32`
8 668×	`lower-fma.f64`
5 812×	`lower-*.f32`
5 798×	`lower-*.f64`
3 982×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	114
0	40	103
1	148	103
2	917	103
0	8416	103

Stop Event

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

Counts

15 → 571

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)
(pow.f64 #s(literal 1 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))

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)) (/.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 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x))) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(-.f64 #s(literal 0 binary64) (neg.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(-.f64 (/.f64 (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 (/.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))) (neg.f64 (tan.f64 (*.f64 x #s(literal 1/2 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 (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 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (sin.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 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (sin.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 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64))))) (/.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #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) (/.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 (cos.f64 x) (/.f64 #s(literal -1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (sin.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)) (neg.f64 (cos.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) (/.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 (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))))
(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) (tan.f64 x)) #s(literal 1 binary64)))
(neg.f64 (neg.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(neg.f64 (.f64 #s(literal 1 binary64) (neg.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))))))
(neg.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (neg.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))))
(neg.f64 (/.f64 (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (cos.f64 (.f64 x #s(literal 1/2 binary64)))))
(/.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 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 (sin.f64 x) (.f64 (sin.f64 x) (cos.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (sin.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.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) (tan.f64 x)) (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x))))) (-.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (tan.f64 (.f64 x #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (sin.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.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)))) (sin.f64 x))))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))
(/.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (*.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (sin.f64 x)))
(/.f64 (-.f64 #s(literal 1 binary64) (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) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (*.f64 (neg.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (neg.f64 (sin.f64 x))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.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 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (+.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (neg.f64 (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))) (neg.f64 (sin.f64 x))))
(/.f64 (-.f64 (sin.f64 x) (.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 (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (neg.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 (neg.f64 (sin.f64 x)) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (*.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (*.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (sin.f64 x))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (neg.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))))
(/.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (/.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 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x))))))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (sin.f64 x)) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))
(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (tan.f64 x)) (sin.f64 x)) (.f64 (sin.f64 x) (tan.f64 x)))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 x))) (.f64 (sin.f64 x) (neg.f64 (cos.f64 x)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
(/.f64 (-.f64 (.f64 #s(literal -1 binary64) (tan.f64 x)) (.f64 (neg.f64 (sin.f64 x)) #s(literal 1 binary64))) (*.f64 (neg.f64 (sin.f64 x)) (tan.f64 x)))
(/.f64 (-.f64 (neg.f64 (sin.f64 x)) (.f64 (neg.f64 (sin.f64 x)) (cos.f64 x))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
(/.f64 (-.f64 (sin.f64 x) (.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 x)))) (.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 x))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) (.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (sin.f64 x))))
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(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64) #s(literal -1/191102976 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64)))) (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/3317760000 binary64) (+.f64 #s(literal 1/331776 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/33177600 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/3317760000 binary64) #s(literal -1/331776 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64)))) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) #s(literal 1/576 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal 1/13824 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 (*.f64 x x) #s(literal 1/5760 binary64))))))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal 1/13824 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/57600 binary64)) #s(literal 1/5760 binary64))))))
(.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) #s(literal -1/576 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal 1/13824 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 (*.f64 x x) #s(literal 1/5760 binary64)))))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) #s(literal -1/576 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/24 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/5760 binary64))))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal 1/13824 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (fma.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/57600 binary64) #s(literal -1/576 binary64)))
(.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/240 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) #s(literal -1/576 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) #s(literal -1/576 binary64))) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal 1/13824 binary64)) (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64) (.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/5760 binary64))) (.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/5760 binary64))) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/5760 binary64))))))) (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/3317760000 binary64) (.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/5760 binary64))) (-.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/5760 binary64))) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/57600 binary64))))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal 1/13824 binary64)) (.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/5760 binary64)))) (+.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) #s(literal -1/576 binary64)) (.f64 (.f64 x x) #s(literal 1/5760 binary64))))) (+.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) #s(literal -1/576 binary64)) (.f64 (.f64 x x) #s(literal 1/5760 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) #s(literal -1/576 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal -1/13824 binary64))) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/5760 binary64)))))

eval354.0ms (5%)

Memory: -24.0MiB live, 195.6MiB allocated
Compiler: Compiled 20 967 to 1 627 computations (92.2% saved)

prune107.0ms (1.5%)

Memory

-3.9MiB live, 160.2MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	737	2	739
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	738	6	744

Accuracy

100.0%

Counts

744 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	71.3%	(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)))
✓	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	47.6%	#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))))
✓	47.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	47.9%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
▶	7.7%	#s(literal 1 binary64)

Compiler

Compiled 55 to 33 computations (40% saved)

simplify5.0ms (0.1%)

Memory

3.4MiB live, 3.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
cost-diff	0	(/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
cost-diff	0	(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))
cost-diff	21376	(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)))

Rules

24×	`lower-*.f32`
20×	`lower-*.f64`
20×	`lower-/.f32`
18×	`lower-/.f64`
10×	`*-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	43
0	14	38
1	21	38
2	22	30
3	24	30
4	31	30
5	39	30
6	46	30
7	49	30
0	49	30

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(literal 1 binary64)
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(literal -1/2 binary64)

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

localize41.0ms (0.6%)

Memory

-41.3MiB live, 43.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
accuracy	0.0703125	(/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
accuracy	0.09375	(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))
accuracy	0.3515625	(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)))

Samples

21.0ms	183×	0	valid
7.0ms	72×	0	invalid
1.0ms	1×	3	valid

Compiler

Compiled 45 to 11 computations (75.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-mult: 9.0ms (42% of total)

ival-tan: 6.0ms (28% of total)

ival-pow: 5.0ms (23.3% of total)

ival-div: 2.0ms (9.3% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

10.5MiB live, 10.5MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#s(alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (tan.f64 (.f64 x #s(literal 1/2 binary64))) (patch (tan.f64 (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())

Outputs
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 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 (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 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 (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor inf x) (#s(alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor inf x) (#s(alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor inf x) (#s(alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor inf x) (#s(alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor -inf x) (#s(alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor -inf x) (#s(alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor -inf x) (#s(alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor -inf x) (#s(alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 1/2)) (taylor 0 x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/48 (* (sqrt (pow x 5)) (/ 1 (sqrt 1/2)))) (* (sqrt x) (sqrt 1/2))) (taylor 0 x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 3) (+ (* 1/480 (* (sqrt (pow x 3)) (/ 1 (sqrt 1/2)))) (* 1/48 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2))))))) (taylor 0 x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 3) (+ (* 1/48 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))) (* (pow x 2) (+ (* -1/4608 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/480 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2))))))))) (taylor 0 x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor inf x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor inf x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor inf x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor inf x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* -1/6 (pow x 2))) x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* (pow x 2) (- (* -1/360 (pow x 2)) 1/6))) x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/15120 (pow x 2)) 1/360)) 1/6))) x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (cos (* 1/2 x)) (sin (* 1/2 x))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (cos (* 1/2 x)) (sin (* 1/2 x))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (cos (* 1/2 x)) (sin (* 1/2 x))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (cos (* 1/2 x)) (sin (* 1/2 x))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (cos (* 1/2 x)) (sin (* 1/2 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (cos (* 1/2 x)) (sin (* 1/2 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (cos (* 1/2 x)) (sin (* 1/2 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (cos (* 1/2 x)) (sin (* 1/2 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#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>) () ())) ())

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(pow (/ 1 (tan (* x 1/2))) -1/2)
1.0ms	x	@	0	(pow (/ 1 (tan (* x 1/2))) -1/2)
1.0ms	x	@	inf	(pow (/ 1 (tan (* x 1/2))) -1/2)
0.0ms	x	@	-inf	(/ 1 (tan (* x 1/2)))
0.0ms	x	@	inf	(/ 1 (tan (* x 1/2)))

simplify342.0ms (4.8%)

Memory

46.5MiB live, 423.1MiB allocated

Algorithm

1×	egg-herbie

Rules

21 674×	`lower-fma.f64`
21 674×	`lower-fma.f32`
5 364×	`lower-*.f64`
5 364×	`lower-*.f32`
3 522×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	546
1	205	533
2	609	526
3	1791	519
4	3701	516
5	6121	511
6	7334	511
0	8097	488

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

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)))
(* (sqrt x) (sqrt 1/2))
(+ (* 1/48 (* (sqrt (pow x 5)) (/ 1 (sqrt 1/2)))) (* (sqrt x) (sqrt 1/2)))
(+ (* (sqrt x) (sqrt 1/2)) (* (pow x 3) (+ (* 1/480 (* (sqrt (pow x 3)) (/ 1 (sqrt 1/2)))) (* 1/48 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))))))
(+ (* (sqrt x) (sqrt 1/2)) (* (pow x 3) (+ (* 1/48 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))) (* (pow x 2) (+ (* -1/4608 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/480 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))))))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(/ 2 x)
(/ (+ 2 (* -1/6 (pow x 2))) x)
(/ (+ 2 (* (pow x 2) (- (* -1/360 (pow x 2)) 1/6))) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/15120 (pow x 2)) 1/360)) 1/6))) 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)) (sin (* 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))))))))
(/ (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)))

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 (.f64 x 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)))
(* (sqrt x) (sqrt 1/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* 1/48 (* (sqrt (pow x 5)) (/ 1 (sqrt 1/2)))) (* (sqrt x) (sqrt 1/2)))
(fma.f64 #s(literal 1/48 binary64) (/.f64 (sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x x))))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* (sqrt x) (sqrt 1/2)) (* (pow x 3) (+ (* 1/480 (* (sqrt (pow x 3)) (/ 1 (sqrt 1/2)))) (* 1/48 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))))))
(fma.f64 (fma.f64 #s(literal 1/48 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/480 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (/.f64 (.f64 x (.f64 x x)) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* (sqrt x) (sqrt 1/2)) (* (pow x 3) (+ (* 1/48 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))) (* (pow x 2) (+ (* -1/4608 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/480 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))))))))
(fma.f64 (.f64 x (.f64 x x)) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 (.f64 x x) #s(literal 19/11520 binary64) #s(literal 1/48 binary64))) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* -1/6 (pow x 2))) x)
(/.f64 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (- (* -1/360 (pow x 2)) 1/6))) x)
(/.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/360 binary64)) #s(literal -1/6 binary64)) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/15120 (pow x 2)) 1/360)) 1/6))) x)
(/.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/15120 binary64)) #s(literal -1/360 binary64))) #s(literal -1/6 binary64)) #s(literal 2 binary64)) x)
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.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 (.f64 x 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)))
(/ (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)))

rewrite63.0ms (0.9%)

Memory

-10.5MiB live, 42.1MiB allocated

Rules

628×	`lower-*.f32`
624×	`lower-*.f64`
370×	`lower-/.f32`
368×	`lower-/.f64`
218×	`lower-pow.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	35
0	14	30
1	42	20
2	175	19
0	1253	19

Stop Event

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

Counts

4 → 173

Calls

Call 1

Inputs
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))

Outputs
(exp.f64 (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(exp.f64 (.f64 (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(neg.f64 (neg.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (neg.f64 (neg.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(/.f64 (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (neg.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 (.f64 #s(literal 1 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (cos.f64 (*.f64 x #s(literal 1/2 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))))) (neg.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 (*.f64 x #s(literal 1/2 binary64))))
(/.f64 (.f64 (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (neg.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))))) (neg.f64 (neg.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))))))
(/.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64))) (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64))))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) #s(literal 4 binary64))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -2 binary64)) (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -2 binary64))) #s(literal -1/4 binary64))
(.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64))))
(.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(.f64 (sqrt.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (sqrt.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(.f64 (sqrt.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 x #s(literal 1/2 binary64)))))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(.f64 #s(literal -1 binary64) (neg.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))))
(.f64 #s(literal -1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64)))
(.f64 (neg.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)))
(.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) (.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)) #s(literal 1 binary64)))
(.f64 (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (*.f64 x #s(literal 1/2 binary64))))
(.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/8 binary64)) (.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/8 binary64)) (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64))))
(.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)) (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)) (/.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 x #s(literal 1/2 binary64)))))
(.f64 (.f64 #s(literal 1 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 1/2 binary64)))))
(.f64 (.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)) #s(literal 1 binary64)) (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)) (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/8 binary64))) (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1/8 binary64)))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))))))
(exp.f64 (.f64 (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal -2 binary64) (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal -1/4 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal 1 binary64)))
(exp.f64 (.f64 (neg.f64 (.f64 (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (neg.f64 (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))))) #s(literal -1/4 binary64) (neg.f64 (.f64 (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/4 binary64)))))
(sqrt.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
(pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -2 binary64)) #s(literal -1/4 binary64))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (neg.f64 (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))))
(.f64 #s(literal 1 binary64) (sqrt.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))))
(.f64 (sqrt.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(.f64 (sqrt.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/8 binary64)) (.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/8 binary64)) (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64))))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/8 binary64))) (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1/8 binary64)))
(exp.f64 (neg.f64 (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(/.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64)))) (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 1/2 binary64)))))
(/.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) (exp.f64 (log.f64 (neg.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64))) (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64))) (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)))
(pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sin.f64 (*.f64 x #s(literal 1/2 binary64)))))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (cos.f64 (*.f64 x #s(literal 1/2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (neg.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))))) (neg.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64)))))
(exp.f64 (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(exp.f64 (.f64 (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(neg.f64 (neg.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (neg.f64 (neg.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(/.f64 (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (neg.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 (.f64 #s(literal 1 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (cos.f64 (*.f64 x #s(literal 1/2 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))))) (neg.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 (*.f64 x #s(literal 1/2 binary64))))
(/.f64 (.f64 (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (neg.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))))) (neg.f64 (neg.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))))))
(/.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64))) (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64))))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) #s(literal 4 binary64))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -2 binary64)) (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -2 binary64))) #s(literal -1/4 binary64))
(.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64))))
(.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(.f64 (sqrt.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (sqrt.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(.f64 (sqrt.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 x #s(literal 1/2 binary64)))))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(.f64 #s(literal -1 binary64) (neg.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))))
(.f64 #s(literal -1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64)))
(.f64 (neg.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)))
(.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) (.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)) #s(literal 1 binary64)))
(.f64 (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (*.f64 x #s(literal 1/2 binary64))))
(.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/8 binary64)) (.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/8 binary64)) (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64))))
(.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)) (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)) (/.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 x #s(literal 1/2 binary64)))))
(.f64 (.f64 #s(literal 1 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 1/2 binary64)))))
(.f64 (.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)) #s(literal 1 binary64)) (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64)) (pow.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/8 binary64))) (pow.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1/8 binary64)))

eval52.0ms (0.7%)

Memory: 9.5MiB live, 80.2MiB allocated
Compiler: Compiled 7 633 to 689 computations (91% saved)

prune68.0ms (1%)

Memory

-14.1MiB live, 130.3MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	373	1	374
Fresh	0	0	0
Picked	1	1	2
Done	0	4	4
Total	374	6	380

Accuracy

100.0%

Counts

380 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	47.6%	(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))))
✓	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	47.6%	#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))))
✓	47.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	47.9%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
✓	7.7%	#s(literal 1 binary64)

Compiler

Compiled 53 to 36 computations (32.1% saved)

simplify4.0ms (0.1%)

Memory

8.6MiB live, 8.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
cost-diff	0	(/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
cost-diff	0	(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))
cost-diff	0	(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))))

Rules

12×	`lower-*.f32`
6×	`*-commutative`
6×	`lower-*.f64`
6×	`lift-*.f64`
4×	`lift-sqrt.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	71
0	25	71
1	30	71
0	30	71

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(literal -1/2 binary64)
#s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 x)
(sqrt.f64 #s(literal 1/2 binary64))

Outputs
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(literal -1/2 binary64)
#s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 x)
(sqrt.f64 #s(literal 1/2 binary64))

localize57.0ms (0.8%)

Memory

-1.5MiB live, 80.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.09375	(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))
accuracy	0.3125	(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	0.3515625	(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))))
accuracy	15.299557816443235	#s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))

Samples

31.0ms	183×	0	valid
12.0ms	72×	0	invalid
1.0ms	1×	3	valid

Compiler

Compiled 61 to 14 computations (77% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-mult: 9.0ms (36.8% of total)

ival-tan: 6.0ms (24.5% of total)

ival-pow: 4.0ms (16.4% of total)

ival-sqrt: 3.0ms (12.3% of total)

ival-div: 2.0ms (8.2% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

9.8MiB live, 9.8MiB allocated

Counts

6 → 72

Calls

Call 1

Inputs
#s(alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#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 #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())

Outputs
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #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 (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #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 (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor inf x) (#s(alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor inf x) (#s(alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor inf x) (#s(alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor inf x) (#s(alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor -inf x) (#s(alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor -inf x) (#s(alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor -inf x) (#s(alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor -inf x) (#s(alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) (patch (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 1/2)) (taylor 0 x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/48 (* (sqrt (pow x 5)) (/ 1 (sqrt 1/2)))) (* (sqrt x) (sqrt 1/2))) (taylor 0 x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 3) (+ (* 1/480 (* (sqrt (pow x 3)) (/ 1 (sqrt 1/2)))) (* 1/48 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2))))))) (taylor 0 x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 3) (+ (* 1/48 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))) (* (pow x 2) (+ (* -1/4608 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/480 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2))))))))) (taylor 0 x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor inf x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor inf x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor inf x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor inf x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* -1/6 (pow x 2))) x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* (pow x 2) (- (* -1/360 (pow x 2)) 1/6))) x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/15120 (pow x 2)) 1/360)) 1/6))) x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (cos (* 1/2 x)) (sin (* 1/2 x))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (cos (* 1/2 x)) (sin (* 1/2 x))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (cos (* 1/2 x)) (sin (* 1/2 x))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (cos (* 1/2 x)) (sin (* 1/2 x))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (cos (* 1/2 x)) (sin (* 1/2 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (cos (* 1/2 x)) (sin (* 1/2 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (cos (* 1/2 x)) (sin (* 1/2 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (cos (* 1/2 x)) (sin (* 1/2 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#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 (* (sqrt x) (sqrt 1/2)) (taylor 0 x) (#s(alt #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/48 (* (sqrt (pow x 5)) (/ 1 (sqrt 1/2)))) (* (sqrt x) (sqrt 1/2))) (taylor 0 x) (#s(alt #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 3) (+ (* 1/480 (* (sqrt (pow x 3)) (/ 1 (sqrt 1/2)))) (* 1/48 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2))))))) (taylor 0 x) (#s(alt #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 3) (+ (* 1/48 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))) (* (pow x 2) (+ (* -1/4608 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/480 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2))))))))) (taylor 0 x) (#s(alt #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor inf x) (#s(alt #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor inf x) (#s(alt #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor inf x) (#s(alt #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor inf x) (#s(alt #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 1/2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 1/2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 1/2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 1/2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 1/2)) (taylor inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 1/2)) (taylor inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 1/2)) (taylor inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 1/2)) (taylor inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 1/2)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 1/2)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 1/2)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 1/2)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())

Calls

18 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(* (sqrt x) (sqrt 1/2))
1.0ms	x	@	0	(* (sqrt x) (sqrt 1/2))
0.0ms	x	@	inf	(* (sqrt x) (sqrt 1/2))
0.0ms	x	@	0	(* (pow (/ 1 (tan (* x 1/2))) -1/2) (pow (/ 1 (tan (* x 1/2))) -1/2))
0.0ms	x	@	0	(pow (/ 1 (tan (* x 1/2))) -1/2)

simplify251.0ms (3.5%)

Memory

-29.6MiB live, 377.2MiB allocated

Algorithm

1×	egg-herbie

Rules

14 506×	`lower-fma.f64`
14 506×	`lower-fma.f32`
4 536×	`lower-*.f64`
4 536×	`lower-*.f32`
2 368×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	91	792
1	220	766
2	670	752
3	1919	738
4	3984	732
5	7156	732
0	8073	704

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

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)))
(* (sqrt x) (sqrt 1/2))
(+ (* 1/48 (* (sqrt (pow x 5)) (/ 1 (sqrt 1/2)))) (* (sqrt x) (sqrt 1/2)))
(+ (* (sqrt x) (sqrt 1/2)) (* (pow x 3) (+ (* 1/480 (* (sqrt (pow x 3)) (/ 1 (sqrt 1/2)))) (* 1/48 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))))))
(+ (* (sqrt x) (sqrt 1/2)) (* (pow x 3) (+ (* 1/48 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))) (* (pow x 2) (+ (* -1/4608 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/480 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))))))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(/ 2 x)
(/ (+ 2 (* -1/6 (pow x 2))) x)
(/ (+ 2 (* (pow x 2) (- (* -1/360 (pow x 2)) 1/6))) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/15120 (pow x 2)) 1/360)) 1/6))) 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)) (sin (* 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))))))))
(/ (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)))
(* (sqrt x) (sqrt 1/2))
(+ (* 1/48 (* (sqrt (pow x 5)) (/ 1 (sqrt 1/2)))) (* (sqrt x) (sqrt 1/2)))
(+ (* (sqrt x) (sqrt 1/2)) (* (pow x 3) (+ (* 1/480 (* (sqrt (pow x 3)) (/ 1 (sqrt 1/2)))) (* 1/48 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))))))
(+ (* (sqrt x) (sqrt 1/2)) (* (pow x 3) (+ (* 1/48 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))) (* (pow x 2) (+ (* -1/4608 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/480 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))))))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* (sqrt x) (sqrt 1/2))
(* (sqrt x) (sqrt 1/2))
(* (sqrt x) (sqrt 1/2))
(* (sqrt x) (sqrt 1/2))
(* (sqrt x) (sqrt 1/2))
(* (sqrt x) (sqrt 1/2))
(* (sqrt x) (sqrt 1/2))
(* (sqrt x) (sqrt 1/2))
(* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 1/2))))
(* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 1/2))))
(* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 1/2))))
(* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 1/2))))

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 (.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 (.f64 x 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)))
(* (sqrt x) (sqrt 1/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* 1/48 (* (sqrt (pow x 5)) (/ 1 (sqrt 1/2)))) (* (sqrt x) (sqrt 1/2)))
(fma.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (.f64 x (.f64 x (.f64 x (*.f64 x x))))) (/.f64 #s(literal 1/48 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (* (sqrt x) (sqrt 1/2)) (* (pow x 3) (+ (* 1/480 (* (sqrt (pow x 3)) (/ 1 (sqrt 1/2)))) (* 1/48 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))))))
(fma.f64 (fma.f64 #s(literal 1/48 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/480 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (/.f64 (.f64 x (.f64 x x)) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* (sqrt x) (sqrt 1/2)) (* (pow x 3) (+ (* 1/48 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))) (* (pow x 2) (+ (* -1/4608 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/480 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))))))))
(fma.f64 (.f64 x (.f64 x x)) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 (.f64 x x) #s(literal -1/2304 binary64) (fma.f64 (.f64 x x) #s(literal 1/480 binary64) #s(literal 1/48 binary64)))) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* -1/6 (pow x 2))) x)
(/.f64 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (- (* -1/360 (pow x 2)) 1/6))) x)
(/.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/360 binary64)) #s(literal -1/6 binary64)) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/15120 (pow x 2)) 1/360)) 1/6))) x)
(/.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/15120 binary64) #s(literal -1/360 binary64)) #s(literal -1/6 binary64)) #s(literal 2 binary64)) x)
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.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 (.f64 x 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)))
(/ (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)))
(* (sqrt x) (sqrt 1/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* 1/48 (* (sqrt (pow x 5)) (/ 1 (sqrt 1/2)))) (* (sqrt x) (sqrt 1/2)))
(fma.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (.f64 x (.f64 x (.f64 x (*.f64 x x))))) (/.f64 #s(literal 1/48 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (* (sqrt x) (sqrt 1/2)) (* (pow x 3) (+ (* 1/480 (* (sqrt (pow x 3)) (/ 1 (sqrt 1/2)))) (* 1/48 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))))))
(fma.f64 (fma.f64 #s(literal 1/48 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/480 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (/.f64 (.f64 x (.f64 x x)) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* (sqrt x) (sqrt 1/2)) (* (pow x 3) (+ (* 1/48 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))) (* (pow x 2) (+ (* -1/4608 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/480 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))))))))
(fma.f64 (.f64 x (.f64 x x)) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 (.f64 x x) #s(literal -1/2304 binary64) (fma.f64 (.f64 x x) #s(literal 1/480 binary64) #s(literal 1/48 binary64)))) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(sqrt (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(sqrt.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x))))
(* (sqrt x) (sqrt 1/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt x) (sqrt 1/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt x) (sqrt 1/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt x) (sqrt 1/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt x) (sqrt 1/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt x) (sqrt 1/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt x) (sqrt 1/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt x) (sqrt 1/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))
(* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 1/2))))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))
(* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 1/2))))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))
(* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 1/2))))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))
(* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 1/2))))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))

rewrite228.0ms (3.2%)

Memory

-0.6MiB live, 282.3MiB allocated

Rules

2 838×	`lower-fma.f64`
2 838×	`lower-fma.f32`
1 710×	`lower-*.f32`
1 704×	`lower-*.f64`
1 276×	`prod-exp`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	17	60
0	25	63
1	52	51
2	142	45
3	605	45
4	3761	39
0	8786	39

Stop Event

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

Counts

6 → 2 152

Calls

Call 1

Inputs
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
#s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))

Outputs
(.f64 #s(literal 1 binary64) (.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (sqrt.f64 (*.f64 x #s(literal 1/2 binary64))))))
(.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (sqrt.f64 (*.f64 x #s(literal 1/2 binary64)))))
(.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (sqrt.f64 (*.f64 x #s(literal 1/2 binary64))))))
(.f64 #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (sqrt.f64 (.f64 x #s(literal 1/2 binary64)))) (tan.f64 (.f64 x #s(literal 1/2 binary64))))
(.f64 (sqrt.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 1/2 binary64))))) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (sqrt.f64 (*.f64 x #s(literal 1/2 binary64))))))
(.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/8 binary64)) (.f64 (pow.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1/8 binary64)) (.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (sqrt.f64 (*.f64 x #s(literal 1/2 binary64)))))))
(.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/8 binary64)) (.f64 (pow.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1/8 binary64)) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (sqrt.f64 (*.f64 x #s(literal 1/2 binary64))))))
(.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) (.f64 (pow.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1/4 binary64)) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (sqrt.f64 (*.f64 x #s(literal 1/2 binary64))))))
(.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) (.f64 (pow.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1/4 binary64)) (.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (sqrt.f64 (*.f64 x #s(literal 1/2 binary64)))))))
(.f64 (.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (sqrt.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal 1 binary64))
(.f64 (.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (sqrt.f64 (.f64 x #s(literal 1/2 binary64))))) (tan.f64 (.f64 x #s(literal 1/2 binary64))))
(.f64 (.f64 #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (sqrt.f64 (.f64 x #s(literal 1/2 binary64)))) (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64))) (pow.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1/4 binary64)))
(.f64 (.f64 (.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (sqrt.f64 (.f64 x #s(literal 1/2 binary64))))) (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/8 binary64))) (pow.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1/8 binary64)))
(.f64 (.f64 #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (sqrt.f64 (.f64 x #s(literal 1/2 binary64)))) (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/8 binary64))) (pow.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1/8 binary64)))
(.f64 (.f64 #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (sqrt.f64 (.f64 x #s(literal 1/2 binary64)))) (sqrt.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 x #s(literal 1/2 binary64))))))
(.f64 (.f64 (.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (sqrt.f64 (.f64 x #s(literal 1/2 binary64))))) (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64))) (pow.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1/4 binary64)))
(exp.f64 (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal -1/2 binary64))) (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))))))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))))))
(exp.f64 (.f64 (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/16 binary64)))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal 1/2 binary64))) (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))))))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal -1/4 binary64))) (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))))))
(exp.f64 (.f64 (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/32 binary64)))
(exp.f64 (.f64 (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal 1/32 binary64)))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (.f64 (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/16 binary64))))
(exp.f64 (.f64 (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal 4 binary64)))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal -2 binary64))) (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))))))
(exp.f64 (.f64 (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -3 binary64)))
(exp.f64 (.f64 (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal 3 binary64)))
(exp.f64 (.f64 (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -3/8 binary64)))
(exp.f64 (.f64 (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -3/2 binary64)))
(exp.f64 (.f64 (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal 1/16 binary64)))
(exp.f64 (.f64 (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal 3/2 binary64)))
(exp.f64 (.f64 (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal 3/8 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (exp.f64 #s(literal -1/2 binary64))) (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (exp.f64 #s(literal -1/2 binary64))) (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 3 binary64)) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal -2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal -1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal -1/32 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal -1/16 binary64)))
(exp.f64 (.f64 #s(literal -1 binary64) (.f64 (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/16 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal -3 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 3 binary64)) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal -3/8 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal -1/8 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/16 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (neg.f64 (log.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))))) #s(literal -1/2 binary64) (.f64 (log.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))))
(exp.f64 (fma.f64 (neg.f64 (log.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))))) #s(literal -1 binary64) (.f64 (log.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64))))
(exp.f64 (fma.f64 (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal 3 binary64) (.f64 (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 3 binary64))))
(exp.f64 (fma.f64 (neg.f64 (log.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))))) #s(literal -1/8 binary64) (.f64 (log.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/8 binary64))))
(exp.f64 (fma.f64 (log.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/8 binary64) (.f64 (neg.f64 (log.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal -1/8 binary64))))
(exp.f64 (fma.f64 (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/16 binary64) (.f64 (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/16 binary64))))
(exp.f64 (fma.f64 (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/16 binary64) (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))))))
(exp.f64 (+.f64 (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 (log.f64 #s(literal -1 binary64)) #s(literal -1/4 binary64))))
(exp.f64 (fma.f64 (neg.f64 (log.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))))) #s(literal 1/4 binary64) (.f64 (log.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1/4 binary64))))
(exp.f64 (fma.f64 (neg.f64 (log.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))))) #s(literal 1/4 binary64) (.f64 (neg.f64 (log.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal -1/4 binary64))))
(exp.f64 (fma.f64 (log.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/4 binary64) (.f64 (log.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1/4 binary64))))
(exp.f64 (fma.f64 (log.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/4 binary64) (.f64 (neg.f64 (log.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal -1/4 binary64))))
(exp.f64 (fma.f64 (log.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal 1/4 binary64) (.f64 (neg.f64 (log.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal 1/4 binary64))))
(exp.f64 (fma.f64 (log.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal 1/4 binary64) (.f64 (log.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/4 binary64))))
(exp.f64 (fma.f64 (neg.f64 (log.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))))) #s(literal -1/4 binary64) (.f64 (neg.f64 (log.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal 1/4 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64) (log.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))))
(exp.f64 (fma.f64 (log.f64 (exp.f64 #s(literal -1/2 binary64))) (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 (log.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 (log.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64))))
(exp.f64 (fma.f64 (neg.f64 (log.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))))) #s(literal 1/2 binary64) (.f64 (neg.f64 (log.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal -1/2 binary64))))
(exp.f64 (fma.f64 (neg.f64 (log.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))))) #s(literal 1/2 binary64) (.f64 (log.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64) (.f64 (neg.f64 (log.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal -1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64) (.f64 (log.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64) (.f64 (log.f64 (exp.f64 #s(literal -1/2 binary64))) (log.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))))))
(exp.f64 (fma.f64 (neg.f64 (log.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))))) #s(literal -1/2 binary64) (.f64 (neg.f64 (log.f64 (cos.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal 1/2 binary64))))
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(exp.f64 (+.f64 (fma.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64) (.f64 (log.f64 x) #s(literal 1/4 binary64))) (fma.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64) (.f64 (log.f64 x) #s(literal 1/4 binary64)))))
(exp.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 x) (.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(exp.f64 (+.f64 (fma.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal 1/2 binary64) (log.f64 x))) (.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(exp.f64 (+.f64 (fma.f64 (log.f64 x) #s(literal 1/4 binary64) (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64)))) (.f64 (log.f64 x) #s(literal 1/4 binary64))))
(exp.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 x) #s(literal 1/4 binary64))) (.f64 (log.f64 x) #s(literal 1/4 binary64))))
(sqrt.f64 (*.f64 x #s(literal 1/2 binary64)))
(sqrt.f64 (exp.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64)))))
(pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1/4 binary64))
(pow.f64 (.f64 (.f64 x #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 1/4 binary64))
(pow.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) #s(literal 1/4 binary64))
(pow.f64 (.f64 x (.f64 #s(literal 1/4 binary64) x)) #s(literal 1/4 binary64))
(pow.f64 (.f64 (.f64 (*.f64 x x) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) x) #s(literal 1/4 binary64))
(pow.f64 (.f64 (.f64 #s(literal 1/4 binary64) x) x) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 x))
(.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (pow.f64 (.f64 (*.f64 x x) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/8 binary64)) (pow.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal 1/4 binary64))))
(.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 (*.f64 x x) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/8 binary64)))
(.f64 (.f64 (pow.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))

eval305.0ms (4.3%)

Memory: 32.4MiB live, 450.0MiB allocated
Compiler: Compiled 50 602 to 5 569 computations (89% saved)

prune396.0ms (5.6%)

Memory

-2.3MiB live, 502.5MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	2 223	1	2 224
Fresh	0	0	0
Picked	1	0	1
Done	0	5	5
Total	2 224	6	2 230

Accuracy

100.0%

Counts

2 230 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
	47.2%	(.f64 #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))))
✓	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	47.6%	#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))))
✓	47.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	47.9%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
✓	7.7%	#s(literal 1 binary64)

Compiler

Compiled 139 to 60 computations (56.8% saved)

regimes9.0ms (0.1%)

Memory

-19.0MiB live, 17.9MiB allocated

Counts

10 → 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)) (.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 #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #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))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) #s(approx (pow (/ 1 (tan (* x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)))

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

Calls

2 calls:

5.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
4.0ms	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)

regimes6.0ms (0.1%)

Memory

12.8MiB live, 12.8MiB allocated

Counts

6 → 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)) (.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 #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64)))) #s(approx (pow (/ 1 (tan ( x 1/2))) -1/2) (*.f64 (sqrt.f64 x) (sqrt.f64 #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) (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

2 calls:

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

Results

Accuracy	Segments	Branch
51.7%	2	`x`
51.5%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes2.0ms (0%)

Memory

4.6MiB live, 4.6MiB 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
51.7%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Memory

6.6MiB live, 6.6MiB 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	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
2.0ms	x

Results

Accuracy	Segments	Branch
51.3%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
51.5%	2	`x`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes31.0ms (0.4%)

Memory

-32.8MiB live, 5.7MiB 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:

29.0ms	x
1.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Results

Accuracy	Segments	Branch
7.7%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
7.7%	1	`x`

Compiler

Compiled 10 to 7 computations (30% saved)

bsearch17.0ms (0.2%)

Memory

17.6MiB live, 17.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	0.0014430007671275128	3.4010812832327404

Samples

10.0ms

128×

valid

Compiler

Compiled 163 to 114 computations (30.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-cos: 3.0ms (37.3% of total)

ival-sin: 3.0ms (37.3% of total)

ival-sub: 1.0ms (12.4% of total)

ival-div: 1.0ms (12.4% 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

1.1MiB live, 1.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.0014430007671275128	3.4010812832327404

Compiler

Compiled 123 to 90 computations (26.8% saved)

bsearch9.0ms (0.1%)

Memory

9.1MiB live, 9.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
8.0ms	0.0014430007671275128	3.4010812832327404

Samples

6.0ms

64×

valid

Compiler

Compiled 83 to 66 computations (20.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-cos: 2.0ms (45.7% of total)

ival-sin: 2.0ms (45.7% of total)

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

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

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

exact: 0.0ms (0% of total)

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

simplify15.0ms (0.2%)

Memory

-25.7MiB live, 9.6MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	68
1	38	68

Stop Event

1×

saturated

Calls

Call 1

Inputs
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 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 3602879701896397/1125899906842624 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 3152519739159347/2251799813685248 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 3602879701896397/1125899906842624 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 3602879701896397/1125899906842624 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 3152519739159347/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3152519739159347/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness689.0ms (9.7%)

Memory

13.6MiB live, 451.4MiB allocated

Rules

19 148×	`lower-fma.f64`
19 148×	`lower-fma.f32`
8 674×	`lower-fma.f32`
8 668×	`lower-fma.f64`
5 812×	`lower-*.f32`

Iterations

Useful iterations: 3 (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
0	25	114
0	40	103
1	148	103
2	917	103
0	8416	103
0	6	15
0	10	12
1	39	12
2	245	12
3	2355	11
0	8885	11

Stop Event

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

Compiler

Compiled 107 to 65 computations (39.3% saved)

preprocess61.0ms (0.9%)

Memory: 5.8MiB live, 125.4MiB allocated
Remove: (negabs x)
Compiler: Compiled 132 to 72 computations (45.5% 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	25	127
0	40	116
1	81	116
2	148	116
3	234	116
4	266	116
5	293	116
6	326	116
7	400	116
8	522	116
9	731	116
10	773	116
11	776	116
12	784	116
13	789	116
14	793	116
15	800	116
16	880	116
17	967	116
18	971	116
0	971	116

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	25	127
0	40	116
1	81	116
2	148	116
3	234	116
4	266	116
5	293	116
6	326	116
7	400	116
8	522	116
9	731	116
10	773	116
11	776	116
12	784	116
13	789	116
14	793	116
15	800	116
16	880	116
17	967	116
18	971	116
0	971	116

start0.0ms (0%)

analyze122.0ms (1.7%)

sample1.9s (26.4%)

explain161.0ms (2.3%)

preprocess44.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify28.0ms (0.4%)

localize117.0ms (1.7%)

series3.0ms (0%)

simplify307.0ms (4.3%)

rewrite314.0ms (4.4%)

eval88.0ms (1.2%)

prune149.0ms (2.1%)

simplify41.0ms (0.6%)

localize166.0ms (2.3%)

series13.0ms (0.2%)

simplify239.0ms (3.4%)

rewrite290.0ms (4.1%)

eval354.0ms (5%)

prune107.0ms (1.5%)

simplify5.0ms (0.1%)

localize41.0ms (0.6%)

series5.0ms (0.1%)

simplify342.0ms (4.8%)

rewrite63.0ms (0.9%)

eval52.0ms (0.7%)

prune68.0ms (1%)

simplify4.0ms (0.1%)

localize57.0ms (0.8%)

series4.0ms (0.1%)

simplify251.0ms (3.5%)

rewrite228.0ms (3.2%)

eval305.0ms (4.3%)

prune396.0ms (5.6%)

regimes9.0ms (0.1%)

regimes6.0ms (0.1%)

regimes2.0ms (0%)

regimes3.0ms (0%)

regimes31.0ms (0.4%)

bsearch17.0ms (0.2%)

bsearch1.0ms (0%)

bsearch9.0ms (0.1%)

simplify15.0ms (0.2%)

soundness689.0ms (9.7%)

preprocess61.0ms (0.9%)

end0.0ms (0%)

Profiling

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

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

Iter	Nodes	Cost
0	25	127
0	40	116
1	81	116
2	148	116
3	234	116
4	266	116
5	293	116
6	326	116
7	400	116
8	522	116
9	731	116
10	773	116
11	776	116
12	784	116
13	789	116
14	793	116
15	800	116
16	880	116
17	967	116
18	971	116
0	971	116