Metrics for tanhf (example 3.4)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze166.0ms (2.5%)

Memory

28.2MiB live, 181.7MiB 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)

sample2.1s (30.6%)

Memory

19.4MiB live, 1 710.0MiB allocated

Samples

730.0ms	2 256×	2	valid
490.0ms	4 212×	0	valid
438.0ms	566×	3	valid
126.0ms	1 217×	1	valid
5.0ms	5×	4	valid

Precisions

Click to see histograms. Total time spent on operations: 1.5s

ival-cos: 1.0s (67.2% of total)

ival-sin: 196.0ms (12.6% of total)

adjust: 109.0ms (7% of total)

ival-div: 100.0ms (6.5% of total)

ival-sub: 90.0ms (5.8% of total)

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

exact: 5.0ms (0.3% of total)

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

Bogosity

explain175.0ms (2.6%)

Memory

12.0MiB live, 198.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
70	1	(-1.2435940706272107e+169)	1	(6.239745199832202e+44)	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
65	0	-	7	(1.0806928041549716e-159)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.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 #s(literal 1 binary64) (cos.f64 x))`	cancellation	70	7
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`	u/n	58	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	58

Confusion

	Predicted +	Predicted -
+	127	2
-	1	126

Precision

0.9921875

Recall

0.9844961240310077

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	127	2	0
-	1	5	121

Precision?

0.9555555555555556

Recall?

1.0

Freqs

test

number	freq
0	128
1	128

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

43.0ms	132×	2	valid
31.0ms	270×	0	valid
12.0ms	36×	3	valid
8.0ms	74×	1	valid

Compiler

Compiled 46 to 22 computations (52.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 77.0ms

ival-cos: 48.0ms (62% of total)

ival-sin: 11.0ms (14.2% of total)

ival-div: 6.0ms (7.7% of total)

adjust: 6.0ms (7.7% of total)

ival-sub: 5.0ms (6.5% of total)

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

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

exact: 0.0ms (0% of total)

preprocess55.0ms (0.8%)

Memory

8.6MiB live, 82.9MiB 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: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.3%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify29.0ms (0.4%)

Memory

-17.2MiB live, 34.5MiB 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)

localize70.0ms (1%)

Memory

-8.8MiB live, 30.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(sin.f64 x)
accuracy	0	(cos.f64 x)
accuracy	14.326622014715849	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
accuracy	14.531701566670526	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Samples

19.0ms	66×	2	valid
14.0ms	135×	0	valid
6.0ms	18×	3	valid
4.0ms	37×	1	valid

Compiler

Compiled 19 to 8 computations (57.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-cos: 20.0ms (59.5% of total)

ival-sin: 5.0ms (14.9% of total)

ival-div: 3.0ms (8.9% of total)

adjust: 3.0ms (8.9% of total)

ival-sub: 2.0ms (6% 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

1.8MiB live, 1.8MiB 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))
1.0ms	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))

simplify313.0ms (4.6%)

Memory

26.7MiB live, 376.3MiB 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)

rewrite583.0ms (8.7%)

Memory

5.9MiB live, 287.1MiB 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 (1.3%)

Memory: -1.0MiB live, 118.8MiB allocated
Compiler: Compiled 14 450 to 1 633 computations (88.7% saved)

prune117.0ms (1.7%)

Memory

-29.2MiB live, 175.7MiB allocated

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	656	6	662
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	656	7	663

Accuracy

100.0%

Counts

663 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	8.0%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
✓	54.3%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
	54.2%	(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
▶	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
▶	49.6%	#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))))
▶	49.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
▶	49.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 106 to 72 computations (32.1% saved)

simplify45.0ms (0.7%)

Memory

19.9MiB live, 53.7MiB 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)

localize184.0ms (2.7%)

Memory

8.8MiB live, 205.0MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
accuracy	0.046875	(.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	0.0859375	(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
accuracy	0.10546875	(*.f64 x #s(literal 1/240 binary64))
accuracy	32.27203791443039	#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	0.0390625	(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
accuracy	0.05078125	(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
accuracy	0.296875	(*.f64 x #s(literal 1/24 binary64))
accuracy	32.246727031773105	#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	32.17494343447687	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
accuracy	0	(*.f64 x #s(literal 1/2 binary64))
accuracy	0.0078125	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))

Samples

85.0ms	135×	0	valid
44.0ms	66×	2	valid
14.0ms	18×	3	valid
13.0ms	37×	1	valid

Compiler

Compiled 109 to 27 computations (75.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 89.0ms

ival-mult: 23.0ms (25.8% of total)

ival-cos: 22.0ms (24.7% of total)

adjust: 10.0ms (11.2% of total)

const: 9.0ms (10.1% of total)

ival-tan: 8.0ms (9% of total)

ival-add: 5.0ms (5.6% of total)

ival-sin: 5.0ms (5.6% of total)

ival-div: 3.0ms (3.4% of total)

ival-sub: 3.0ms (3.4% of total)

ival-pow: 2.0ms (2.2% of total)

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

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

exact: 0.0ms (0% of total)

series18.0ms (0.3%)

Memory

-16.9MiB live, 26.8MiB 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>) () ())) ())
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#s(alt (* 1/2 x) (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 (* 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
5.0ms	x	@	0	(* x x)
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))

simplify261.0ms (3.9%)

Memory

29.1MiB live, 259.2MiB 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))

rewrite372.0ms (5.5%)

Memory

-29.6MiB live, 394.2MiB 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))))
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(/.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal -1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (neg.f64 (sin.f64 x))))
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(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64))) (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64)) #s(literal 1/2641807540224 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)))))) (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 #s(literal 1/191102976 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1/191102976000 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64) #s(literal -1/191102976 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)))))) (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 (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)))))

eval106.0ms (1.6%)

Memory: 30.7MiB live, 205.6MiB allocated
Compiler: Compiled 20 967 to 1 627 computations (92.2% saved)

prune120.0ms (1.8%)

Memory

-14.7MiB live, 198.0MiB allocated

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	737	2	739
Fresh	0	1	1
Picked	1	4	5
Done	0	1	1
Total	738	8	746

Accuracy

100.0%

Counts

746 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.3%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
▶	54.2%	(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
✓	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
▶	49.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
✓	49.6%	#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))))
✓	49.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	49.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
▶	8.0%	#s(literal 1 binary64)

Compiler

Compiled 67 to 44 computations (34.3% saved)

simplify36.0ms (0.5%)

Memory

-3.0MiB live, 34.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Rules

346×	`lower-fma.f32`
344×	`lower-fma.f64`
226×	`lower-*.f32`
220×	`lower-*.f64`
152×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	66
0	28	57
1	47	57
2	72	57
3	99	57
4	128	57
5	173	57
6	246	57
7	372	57
8	638	57
9	701	57
10	722	57
11	732	57
12	738	57
13	742	57
14	749	57
15	782	57
16	805	57
17	807	57
0	807	57

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize358.0ms (5.3%)

Memory

12.3MiB live, 284.3MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(sin.f64 x)
accuracy	0.13671875	(/.f64 #s(literal 1 binary64) (sin.f64 x))
accuracy	0.15625	(/.f64 #s(literal 1 binary64) (tan.f64 x))
accuracy	29.298677831265167	(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
accuracy	0	(*.f64 x #s(literal 1/2 binary64))
accuracy	0.0703125	(.f64 x (.f64 x x))
accuracy	0.07421875	(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))
accuracy	32.246727031773105	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))

Samples

222.0ms	66×	2	valid
62.0ms	18×	3	valid
41.0ms	134×	0	valid
13.0ms	38×	1	valid

Compiler

Compiled 58 to 19 computations (67.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 322.0ms

ival-tan: 200.0ms (62.2% of total)

ival-sin: 57.0ms (17.7% of total)

ival-cos: 20.0ms (6.2% of total)

ival-mult: 18.0ms (5.6% of total)

ival-div: 9.0ms (2.8% of total)

adjust: 7.0ms (2.2% of total)

ival-sub: 5.0ms (1.6% of total)

const: 4.0ms (1.2% of total)

ival-add: 1.0ms (0.3% of total)

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

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

exact: 0.0ms (0% of total)

series7.0ms (0.1%)

Memory

15.7MiB live, 15.7MiB allocated

Counts

9 → 108

Calls

Call 1

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

Outputs
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 3)) (taylor inf x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 3)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64)))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
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#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) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
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#s(alt (- (/ 1 (sin x)) (/ (cos x) (sin x))) (taylor inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) #<representation binary64>) () ())) ())
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#s(alt (/ (+ 1 (* 1/6 (pow x 2))) x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sin.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* (pow x 2) (+ 1/6 (* 7/360 (pow x 2))))) x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sin.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 7/360 (* 31/15120 (pow x 2))))))) x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sin.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (sin x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sin.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (sin x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sin.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (sin x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sin.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (sin x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sin.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (sin x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sin.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (sin x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sin.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (sin x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sin.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (sin x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sin.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sin.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>) () ())) ())
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#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>) () ())) ())
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#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1/3 (pow x 2))) x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (cos x) (sin x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (tan.f64 x)) (patch (/.f64 #s(literal 1 binary64) (tan.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 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>) () ())) ())

Calls

27 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(- (/ 1 (sin x)) (/ 1 (tan x)))
1.0ms	x	@	-inf	(- (/ 1 (sin x)) (/ 1 (tan x)))
0.0ms	x	@	inf	(+ (* (* x (* x x)) 1/24) (* x 1/2))
0.0ms	x	@	0	(- (/ 1 (sin x)) (/ 1 (tan x)))
0.0ms	x	@	-inf	(* x (* x x))

simplify237.0ms (3.5%)

Memory

-40.6MiB live, 327.1MiB allocated

Algorithm

1×	egg-herbie

Rules

11 510×	`lower-fma.f64`
11 510×	`lower-fma.f32`
4 294×	`lower-*.f64`
4 294×	`lower-*.f32`
2 358×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	95	592
1	239	586
2	587	586
3	1713	586
4	2948	586
5	5397	586
6	6697	586
7	7704	586
0	8076	547

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 107

Calls

Call 1

Inputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 x)
(* 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 (sin x)) (/ (cos x) (sin x)))
(- (/ 1 (sin x)) (/ (cos x) (sin x)))
(- (/ 1 (sin x)) (/ (cos x) (sin x)))
(- (/ 1 (sin x)) (/ (cos x) (sin x)))
(- (/ 1 (sin x)) (/ (cos x) (sin x)))
(- (/ 1 (sin x)) (/ (cos x) (sin x)))
(- (/ 1 (sin x)) (/ (cos x) (sin x)))
(- (/ 1 (sin x)) (/ (cos x) (sin x)))
(/ 1 x)
(/ (+ 1 (* 1/6 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (+ 1/6 (* 7/360 (pow x 2))))) x)
(/ (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 7/360 (* 31/15120 (pow x 2))))))) x)
(/ 1 (sin x))
(/ 1 (sin x))
(/ 1 (sin x))
(/ 1 (sin x))
(/ 1 (sin x))
(/ 1 (sin x))
(/ 1 (sin x))
(/ 1 (sin 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)
(/ 1 x)
(/ (+ 1 (* -1/3 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(* 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)

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 (* 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 #s(literal 1/24 binary64) (*.f64 x x)))
(* (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 #s(literal 1/24 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.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)))
(/ (- 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))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 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)))
(- (/ 1 (sin x)) (/ (cos x) (sin x)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(- (/ 1 (sin x)) (/ (cos x) (sin x)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(- (/ 1 (sin x)) (/ (cos x) (sin x)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(- (/ 1 (sin x)) (/ (cos x) (sin x)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(- (/ 1 (sin x)) (/ (cos x) (sin x)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(- (/ 1 (sin x)) (/ (cos x) (sin x)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(- (/ 1 (sin x)) (/ (cos x) (sin x)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(- (/ 1 (sin x)) (/ (cos x) (sin x)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* 1/6 (pow x 2))) x)
(/.f64 (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 2) (+ 1/6 (* 7/360 (pow x 2))))) x)
(/.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 7/360 binary64)) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 7/360 (* 31/15120 (pow x 2))))))) x)
(/.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 31/15120 binary64)) #s(literal 7/360 binary64)) #s(literal 1/6 binary64))) #s(literal 1 binary64)) x)
(/ 1 (sin x))
(/.f64 #s(literal 1 binary64) (sin.f64 x))
(/ 1 (sin x))
(/.f64 #s(literal 1 binary64) (sin.f64 x))
(/ 1 (sin x))
(/.f64 #s(literal 1 binary64) (sin.f64 x))
(/ 1 (sin x))
(/.f64 #s(literal 1 binary64) (sin.f64 x))
(/ 1 (sin x))
(/.f64 #s(literal 1 binary64) (sin.f64 x))
(/ 1 (sin x))
(/.f64 #s(literal 1 binary64) (sin.f64 x))
(/ 1 (sin x))
(/.f64 #s(literal 1 binary64) (sin.f64 x))
(/ 1 (sin x))
(/.f64 #s(literal 1 binary64) (sin.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 x (.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 x (.f64 (.f64 x x) (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))) 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)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* -1/3 (pow x 2))) x)
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)
(/.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -2/945 binary64) #s(literal -1/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64)) x)
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(* 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)

rewrite266.0ms (3.9%)

Memory

33.8MiB live, 269.3MiB allocated

Rules

7 654×	`lower-fma.f32`
7 652×	`lower-fma.f64`
5 084×	`lower-*.f32`
5 078×	`lower-*.f64`
3 650×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	58
0	28	44
1	109	44
2	884	44
0	8625	44

Stop Event

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

Counts

9 → 445

Calls

Call 1

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

Outputs
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 (.f64 x #s(literal 1/24 binary64)) x)))
(+.f64 (.f64 x (.f64 (.f64 x #s(literal 1/24 binary64)) x)) (.f64 x #s(literal 1/2 binary64)))
(+.f64 (/.f64 (.f64 x (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64)))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
(-.f64 (/.f64 (.f64 x (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64)))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))))) (/.f64 (.f64 x (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64)))) (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))))))
(fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 (*.f64 x #s(literal 1/24 binary64)) x)))
(fma.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64))) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 x (.f64 (.f64 x #s(literal 1/24 binary64)) x) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/24 binary64)) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (.f64 x (.f64 (*.f64 x #s(literal 1/24 binary64)) x)))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 (.f64 x #s(literal 1/24 binary64)) x)))
(fma.f64 (.f64 x (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
(fma.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) x (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (neg.f64 x) #s(literal -1/2 binary64) (.f64 x (.f64 (*.f64 x #s(literal 1/24 binary64)) x)))
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/24 binary64)) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 #s(literal 1/24 binary64) x) (.f64 x x) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x x) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x x) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 x x) x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 x (.f64 x x)) x) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64)) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 #s(literal 1/24 binary64) x) (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 (.f64 x #s(literal 1/24 binary64)) x)))) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
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(fma.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) x) (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))
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(.f64 (/.f64 (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (+.f64 (pow.f64 (sin.f64 x) #s(literal -3 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 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) (neg.f64 (tan.f64 x)))))
(.f64 (/.f64 (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (+.f64 (tan.f64 x) (sin.f64 x))) (.f64 (sin.f64 x) (tan.f64 x)))
(.f64 (/.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 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 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64)))))
(.f64 (/.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))
(.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (sin.f64 x)) (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (-.f64 (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 1 binary64)))))
(.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (sin.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(.f64 (/.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 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(.f64 (/.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) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (+.f64 (cos.f64 x) #s(literal -1 binary64)))))
(*.f64 (/.f64 (/.f64 (-.f64 (tan.f64 x) (sin.f64 x)) (sin.f64 x)) (neg.f64 (tan.f64 x))) #s(literal -1 binary64))
(*.f64 (/.f64 (/.f64 (-.f64 (tan.f64 x) (sin.f64 x)) (sin.f64 x)) (neg.f64 (sin.f64 x))) (neg.f64 (cos.f64 x)))
(exp.f64 (neg.f64 (log.f64 (sin.f64 x))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 x)))
(neg.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (sin.f64 x))
(/.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 x)))
(pow.f64 (sin.f64 x) #s(literal -1 binary64))
(pow.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 x)))
(*.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) #s(literal -1 binary64))
(*.f64 (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 x) #s(literal -1/2 binary64))) (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(exp.f64 (log.f64 (sin.f64 x)))
(-.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x)))
(sin.f64 x)
(neg.f64 (neg.f64 (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(/.f64 (sin.f64 x) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 x)))
(/.f64 (neg.f64 (sin.f64 x)) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 x) #s(literal -1/2 binary64))) (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (sin.f64 x))
(*.f64 (sin.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 x)))
(*.f64 (neg.f64 (sin.f64 x)) #s(literal -1 binary64))
(exp.f64 (neg.f64 (log.f64 (tan.f64 x))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x))) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(neg.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) (tan.f64 x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (tan.f64 x)))
(/.f64 (neg.f64 (cos.f64 x)) (neg.f64 (sin.f64 x)))
(/.f64 (/.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x))
(/.f64 (/.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64)) (sin.f64 x))
(pow.f64 (tan.f64 x) #s(literal -1 binary64))
(pow.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(*.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (cos.f64 x))
(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal -1 binary64))
(*.f64 (neg.f64 (cos.f64 x)) (/.f64 #s(literal -1 binary64) (sin.f64 x)))
(*.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x)))
(*.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (cos.f64 x)))
(*.f64 (/.f64 (cos.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64))) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)))
(.f64 (.f64 (cos.f64 x) (pow.f64 (sin.f64 x) #s(literal -1/2 binary64))) (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(neg.f64 (*.f64 x #s(literal -1/2 binary64)))
(/.f64 x #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) x)))
(/.f64 (neg.f64 x) #s(literal -2 binary64))
(/.f64 (neg.f64 (neg.f64 x)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))
(*.f64 (neg.f64 x) #s(literal -1/2 binary64))

eval72.0ms (1.1%)

Memory: 0.2MiB live, 120.5MiB allocated
Compiler: Compiled 11 921 to 1 189 computations (90% saved)

prune95.0ms (1.4%)

Memory

-28.0MiB live, 87.0MiB allocated

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	552	0	552
Fresh	0	0	0
Picked	0	3	3
Done	0	5	5
Total	552	8	560

Accuracy

100.0%

Counts

560 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.3%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
✓	54.2%	(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
✓	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	49.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
✓	49.6%	#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))))
✓	49.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	49.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
✓	8.0%	#s(literal 1 binary64)

Compiler

Compiled 130 to 72 computations (44.6% saved)

regimes7.0ms (0.1%)

Memory

6.1MiB live, 6.1MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes6.0ms (0.1%)

Memory

13.2MiB live, 13.2MiB 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)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #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))

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

Results

Accuracy	Segments	Branch
53.8%	2	`x`
53.6%	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

5.3MiB live, 5.3MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
53.8%	2	`x`

Compiler

Compiled 2 to 1 computations (50% 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
53.8%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Memory

7.7MiB live, 7.7MiB 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))
1.0ms	x

Results

Accuracy	Segments	Branch
53.3%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
53.5%	2	`x`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes7.0ms (0.1%)

Memory

-49.8MiB live, 4.3MiB 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:

6.0ms	x
1.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Results

Accuracy	Segments	Branch
8.0%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
8.0%	1	`x`

Compiler

Compiled 10 to 7 computations (30% saved)

bsearch21.0ms (0.3%)

Memory

25.5MiB live, 25.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	0.0015113419209430705	2478.8778364667

Samples

14.0ms

144×

valid

Compiler

Compiled 182 to 127 computations (30.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-cos: 4.0ms (37.9% of total)

ival-sin: 4.0ms (37.9% of total)

ival-sub: 1.0ms (9.5% of total)

ival-div: 1.0ms (9.5% 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

1.8MiB live, 1.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.0015113419209430705	2478.8778364667

Compiler

Compiled 155 to 109 computations (29.7% saved)

bsearch1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.0015113419209430705	2478.8778364667

Compiler

Compiled 137 to 100 computations (27% saved)

bsearch17.0ms (0.3%)

Memory

-11.8MiB live, 26.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	0.0015113419209430705	2478.8778364667

Samples

12.0ms

128×

valid

Compiler

Compiled 92 to 73 computations (20.7% saved)

Precisions

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

ival-cos: 5.0ms (55% of total)

ival-sin: 3.0ms (33% of total)

ival-sub: 1.0ms (11% of total)

ival-div: 1.0ms (11% of total)

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

exact: 0.0ms (0% of total)

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

simplify6.0ms (0.1%)

Memory

12.4MiB live, 12.4MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	91
1	43	91

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)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 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)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 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)

soundness690.0ms (10.2%)

Memory

9.4MiB live, 468.9MiB 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×	done
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 147 to 84 computations (42.9% saved)

preprocess140.0ms (2.1%)

Memory: -18.8MiB live, 156.6MiB allocated
Remove: (negabs x)
Compiler: Compiled 164 to 78 computations (52.4% 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	18	66
0	28	57
1	47	57
2	72	57
3	99	57
4	128	57
5	173	57
6	246	57
7	372	57
8	638	57
9	701	57
10	722	57
11	732	57
12	738	57
13	742	57
14	749	57
15	782	57
16	805	57
17	807	57
0	807	57

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	18	66
0	28	57
1	47	57
2	72	57
3	99	57
4	128	57
5	173	57
6	246	57
7	372	57
8	638	57
9	701	57
10	722	57
11	732	57
12	738	57
13	742	57
14	749	57
15	782	57
16	805	57
17	807	57
0	807	57

start0.0ms (0%)

analyze166.0ms (2.5%)

sample2.1s (30.6%)

explain175.0ms (2.6%)

preprocess55.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify29.0ms (0.4%)

localize70.0ms (1%)

series3.0ms (0%)

simplify313.0ms (4.6%)

rewrite583.0ms (8.7%)

eval88.0ms (1.3%)

prune117.0ms (1.7%)

simplify45.0ms (0.7%)

localize184.0ms (2.7%)

series18.0ms (0.3%)

simplify261.0ms (3.9%)

rewrite372.0ms (5.5%)

eval106.0ms (1.6%)

prune120.0ms (1.8%)

simplify36.0ms (0.5%)

localize358.0ms (5.3%)

series7.0ms (0.1%)

simplify237.0ms (3.5%)

rewrite266.0ms (3.9%)

eval72.0ms (1.1%)

prune95.0ms (1.4%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes3.0ms (0%)

regimes7.0ms (0.1%)

bsearch21.0ms (0.3%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch17.0ms (0.3%)

simplify6.0ms (0.1%)

soundness690.0ms (10.2%)

preprocess140.0ms (2.1%)

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

Iter	Nodes	Cost
0	18	66
0	28	57
1	47	57
2	72	57
3	99	57
4	128	57
5	173	57
6	246	57
7	372	57
8	638	57
9	701	57
10	722	57
11	732	57
12	738	57
13	742	57
14	749	57
15	782	57
16	805	57
17	807	57
0	807	57