Metrics for cos2 (problem 3.4.1)

analyze3.0ms (0%)

Memory

-36.5MiB live, 2.2MiB 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
50%	50%	50%	0%	0%	0%	0%	2
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 10 to 8 computations (20% saved)

sample2.0s (18.2%)

Memory

17.9MiB live, 2 122.9MiB allocated

Samples

793.0ms	2 255×	2	valid
331.0ms	4 224×	0	valid
196.0ms	549×	3	valid
131.0ms	1 228×	1	valid

Precisions

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

ival-cos: 828.0ms (68.8% of total)

adjust: 113.0ms (9.4% of total)

ival-div: 97.0ms (8.1% of total)

ival-sub: 85.0ms (7.1% of total)

ival-mult: 67.0ms (5.6% of total)

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

exact: 5.0ms (0.4% of total)

ival-assert: 4.0ms (0.3% of total)

Bogosity

preprocess60.0ms (0.6%)

Memory

3.8MiB live, 118.2MiB allocated

Algorithm

1×	egg-herbie

Rules

408×	`lower-fma.f64`
408×	`lower-fma.f32`
324×	`times-frac`
284×	`times-frac`
272×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	32	17
2	102	16
3	299	16
4	757	16
5	1185	16
6	1294	16
7	1310	16
0	6	8
0	10	8
1	19	8
2	30	8
3	46	8
4	82	8
5	131	8
6	188	8
7	323	8
8	621	8
9	1027	8
10	1138	8
0	1138	8

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)) (*.f64 x x))

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

Symmetry

(abs x)

explain141.0ms (1.3%)

Memory

26.7MiB live, 276.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
85	-	3	(2.396074214612259e+57)	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
62	-	1	(1.1542221628286353e-158)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(cos.f64 x)`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	82	6
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`	u/u	57	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	57
↳	`(*.f64 x x)`	underflow	57
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`	n/o	4	0
↳	`(*.f64 x x)`	overflow	43

Confusion

	Predicted +	Predicted -
+	143	1
-	0	112

Precision

1.0

Recall

0.9930555555555556

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	143	1	0
-	0	5	107

Precision?

0.9664429530201343

Recall?

1.0

Freqs

test

number	freq
0	113
1	143

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

46.0ms	152×	2	valid
19.0ms	242×	0	valid
16.0ms	30×	3	valid
9.0ms	88×	1	valid

Compiler

Compiled 60 to 28 computations (53.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 71.0ms

ival-cos: 47.0ms (66.4% of total)

adjust: 8.0ms (11.3% of total)

ival-div: 6.0ms (8.5% of total)

ival-sub: 5.0ms (7.1% of total)

ival-mult: 4.0ms (5.7% of total)

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	46.9%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify32.0ms (0.3%)

Memory

-5.5MiB live, 73.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(cos.f64 x)
✓	cost-diff	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	cost-diff	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Rules

408×	`lower-fma.f64`
408×	`lower-fma.f32`
284×	`times-frac`
272×	`lower-*.f32`
270×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
0	10	19
1	19	19
2	30	19
3	46	19
4	82	19
5	131	19
6	188	19
7	323	19
8	621	19
9	1027	19
10	1138	19
0	1138	19

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize85.0ms (0.8%)

Memory

-26.2MiB live, 94.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	77.1%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
✓	accuracy	71.7%	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Samples

36.0ms	44×	1	valid
23.0ms	76×	2	valid
9.0ms	121×	0	valid
6.0ms	15×	3	valid

Compiler

Compiled 21 to 8 computations (61.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 51.0ms

ival-div: 22.0ms (42.7% of total)

ival-cos: 22.0ms (42.7% of total)

adjust: 3.0ms (5.8% of total)

ival-sub: 3.0ms (5.8% of total)

ival-mult: 2.0ms (3.9% 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

7.1MiB live, 7.1MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

12 calls:

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

simplify460.0ms (4.3%)

Memory

19.1MiB live, 571.4MiB allocated

Algorithm

1×	egg-herbie

Rules

16 752×	`lower-fma.f64`
16 752×	`lower-fma.f32`
3 896×	`lower-*.f64`
3 896×	`lower-*.f32`
1 568×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	284
1	105	284
2	258	284
3	609	284
4	1279	284
5	2001	284
6	2304	284
7	3158	284
8	4639	284
9	6288	284
10	7157	284
11	7373	284
12	7391	284
13	7393	284
14	7798	284
0	8007	266

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(- 1 (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)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 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)) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x 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 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x 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 x (.f64 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 x (.f64 x #s(literal 1/24 binary64)) #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 (*.f64 x 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)
(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)

rewrite298.0ms (2.8%)

Memory

18.2MiB live, 400.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 736×	`lower-/.f32`
4 734×	`lower-/.f64`
3 980×	`lower-fma.f64`
3 980×	`lower-fma.f32`
3 064×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
0	10	17
1	40	17
2	268	17
3	2810	17
0	9656	17

Stop Event

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

Counts

4 → 629

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) #s(literal -1 binary64)))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x (neg.f64 x))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) (*.f64 x (neg.f64 x)))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (neg.f64 (cos.f64 x))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (/.f64 (cos.f64 x) (*.f64 x (neg.f64 x))) #s(literal 1 binary64)))
(+.f64 (/.f64 (cos.f64 x) (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(+.f64 (/.f64 (cos.f64 x) (.f64 x (neg.f64 x))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (neg.f64 (cos.f64 x))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (*.f64 x x)))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x (neg.f64 x))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (.f64 x (.f64 x (cos.f64 x))) (.f64 x (.f64 x (.f64 x x)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (.f64 (.f64 x (neg.f64 x)) (neg.f64 (cos.f64 x))) (.f64 x (.f64 x (.f64 x x)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (.f64 x (/.f64 (cos.f64 x) x)) (*.f64 x x)))
(-.f64 (/.f64 (cos.f64 x) (.f64 x (neg.f64 x))) (/.f64 #s(literal -1 binary64) (.f64 x x)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 x)) (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (*.f64 x x)))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (.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))) (.f64 x 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))) (.f64 x x)))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (.f64 x 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))) (.f64 x x)))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x 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 (.f64 x 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 x (.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 x (.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (fma.f64 (/.f64 (cos.f64 x) (.f64 x x)) (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 (pow.f64 (/.f64 (cos.f64 x) (.f64 x x)) #s(literal 3 binary64)) (fma.f64 (/.f64 (cos.f64 x) (.f64 x x)) (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 x x))) (/.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (.f64 x (.f64 x (.f64 x x)))) (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 x x))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))) (.f64 x (neg.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))) (.f64 x (neg.f64 x))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 x) #s(literal -1 binary64))) (.f64 x (neg.f64 x))) (/.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (cos.f64 x) #s(literal -1 binary64))) (.f64 x (neg.f64 x))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (.f64 (.f64 x x) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 9 binary64)) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (.f64 (.f64 x x) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))))
(-.f64 (/.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (.f64 (.f64 x x) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (.f64 (.f64 x 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 (neg.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (.f64 x (neg.f64 x)))) (/.f64 (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))) (.f64 x (neg.f64 x)))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 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))) (.f64 x (neg.f64 x)))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 9 binary64)) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 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))) (.f64 x (neg.f64 x)))))
(-.f64 (/.f64 (/.f64 #s(literal -1 binary64) (+.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))) (.f64 x (neg.f64 x)))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (+.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))) (.f64 x (neg.f64 x)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (neg.f64 x)) (neg.f64 (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 (.f64 x (neg.f64 x)) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (.f64 (.f64 x (neg.f64 x)) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 9 binary64)) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (.f64 (.f64 x (neg.f64 x)) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))))))
(-.f64 (/.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (.f64 (.f64 x (neg.f64 x)) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (.f64 (.f64 x (neg.f64 x)) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))))))
(-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x))))) (/.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) (.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64))) (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x))))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64))) (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x))))) (/.f64 (/.f64 (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 x (.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (.f64 x (neg.f64 x)))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (.f64 x (neg.f64 x)))))
(-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (.f64 x (neg.f64 x)))) (/.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) (.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (*.f64 x (neg.f64 x)))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64))) (.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (.f64 x (neg.f64 x)))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64))) (.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (.f64 x (neg.f64 x)))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (.f64 x (neg.f64 x)))) (/.f64 (/.f64 (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 (cos.f64 x) #s(literal -1 binary64)) (.f64 x (neg.f64 x)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (neg.f64 x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (.f64 (.f64 x (neg.f64 x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))))
(-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x (neg.f64 x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))) (/.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) (.f64 (*.f64 x (neg.f64 x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64))) (.f64 (.f64 x (neg.f64 x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64))) (.f64 (.f64 x (neg.f64 x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 (.f64 x (neg.f64 x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))) (/.f64 (/.f64 (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 x (neg.f64 x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))))
(-.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) x) x) (/.f64 (/.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))) x) x))
(-.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) x) x) (/.f64 (/.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))) x) x))
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(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal -1 binary64)))
(*.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))))
(.f64 (/.f64 (sin.f64 x) (+.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) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(.f64 (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x 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) (cos.f64 x)) #s(literal 1 binary64)))
(.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(.f64 (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))))
(.f64 (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 3 binary64)))) (fma.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)) #s(literal 1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 x) #s(literal -1 binary64))))
(*.f64 (pow.f64 (/.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 9 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(*.f64 (pow.f64 (/.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(exp.f64 (log.f64 (cos.f64 x)))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64)))
(cos.f64 x)
(-.f64 #s(literal 0 binary64) (neg.f64 (cos.f64 x)))
(neg.f64 (neg.f64 (cos.f64 x)))
(pow.f64 (cos.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (cos.f64 x))
(*.f64 (cos.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 x)))
(*.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (*.f64 x x)))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x (neg.f64 x)))
(neg.f64 (*.f64 x (neg.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 x (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 x x) #s(literal 1 binary64))
(/.f64 (*.f64 x (neg.f64 x)) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(/.f64 (neg.f64 x) (neg.f64 (/.f64 #s(literal 1 binary64) x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 x x)
(*.f64 x (neg.f64 (neg.f64 x)))
(*.f64 x (/.f64 x #s(literal 1 binary64)))
(*.f64 x (pow.f64 (/.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 x (pow.f64 (neg.f64 (neg.f64 x)) #s(literal 1 binary64)))
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (.f64 x (neg.f64 x)))
(.f64 #s(literal -1 binary64) (pow.f64 (.f64 x (neg.f64 x)) #s(literal 1 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 (.f64 #s(literal 1 binary64) x) x)
(*.f64 (neg.f64 (neg.f64 x)) x)
(*.f64 (pow.f64 (neg.f64 x) #s(literal 1 binary64)) (pow.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (pow.f64 (neg.f64 (neg.f64 x)) #s(literal 1 binary64)) x)
(.f64 (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)

eval119.0ms (1.1%)

Memory: -4.7MiB live, 161.4MiB allocated
Compiler: Compiled 15 767 to 1 639 computations (89.6% saved)

prune114.0ms (1.1%)

Memory

3.9MiB live, 280.3MiB allocated

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	655	22	677
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	655	23	678

Accuracy

100.0%

Counts

678 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	46.9%	(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (*.f64 x (neg.f64 x))))
	46.9%	(fma.f64 (cos.f64 x) (/.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
	30.8%	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x x)) (*.f64 x x))
	48.6%	(/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x) (neg.f64 x))
	23.3%	(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	14.3%	(/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x (.f64 x (.f64 x x))))
	35.4%	(/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x (*.f64 x x)))
	47.1%	(/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (/.f64 (cos.f64 x) x))) (.f64 x x))
	46.9%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
✓	46.9%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
	18.6%	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
	46.7%	(/.f64 (+.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (neg.f64 (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
	76.4%	(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 x x))
	14.3%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x))))))
▶	47.3%	(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
	48.5%	(*.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
▶	76.6%	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
▶	46.9%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
	76.2%	(.f64 (sin.f64 x) (/.f64 (sin.f64 x) (.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
	55.1%	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
	54.8%	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 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)))
	54.5%	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
▶	55.3%	#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))

Compiler

Compiled 587 to 344 computations (41.4% saved)

simplify92.0ms (0.8%)

Memory

0.5MiB live, 76.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(/.f64 (cos.f64 x) (*.f64 x (neg.f64 x)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	1728	(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (*.f64 x (neg.f64 x))))
✓	cost-diff	0	(/.f64 (cos.f64 x) (*.f64 x x))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	cost-diff	1024	(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
✓	cost-diff	0	(+.f64 (cos.f64 x) #s(literal -1 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(/.f64 #s(literal -1 binary64) (*.f64 x x))
✓	cost-diff	320	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
✓	cost-diff	0	#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
✓	cost-diff	0	(sin.f64 x)
✓	cost-diff	0	(/.f64 (sin.f64 x) (*.f64 x x))
✓	cost-diff	0	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
✓	cost-diff	384	(/.f64 x #s(literal 2 binary64))

Rules

824×	`lower-fma.f32`
822×	`lower-fma.f64`
688×	`lower-*.f32`
680×	`lower-*.f64`
620×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	132
0	47	120
1	85	120
2	148	120
3	220	120
4	331	120
5	455	120
6	741	120
7	1270	120
8	1659	120
9	2132	120
10	2356	120
11	2559	120
12	2646	120
13	2662	120
14	2662	120
15	2662	120
0	2662	120

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize186.0ms (1.7%)

Memory

4.2MiB live, 247.2MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(neg.f64 x)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	98.8%	(/.f64 (cos.f64 x) (*.f64 x (neg.f64 x)))
✓	accuracy	47.7%	(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (*.f64 x (neg.f64 x))))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	98.8%	(/.f64 (cos.f64 x) (*.f64 x x))
✓	accuracy	98.8%	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	accuracy	49.0%	(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	98.8%	(/.f64 #s(literal -1 binary64) (*.f64 x x))
✓	accuracy	76.6%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
✓	accuracy	71.7%	(+.f64 (cos.f64 x) #s(literal -1 binary64))
✓	accuracy	55.3%	#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))
✓	accuracy	99.7%	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
✓	accuracy	77.6%	(/.f64 (sin.f64 x) (*.f64 x x))

Samples

81.0ms	135×	1	valid
60.0ms	121×	0	valid

Compiler

Compiled 133 to 28 computations (78.9% saved)

Precisions

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

adjust: 24.0ms (24.4% of total)

ival-cos: 20.0ms (20.3% of total)

ival-div: 18.0ms (18.3% of total)

ival-mult: 15.0ms (15.2% of total)

ival-sin: 8.0ms (8.1% of total)

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

ival-sub: 4.0ms (4.1% of total)

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

exact: 1.0ms (1% of total)

ival-neg: 1.0ms (1% of total)

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

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

series18.0ms (0.2%)

Memory

-0.6MiB live, 34.3MiB allocated

Counts

18 → 216

Calls

Call 1

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

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

Calls

54 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(/ (sin x) (* x x))
2.0ms	x	@	inf	(* (/ -1 (* x x)) (+ (cos x) -1))
1.0ms	x	@	inf	(* (/ (sin x) (* x x)) (tan (/ x 2)))
1.0ms	x	@	-inf	(* (/ (sin x) (* x x)) (tan (/ x 2)))
1.0ms	x	@	0	(* (/ (sin x) (* x x)) (tan (/ x 2)))

simplify359.0ms (3.3%)

Memory

-2.5MiB live, 599.7MiB allocated

Algorithm

1×	egg-herbie

Rules

15 370×	`lower-fma.f64`
15 370×	`lower-fma.f32`
4 006×	`lower-*.f64`
4 006×	`lower-*.f32`
3 150×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	118	1474
1	296	1474
2	770	1460
3	2315	1456
4	4433	1456
5	7280	1452
0	8022	1384

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 215

Calls

Call 1

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

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

rewrite268.0ms (2.5%)

Memory

7.9MiB live, 478.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 250×	`lower-fma.f32`
4 248×	`lower-fma.f64`
3 856×	`lower-/.f32`
3 842×	`lower-/.f64`
2 558×	`lower-*.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	109
0	47	97
1	187	94
2	1827	94
0	8878	94

Stop Event

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

Counts

18 → 1 304

Calls

Call 1

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

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

eval377.0ms (3.5%)

Memory: 6.8MiB live, 313.9MiB allocated
Compiler: Compiled 33 696 to 1 971 computations (94.2% saved)

prune263.0ms (2.4%)

Memory

13.0MiB live, 296.0MiB allocated

Pruning

33 alts after pruning (28 fresh and 5 done)

	Pruned	Kept	Total
New	1 678	22	1 700
Fresh	11	6	17
Picked	1	4	5
Done	0	1	1
Total	1 690	33	1 723

Accuracy

100.0%

Counts

1 723 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
	47.5%	(fma.f64 (/.f64 (cos.f64 x) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	46.9%	(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (*.f64 x (neg.f64 x))))
	19.0%	(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x) #s(approx (/ (cos x) (* x (neg x))) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
	46.9%	(fma.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (cos.f64 x) (/.f64 #s(literal 1 binary64) (.f64 x x)))
▶	20.5%	(/.f64 (fma.f64 (/.f64 (cos.f64 x) x) (.f64 x (neg.f64 x)) x) (.f64 x (*.f64 x x)))
	47.2%	(/.f64 (fma.f64 (/.f64 (cos.f64 x) x) x (/.f64 (neg.f64 x) x)) (*.f64 x (neg.f64 x)))
	35.5%	(/.f64 (fma.f64 (neg.f64 (cos.f64 x)) x x) (.f64 x (.f64 x x)))
	14.7%	(/.f64 (fma.f64 x (neg.f64 x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x (.f64 x (*.f64 x (neg.f64 x)))))
	30.8%	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x x)) (*.f64 x x))
	48.6%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	14.3%	(/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x (.f64 x (.f64 x x))))
	35.4%	(/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x (*.f64 x x)))
	47.1%	(/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (/.f64 (cos.f64 x) x))) (.f64 x x))
✓	46.9%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
	18.6%	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
▶	48.6%	(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal -1 binary64) (cos.f64 x))) x)
	76.4%	(/.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (*.f64 x x))
	14.4%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 (cos.f64 x) (.f64 x (neg.f64 x)) (*.f64 x x))))
✓	47.3%	(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
	47.8%	(*.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
	48.5%	(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) (/.f64 #s(literal 1 binary64) x))
▶	76.6%	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
	46.9%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (cos.f64 x)))))
✓	46.9%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
▶	30.7%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
	31.0%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
	35.4%	(.f64 (-.f64 x (.f64 x (cos.f64 x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
	76.6%	(.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (*.f64 x x)))
	75.6%	(.f64 (sin.f64 x) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (tan.f64 (.f64 x #s(literal 1/2 binary64)))))
	55.1%	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
	54.8%	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
▶	54.5%	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
✓	55.3%	#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))

Compiler

Compiled 859 to 492 computations (42.7% saved)

simplify546.0ms (5%)

Memory

-18.3MiB live, 158.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(/.f64 (cos.f64 x) x)
✓	cost-diff	640	(/.f64 (fma.f64 (/.f64 (cos.f64 x) x) (.f64 x (neg.f64 x)) x) (.f64 x (*.f64 x x)))
✓	cost-diff	1024	(fma.f64 (/.f64 (cos.f64 x) x) (*.f64 x (neg.f64 x)) x)
✓	cost-diff	0	(+.f64 #s(literal -1 binary64) (cos.f64 x))
✓	cost-diff	0	(/.f64 #s(literal -1 binary64) x)
✓	cost-diff	320	(*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal -1 binary64) (cos.f64 x)))
✓	cost-diff	384	(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal -1 binary64) (cos.f64 x))) x)
✓	cost-diff	0	#s(approx (+ (cos x) -1) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(/.f64 #s(literal -1 binary64) (*.f64 x x))
✓	cost-diff	192	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 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	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(sin.f64 x)
✓	cost-diff	0	(/.f64 (sin.f64 x) (*.f64 x x))
✓	cost-diff	0	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))

Rules

5 338×	`lower-fma.f32`
5 328×	`lower-fma.f64`
2 918×	`lower-*.f32`
2 896×	`lower-*.f64`
1 252×	`lower-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	43	278
0	76	266
1	159	263
2	339	263
3	770	259
4	1699	259
5	3338	259
6	5660	259
7	7066	259
0	8025	259

Stop Event

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

Calls

Call 1

Inputs
(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
(/.f64 (sin.f64 x) (*.f64 x x))
(sin.f64 x)
x
(*.f64 x x)
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (* x 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))
x
(*.f64 x #s(literal -1/24 binary64))
#s(literal -1/24 binary64)
#s(literal 1/2 binary64)
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
#s(literal -1 binary64)
(*.f64 x x)
x
#s(approx (+ (cos x) -1) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))
(.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))
(fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))
(.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64)))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)))
(fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))
#s(literal 1/40320 binary64)
#s(literal -1/720 binary64)
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal -1 binary64) (cos.f64 x))) x)
(*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal -1 binary64) (cos.f64 x)))
(/.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
x
(+.f64 #s(literal -1 binary64) (cos.f64 x))
(cos.f64 x)
(/.f64 (fma.f64 (/.f64 (cos.f64 x) x) (.f64 x (neg.f64 x)) x) (.f64 x (*.f64 x x)))
(fma.f64 (/.f64 (cos.f64 x) x) (*.f64 x (neg.f64 x)) x)
(/.f64 (cos.f64 x) x)
(cos.f64 x)
x
(*.f64 x (neg.f64 x))
(neg.f64 x)
(.f64 x (.f64 x x))
(*.f64 x x)

Outputs
(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
(/.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (*.f64 x x))
(/.f64 (sin.f64 x) (*.f64 x x))
(sin.f64 x)
x
(*.f64 x x)
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (* x 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))
x
(*.f64 x #s(literal -1/24 binary64))
#s(literal -1/24 binary64)
#s(literal 1/2 binary64)
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
(/.f64 #s(approx (+ (cos x) -1) (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 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))))) (.f64 x (neg.f64 x)))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
#s(literal -1 binary64)
(*.f64 x x)
x
#s(approx (+ (cos x) -1) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))
#s(approx (+ (cos x) -1) (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 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)))))
(.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))
(.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 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))))
(fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/40320 binary64)) #s(literal -1/720 binary64))) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
(.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64)))
(.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/40320 binary64)) #s(literal -1/720 binary64))) #s(literal 1/24 binary64)))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))
(fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/40320 binary64)) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/40320 binary64)) #s(literal -1/720 binary64)))
(fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))
(fma.f64 x (*.f64 x #s(literal 1/40320 binary64)) #s(literal -1/720 binary64))
#s(literal 1/40320 binary64)
#s(literal -1/720 binary64)
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal -1 binary64) (cos.f64 x))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal -1 binary64) (cos.f64 x)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
(/.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
x
(+.f64 #s(literal -1 binary64) (cos.f64 x))
(cos.f64 x)
(/.f64 (fma.f64 (/.f64 (cos.f64 x) x) (.f64 x (neg.f64 x)) x) (.f64 x (*.f64 x x)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(fma.f64 (/.f64 (cos.f64 x) x) (*.f64 x (neg.f64 x)) x)
(-.f64 x (*.f64 x (cos.f64 x)))
(/.f64 (cos.f64 x) x)
(cos.f64 x)
x
(*.f64 x (neg.f64 x))
(neg.f64 x)
(.f64 x (.f64 x x))
(*.f64 x x)

localize490.0ms (4.5%)

Memory

9.1MiB live, 398.9MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	99.8%	(/.f64 (cos.f64 x) x)
✓	accuracy	55.2%	(/.f64 (fma.f64 (/.f64 (cos.f64 x) x) (.f64 x (neg.f64 x)) x) (.f64 x (*.f64 x x)))
✓	accuracy	33.7%	(fma.f64 (/.f64 (cos.f64 x) x) (*.f64 x (neg.f64 x)) x)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	99.9%	(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal -1 binary64) (cos.f64 x))) x)
✓	accuracy	78.6%	(*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal -1 binary64) (cos.f64 x)))
✓	accuracy	71.7%	(+.f64 #s(literal -1 binary64) (cos.f64 x))
✓	accuracy	98.8%	(fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))
✓	accuracy	98.8%	(/.f64 #s(literal -1 binary64) (*.f64 x x))
✓	accuracy	77.0%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
✓	accuracy	54.5%	#s(approx (+ (cos x) -1) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))
✓	accuracy	99.9%	(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
✓	accuracy	99.5%	(*.f64 x #s(literal -1/24 binary64))
✓	accuracy	54.5%	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	accuracy	99.7%	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
✓	accuracy	78.0%	(/.f64 (sin.f64 x) (*.f64 x x))

Samples

290.0ms	121×	0	valid
75.0ms	76×	2	valid
31.0ms	44×	1	valid
16.0ms	14×	3	valid
2.0ms	1×	5	exit

Compiler

Compiled 246 to 46 computations (81.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 272.0ms

const: 133.0ms (48.8% of total)

ival-mult: 51.0ms (18.7% of total)

ival-cos: 23.0ms (8.4% of total)

ival-div: 20.0ms (7.3% of total)

adjust: 15.0ms (5.5% of total)

ival-add: 15.0ms (5.5% of total)

ival-sin: 6.0ms (2.2% of total)

ival-tan: 5.0ms (1.8% of total)

ival-sub: 3.0ms (1.1% of total)

exact: 1.0ms (0.4% of total)

ival-neg: 1.0ms (0.4% of total)

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

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

series16.0ms (0.1%)

Memory

-7.2MiB live, 29.7MiB allocated

Counts

21 → 252

Calls

Call 1

Inputs
#s(alt (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 x) (.f64 x x)) (patch (/.f64 (sin.f64 x) (.f64 x x)) #<representation binary64>) () ())
#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) (patch #s(approx (/ (- 1 (cos x)) ( x 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 (.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) (patch (.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) (.f64 x x)) (patch (/.f64 #s(literal -1 binary64) (.f64 x x)) #<representation binary64>) () ())
#s(alt #s(approx (+ (cos x) -1) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (patch #s(approx (+ (cos x) -1) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal -1 binary64) (cos.f64 x))) x) (patch (/.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal -1 binary64) (cos.f64 x))) x) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal -1 binary64) (cos.f64 x))) (patch (.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal -1 binary64) (cos.f64 x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) x) (patch (/.f64 #s(literal -1 binary64) x) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal -1 binary64) (cos.f64 x)) (patch (+.f64 #s(literal -1 binary64) (cos.f64 x)) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 (cos.f64 x) x) (.f64 x (neg.f64 x)) x) (patch (fma.f64 (/.f64 (cos.f64 x) x) (.f64 x (neg.f64 x)) x) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 (/.f64 (cos.f64 x) x) (.f64 x (neg.f64 x)) x) (.f64 x (.f64 x x))) (patch (/.f64 (fma.f64 (/.f64 (cos.f64 x) x) (.f64 x (neg.f64 x)) x) (.f64 x (.f64 x x))) #<representation binary64>) () ())
#s(alt (/.f64 (cos.f64 x) x) (patch (/.f64 (cos.f64 x) x) #<representation binary64>) () ())
#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())
#s(alt (tan.f64 (.f64 x #s(literal 1/2 binary64))) (patch (tan.f64 (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())

Outputs
#s(alt 1/2 (taylor 0 x) (#s(alt (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/24 (pow x 2))) (taylor 0 x) (#s(alt (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
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#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 (* 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 -1/720 (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/40320 (pow x 2)) 1/720) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/40320 (pow x 2)) 1/720) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/40320 (pow x 2)) 1/720) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/40320 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/40320 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())

Calls

63 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(/ (cos x) x)
1.0ms	x	@	inf	(/ (+ (* (/ (cos x) x) (* x (neg x))) x) (* x (* x x)))
0.0ms	x	@	inf	(* (/ -1 x) (+ -1 (cos x)))
0.0ms	x	@	-inf	(/ (cos x) x)
0.0ms	x	@	inf	(+ (* (/ (cos x) x) (* x (neg x))) x)

simplify440.0ms (4.1%)

Memory

-16.8MiB live, 751.9MiB allocated

Algorithm

1×	egg-herbie

Rules

18 410×	`lower-fma.f64`
18 410×	`lower-fma.f32`
5 194×	`lower-*.f64`
5 194×	`lower-*.f32`
3 534×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	129	1734
1	348	1720
2	871	1720
3	2544	1720
4	5861	1720
0	9055	1618

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 251

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ 1 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))) x)
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(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
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (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) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -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
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* -1 (/ (- (cos x) 1) x))
(* -1 (/ (- (cos x) 1) x))
(* -1 (/ (- (cos x) 1) x))
(* -1 (/ (- (cos x) 1) x))
(* -1 (/ (- (cos x) 1) x))
(* -1 (/ (- (cos x) 1) x))
(* -1 (/ (- (cos x) 1) x))
(* -1 (/ (- (cos x) 1) x))
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(* 1/2 (pow x 3))
(* (pow x 3) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 3) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 3) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* x (+ 1 (* -1 (cos x))))
(* x (+ 1 (* -1 (cos x))))
(* x (+ 1 (* -1 (cos x))))
(* x (+ 1 (* -1 (cos x))))
(* -1 (* x (- (cos x) 1)))
(* -1 (* x (- (cos x) 1)))
(* -1 (* x (- (cos x) 1)))
(* -1 (* x (- (cos x) 1)))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/ 1 x)
(/ (+ 1 (* -1/2 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) 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)
(* 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)))
-1/720
(- (* 1/40320 (pow x 2)) 1/720)
(- (* 1/40320 (pow x 2)) 1/720)
(- (* 1/40320 (pow x 2)) 1/720)
(* 1/40320 (pow x 2))
(* (pow x 2) (- 1/40320 (* 1/720 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/40320 (* 1/720 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/40320 (* 1/720 (/ 1 (pow x 2)))))
(* 1/40320 (pow x 2))
(* (pow x 2) (- 1/40320 (* 1/720 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/40320 (* 1/720 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/40320 (* 1/720 (/ 1 (pow x 2)))))
(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)

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

rewrite370.0ms (3.4%)

Memory

6.9MiB live, 601.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 900×	`lower-/.f32`
4 888×	`lower-/.f64`
3 794×	`lower-*.f32`
3 772×	`lower-*.f64`
3 596×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	179
0	76	173
1	296	169
2	2075	163
0	8255	161

Stop Event

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

Counts

21 → 760

Calls

Call 1

Inputs
(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
(/.f64 (sin.f64 x) (*.f64 x x))
(sin.f64 x)
(*.f64 x x)
#s(approx (/ (- 1 (cos x)) (* x 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))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
#s(approx (+ (cos x) -1) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal -1 binary64) (cos.f64 x))) x)
(*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal -1 binary64) (cos.f64 x)))
(/.f64 #s(literal -1 binary64) x)
(+.f64 #s(literal -1 binary64) (cos.f64 x))
(fma.f64 (/.f64 (cos.f64 x) x) (*.f64 x (neg.f64 x)) x)
(/.f64 (fma.f64 (/.f64 (cos.f64 x) x) (.f64 x (neg.f64 x)) x) (.f64 x (*.f64 x x)))
(/.f64 (cos.f64 x) x)
(cos.f64 x)
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))
(.f64 x (.f64 x x))

Outputs
(/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 (.f64 x x) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) (sin.f64 x)) (tan.f64 (.f64 x #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x x) (cos.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 (.f64 x x) (sin.f64 x)) (cos.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 #s(literal 1 binary64) (sin.f64 (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (neg.f64 (.f64 x x)) (cos.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (cos.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 (/.f64 (sin.f64 x) x) (sin.f64 (.f64 x #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) (.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) (sin.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 (.f64 x x) (sin.f64 x))) (.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) (neg.f64 (.f64 x x))) (.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) x) (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 (sin.f64 x) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (sin.f64 (.f64 x #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) (sin.f64 x)) (.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (.f64 x x)) (.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 x (.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 (sin.f64 x) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) (sin.f64 x)) (.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (.f64 x x)) (.f64 (neg.f64 (sin.f64 x)) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 x (.f64 (/.f64 (sin.f64 x) x) (tan.f64 (.f64 x #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 (sin.f64 x) (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))))
(/.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (*.f64 x x))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 (.f64 x x) (cos.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 (/.f64 (.f64 x x) (sin.f64 x)) (cos.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (.f64 (neg.f64 (sin.f64 x)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 (neg.f64 (.f64 x x)) (cos.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (.f64 (/.f64 (sin.f64 x) x) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 x (cos.f64 (.f64 x #s(literal 1/2 binary64)))))
(/.f64 (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) (*.f64 x x)))
(/.f64 (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)) (.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 (*.f64 x x) (sin.f64 x))))
(/.f64 (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x))) (.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) (neg.f64 (*.f64 x x))))
(/.f64 (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 (sin.f64 x) x)) (.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) x))
(/.f64 (neg.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64))))) (neg.f64 (*.f64 x x)))
(/.f64 (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/.f64 (.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 x x) (sin.f64 x)))
(/.f64 (.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x))) (neg.f64 (*.f64 x x)))
(/.f64 (.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 (sin.f64 x) x)) x)
(/.f64 (.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (/.f64 (*.f64 x x) (sin.f64 x)))
(/.f64 (.f64 (neg.f64 (sin.f64 x)) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (neg.f64 (*.f64 x x)))
(/.f64 (.f64 (/.f64 (sin.f64 x) x) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) x)
(/.f64 (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 (sin.f64 x) (.f64 x x))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/.f64 (/.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) x) x)
(/.f64 (neg.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (.f64 x x) (sin.f64 x))))
(/.f64 (neg.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 x #s(literal 1/2 binary64))))) (neg.f64 (.f64 (.f64 x x) (cos.f64 (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64))))) (neg.f64 (.f64 (/.f64 (.f64 x x) (sin.f64 x)) (cos.f64 (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (.f64 (neg.f64 (sin.f64 x)) (sin.f64 (.f64 x #s(literal 1/2 binary64))))) (neg.f64 (.f64 (neg.f64 (.f64 x x)) (cos.f64 (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (.f64 (/.f64 (sin.f64 x) x) (sin.f64 (.f64 x #s(literal 1/2 binary64))))) (neg.f64 (.f64 x (cos.f64 (.f64 x #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x))) (neg.f64 (.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) (*.f64 x x))))
(/.f64 (neg.f64 (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))) (neg.f64 (.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 (*.f64 x x) (sin.f64 x)))))
(/.f64 (neg.f64 (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))) (neg.f64 (.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) (neg.f64 (*.f64 x x)))))
(/.f64 (neg.f64 (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 (sin.f64 x) x))) (neg.f64 (.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) x)))
(/.f64 (neg.f64 (neg.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64)))))) (neg.f64 (neg.f64 (*.f64 x x))))
(/.f64 (neg.f64 (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (sin.f64 (.f64 x #s(literal 1/2 binary64))))) (neg.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))) (neg.f64 (/.f64 (*.f64 x x) (sin.f64 x))))
(/.f64 (neg.f64 (.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))) (neg.f64 (neg.f64 (*.f64 x x))))
(/.f64 (neg.f64 (.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 (sin.f64 x) x))) (neg.f64 x))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64))))) (neg.f64 (/.f64 (*.f64 x x) (sin.f64 x))))
(/.f64 (neg.f64 (.f64 (neg.f64 (sin.f64 x)) (tan.f64 (.f64 x #s(literal 1/2 binary64))))) (neg.f64 (neg.f64 (*.f64 x x))))
(/.f64 (neg.f64 (.f64 (/.f64 (sin.f64 x) x) (tan.f64 (.f64 x #s(literal 1/2 binary64))))) (neg.f64 x))
(/.f64 (neg.f64 (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 (sin.f64 x) (.f64 x x)))) (neg.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (/.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) x)) (neg.f64 x))
(pow.f64 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal -1 binary64))
(.f64 (sin.f64 x) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (tan.f64 (.f64 x #s(literal 1/2 binary64)))))
(.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (*.f64 x x)))
(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
(.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 (sin.f64 x) (*.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sin.f64 x))))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 x (sin.f64 x))))
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(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1625702400 binary64)) (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal 1/720 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/518400 binary64) (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal 1/720 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1625702400 binary64)) (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal 1/720 binary64))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1625702400 binary64)) (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal 1/720 binary64))) (fma.f64 (/.f64 #s(literal 1/518400 binary64) (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal 1/720 binary64))) (/.f64 #s(literal 1/518400 binary64) (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal 1/720 binary64))) (.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1625702400 binary64)) (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal 1/720 binary64))) (/.f64 #s(literal 1/518400 binary64) (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal 1/720 binary64)))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/65548320768000 binary64)) #s(literal -1/373248000 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1625702400 binary64) #s(literal 1/518400 binary64)) (.f64 (*.f64 x x) #s(literal -1/29030400 binary64)))))
(.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1625702400 binary64) #s(literal -1/518400 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal 1/720 binary64))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))

eval143.0ms (1.3%)

Memory: 7.4MiB live, 295.3MiB allocated
Compiler: Compiled 22 597 to 2 606 computations (88.5% saved)

prune311.0ms (2.9%)

Memory

16.2MiB live, 371.3MiB allocated

Pruning

40 alts after pruning (31 fresh and 9 done)

	Pruned	Kept	Total
New	1 107	12	1 119
Fresh	4	19	23
Picked	1	4	5
Done	0	5	5
Total	1 112	40	1 152

Accuracy

100.0%

Counts

1 152 → 40

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	47.5%	(fma.f64 (/.f64 (cos.f64 x) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	46.9%	(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (*.f64 x (neg.f64 x))))
	19.0%	(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x) #s(approx (/ (cos x) (* x (neg x))) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
✓	20.5%	(/.f64 (fma.f64 (/.f64 (cos.f64 x) x) (.f64 x (neg.f64 x)) x) (.f64 x (*.f64 x x)))
	3.9%	(/.f64 (fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x) (.f64 x (neg.f64 x)) x) (.f64 x (*.f64 x x)))
	20.4%	(/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) x) (.f64 x (*.f64 x x)))
	35.5%	(/.f64 (fma.f64 (neg.f64 (cos.f64 x)) x x) (.f64 x (.f64 x x)))
	14.7%	(/.f64 (fma.f64 x (neg.f64 x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x (.f64 x (*.f64 x (neg.f64 x)))))
	46.8%	(/.f64 (/.f64 (fma.f64 #s(literal 1 binary64) x (.f64 x (neg.f64 (cos.f64 x)))) (.f64 x x)) x)
	30.8%	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x x)) (*.f64 x x))
	48.6%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	48.6%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))) x)
	14.3%	(/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x (.f64 x (.f64 x x))))
	35.4%	(/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x (*.f64 x x)))
✓	46.9%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
▶	18.6%	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
	48.1%	(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (fma.f64 (/.f64 (cos.f64 x) x) x #s(literal -1 binary64))) x)
	48.1%	(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal -1 binary64))) x)
✓	48.6%	(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal -1 binary64) (cos.f64 x))) x)
	32.8%	(/.f64 (.f64 (/.f64 #s(literal -1 binary64) x) #s(approx (+ -1 (cos x)) (.f64 (*.f64 x x) #s(literal -1/2 binary64)))) x)
	76.4%	(/.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (*.f64 x x))
	32.1%	(/.f64 (neg.f64 #s(approx (+ (cos x) -1) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) (.f64 x x))
▶	54.8%	(/.f64 #s(approx (* (/ -1 x) (+ -1 (cos x))) (.f64 x (fma.f64 x (.f64 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)))) x)
	14.4%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 (cos.f64 x) (.f64 x (neg.f64 x)) (*.f64 x x))))
	47.6%	(/.f64 #s(literal 1 binary64) (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
✓	47.3%	(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
▶	47.8%	(*.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
	48.5%	(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) (/.f64 #s(literal 1 binary64) x))
✓	76.6%	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
	46.9%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (cos.f64 x)))))
✓	46.9%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
	31.0%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))
	30.7%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))
	35.4%	(.f64 (-.f64 x (.f64 x (cos.f64 x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
▶	76.6%	(.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (*.f64 x x)))
	75.6%	(.f64 (sin.f64 x) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (tan.f64 (.f64 x #s(literal 1/2 binary64)))))
	55.1%	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
	54.8%	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
✓	54.5%	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
✓	55.3%	#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))

Compiler

Compiled 1 061 to 607 computations (42.8% saved)

simplify187.0ms (1.7%)

Memory

5.3MiB live, 244.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal -1 binary64) x)
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(/.f64 (cos.f64 x) x)
✓	cost-diff	1600	(fma.f64 (/.f64 (cos.f64 x) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	cost-diff	0	(+.f64 (cos.f64 x) #s(literal -1 binary64))
✓	cost-diff	0	(/.f64 #s(literal -1 binary64) x)
✓	cost-diff	320	(*.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
✓	cost-diff	384	(/.f64 (/.f64 #s(literal -1 binary64) x) x)
✓	cost-diff	0	(fma.f64 x (.f64 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))
✓	cost-diff	0	(.f64 x (fma.f64 x (.f64 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)))
✓	cost-diff	0	#s(approx (* (/ -1 x) (+ -1 (cos x))) (.f64 x (fma.f64 x (.f64 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))))
✓	cost-diff	0	(/.f64 #s(approx (* (/ -1 x) (+ -1 (cos x))) (.f64 x (fma.f64 x (.f64 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)))) x)
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	#s(approx (cos x) #s(literal 1 binary64))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
✓	cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
✓	cost-diff	0	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))
✓	cost-diff	0	(sin.f64 x)
✓	cost-diff	0	(.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (*.f64 x x)))

Rules

6 116×	`lower-fma.f32`
6 108×	`lower-fma.f64`
2 222×	`lower-*.f32`
2 208×	`lower-*.f64`
1 254×	`lower--.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	248
0	64	245
1	136	241
2	279	241
3	560	237
4	1059	237
5	1373	237
6	1605	237
7	2290	237
8	3333	237
9	5824	237
10	7387	237
0	8060	237

Stop Event

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

Calls

Call 1

Inputs
(.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (*.f64 x x)))
(sin.f64 x)
x
(/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 x x)
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (cos x) #s(literal 1 binary64))
(*.f64 x x)
x
(/.f64 #s(approx (* (/ -1 x) (+ -1 (cos x))) (.f64 x (fma.f64 x (.f64 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)))) x)
#s(approx (* (/ -1 x) (+ -1 (cos x))) (.f64 x (fma.f64 x (.f64 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))))
(.f64 x (fma.f64 x (.f64 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)))
x
(fma.f64 x (.f64 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))
(.f64 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)))
(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))
(*.f64 x x)
(fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))
(*.f64 x #s(literal -1/40320 binary64))
#s(literal -1/40320 binary64)
#s(literal 1/720 binary64)
#s(literal -1/24 binary64)
#s(literal 1/2 binary64)
(*.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) x) x)
(/.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
x
(+.f64 (cos.f64 x) #s(literal -1 binary64))
(cos.f64 x)
(fma.f64 (/.f64 (cos.f64 x) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (cos.f64 x) x)
(cos.f64 x)
x
(/.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
(/.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)

Outputs
(.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (*.f64 x x)))
(/.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (*.f64 x x))
(sin.f64 x)
x
(/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 x x)
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (cos x) #s(literal 1 binary64))
(*.f64 x x)
x
(/.f64 #s(approx (* (/ -1 x) (+ -1 (cos x))) (.f64 x (fma.f64 x (.f64 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)))) x)
#s(approx (* (/ -1 x) (+ -1 (cos x))) (.f64 x (fma.f64 x (.f64 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))))
(.f64 x (fma.f64 x (.f64 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)))
x
(fma.f64 x (.f64 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))
(.f64 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)))
(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))
(*.f64 x x)
(fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))
(*.f64 x #s(literal -1/40320 binary64))
#s(literal -1/40320 binary64)
#s(literal 1/720 binary64)
#s(literal -1/24 binary64)
#s(literal 1/2 binary64)
(*.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/.f64 (/.f64 #s(literal -1 binary64) x) x)
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
x
(+.f64 (cos.f64 x) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (cos.f64 x))
(cos.f64 x)
(fma.f64 (/.f64 (cos.f64 x) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/.f64 (cos.f64 x) x)
(cos.f64 x)
x
(/.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
(/.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)

localize196.0ms (1.8%)

Memory

2.5MiB live, 277.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	99.8%	(/.f64 (cos.f64 x) x)
✓	accuracy	98.8%	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	accuracy	48.4%	(fma.f64 (/.f64 (cos.f64 x) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	99.8%	(/.f64 (/.f64 #s(literal -1 binary64) x) x)
✓	accuracy	76.6%	(*.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
✓	accuracy	71.7%	(+.f64 (cos.f64 x) #s(literal -1 binary64))
✓	accuracy	99.9%	(fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))
✓	accuracy	99.9%	(/.f64 #s(approx (* (/ -1 x) (+ -1 (cos x))) (.f64 x (fma.f64 x (.f64 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)))) x)
✓	accuracy	99.6%	(.f64 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)))
✓	accuracy	54.7%	#s(approx (* (/ -1 x) (+ -1 (cos x))) (.f64 x (fma.f64 x (.f64 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))))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	77.1%	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
✓	accuracy	71.7%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
✓	accuracy	58.9%	#s(approx (cos x) #s(literal 1 binary64))
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	accuracy	99.7%	(.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (*.f64 x x)))
✓	accuracy	77.6%	(/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))

Samples

99.0ms	134×	1	valid
47.0ms	121×	0	valid
1.0ms	1×	3	valid

Compiler

Compiled 218 to 38 computations (82.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 117.0ms

ival-mult: 24.0ms (20.4% of total)

const: 21.0ms (17.9% of total)

ival-cos: 21.0ms (17.9% of total)

ival-div: 16.0ms (13.6% of total)

ival-add: 10.0ms (8.5% of total)

ival-sin: 9.0ms (7.7% of total)

adjust: 8.0ms (6.8% of total)

ival-sub: 4.0ms (3.4% of total)

ival-tan: 4.0ms (3.4% of total)

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

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

exact: 0.0ms (0% of total)

series30.0ms (0.3%)

Memory

-21.7MiB live, 15.8MiB allocated

Counts

22 → 264

Calls

Call 1

Inputs
#s(alt (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) (patch (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) #<representation binary64>) () ())
#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())
#s(alt (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) (patch (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) #<representation binary64>) () ())
#s(alt (tan.f64 (.f64 x #s(literal 1/2 binary64))) (patch (tan.f64 (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (.f64 x x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (.f64 x x)) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (* (/ -1 x) (+ -1 (cos x))) (.f64 x (fma.f64 x (.f64 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)))) x) (patch (/.f64 #s(approx (* (/ -1 x) (+ -1 (cos x))) (.f64 x (fma.f64 x (.f64 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)))) x) #<representation binary64>) () ())
#s(alt #s(approx (* (/ -1 x) (+ -1 (cos x))) (.f64 x (fma.f64 x (.f64 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)))) (patch #s(approx (* (/ -1 x) (+ -1 (cos x))) (.f64 x (fma.f64 x (.f64 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)))) #<representation binary64>) () ())
#s(alt (.f64 x (fma.f64 x (.f64 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))) (patch (.f64 x (fma.f64 x (.f64 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))) #<representation binary64>) () ())
#s(alt (fma.f64 x (.f64 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)) (patch (fma.f64 x (.f64 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)) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 #s(literal -1 binary64) x) x) (patch (/.f64 (/.f64 #s(literal -1 binary64) x) x) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) (+.f64 (cos.f64 x) #s(literal -1 binary64))) (patch (.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) (+.f64 (cos.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) x) (patch (/.f64 #s(literal -1 binary64) x) #<representation binary64>) () ())
#s(alt (+.f64 (cos.f64 x) #s(literal -1 binary64)) (patch (+.f64 (cos.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 (cos.f64 x) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x x))) (patch (fma.f64 (/.f64 (cos.f64 x) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())
#s(alt (/.f64 (cos.f64 x) x) (patch (/.f64 (cos.f64 x) x) #<representation binary64>) () ())
#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())
#s(alt (.f64 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))) (patch (.f64 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))) #<representation binary64>) () ())
#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())

Outputs
#s(alt 1/2 (taylor 0 x) (#s(alt (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) (patch (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/24 (pow x 2))) (taylor 0 x) (#s(alt (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) (patch (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))) (taylor 0 x) (#s(alt (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) (patch (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))) (taylor 0 x) (#s(alt (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) (patch (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x)))) (taylor inf x) (#s(alt (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) (patch (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x)))) (taylor inf x) (#s(alt (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) (patch (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x)))) (taylor inf x) (#s(alt (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) (patch (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x)))) (taylor inf x) (#s(alt (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) (patch (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) (patch (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) (patch (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) (patch (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))) (patch (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x 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>) () ())) ())
#s(alt (/ 1/2 x) (taylor 0 x) (#s(alt (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) (patch (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* 1/24 (pow x 2))) x) (taylor 0 x) (#s(alt (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) (patch (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))) x) (taylor 0 x) (#s(alt (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) (patch (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))) x) (taylor 0 x) (#s(alt (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) (patch (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x)))) (taylor inf x) (#s(alt (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) (patch (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x)))) (taylor inf x) (#s(alt (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) (patch (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x)))) (taylor inf x) (#s(alt (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) (patch (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x)))) (taylor inf x) (#s(alt (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) (patch (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) (patch (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) (patch (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) (patch (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) (patch (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (tan.f64 (.f64 x #s(literal 1/2 binary64))) (patch (tan.f64 (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (tan.f64 (.f64 x #s(literal 1/2 binary64))) (patch (tan.f64 (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))) (taylor 0 x) (#s(alt (tan.f64 (.f64 x #s(literal 1/2 binary64))) (patch (tan.f64 (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))) (taylor 0 x) (#s(alt (tan.f64 (.f64 x #s(literal 1/2 binary64))) (patch (tan.f64 (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor inf x) (#s(alt (tan.f64 (.f64 x #s(literal 1/2 binary64))) (patch (tan.f64 (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor inf x) (#s(alt (tan.f64 (.f64 x #s(literal 1/2 binary64))) (patch (tan.f64 (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor inf x) (#s(alt (tan.f64 (.f64 x #s(literal 1/2 binary64))) (patch (tan.f64 (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor inf x) (#s(alt (tan.f64 (.f64 x #s(literal 1/2 binary64))) (patch (tan.f64 (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor -inf x) (#s(alt (tan.f64 (.f64 x #s(literal 1/2 binary64))) (patch (tan.f64 (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor -inf x) (#s(alt (tan.f64 (.f64 x #s(literal 1/2 binary64))) (patch (tan.f64 (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor -inf x) (#s(alt (tan.f64 (.f64 x #s(literal 1/2 binary64))) (patch (tan.f64 (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor -inf x) (#s(alt (tan.f64 (.f64 x #s(literal 1/2 binary64))) (patch (tan.f64 (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (.f64 x x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/24 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (.f64 x x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (.f64 x x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (.f64 x x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (pow x 2)) (taylor inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (.f64 x x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
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#s(alt (* -1/40320 (pow x 5)) (taylor -inf x) (#s(alt (.f64 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))) (patch (.f64 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))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- 1/40320 (* 1/720 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 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))) (patch (.f64 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))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 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))) (patch (.f64 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))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 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))) (patch (.f64 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))) #<representation binary64>) () ())) ())
#s(alt 1/720 (taylor 0 x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/720 (* -1/40320 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/720 (* -1/40320 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/720 (* -1/40320 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/40320 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320)) (taylor inf x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320)) (taylor inf x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320)) (taylor inf x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/40320 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320)) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320)) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320)) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) (patch (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())

Calls

66 calls:

Time	Variable		Point	Expression
15.0ms	x	@	inf	(/ (/ -1 x) x)
3.0ms	x	@	inf	(* x (+ (* x (* x (+ (* (* x x) (+ (* x (* x -1/40320)) 1/720)) -1/24))) 1/2))
0.0ms	x	@	inf	(* x (+ (* (* x x) (+ (* x (* x -1/40320)) 1/720)) -1/24))
0.0ms	x	@	inf	(/ (tan (* x 1/2)) (* x x))
0.0ms	x	@	-inf	(* x (+ (* x (* x (+ (* (* x x) (+ (* x (* x -1/40320)) 1/720)) -1/24))) 1/2))

simplify347.0ms (3.2%)

Memory

14.5MiB live, 454.4MiB allocated

Algorithm

1×	egg-herbie

Rules

11 662×	`lower-fma.f64`
11 662×	`lower-fma.f32`
3 600×	`lower-*.f64`
3 600×	`lower-*.f32`
2 840×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	163	2110
1	426	2102
2	1098	2096
3	3366	2096
4	5959	2096
0	8165	1986

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 263

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 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)
(/ 1/2 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))))))) x)
(/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))
(/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))
(/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))
(/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))
(/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))
(/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))
(/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))
(/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(- 1 (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)
(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
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* -1 (/ (- (cos x) 1) x))
(* -1 (/ (- (cos x) 1) x))
(* -1 (/ (- (cos x) 1) x))
(* -1 (/ (- (cos x) 1) x))
(* -1 (/ (- (cos x) 1) x))
(* -1 (/ (- (cos x) 1) x))
(* -1 (/ (- (cos x) 1) x))
(* -1 (/ (- (cos x) 1) x))
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* -1/40320 (pow x 7))
(* (pow x 7) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 7) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 7) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/40320 (pow x 7))
(* -1 (* (pow x 7) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/40320 (/ 1/24 (pow x 4))) (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(* -1/40320 (pow x 6))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/40320 (pow x 6))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
(/ -1 (pow x 2))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ 1 x)
(/ (+ 1 (* -1/2 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) 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)
(* -1/24 x)
(* x (- (* 1/720 (pow x 2)) 1/24))
(* x (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))
(* x (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))
(* -1/40320 (pow x 5))
(* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/40320 (pow x 5))
(* -1 (* (pow x 5) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2))))))
1/720
(+ 1/720 (* -1/40320 (pow x 2)))
(+ 1/720 (* -1/40320 (pow x 2)))
(+ 1/720 (* -1/40320 (pow x 2)))
(* -1/40320 (pow x 2))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* -1/40320 (pow x 2))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))

Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
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(.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (+.f64 (/.f64 #s(literal 1/720 binary64) (.f64 x x)) (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))
(* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (+.f64 (/.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (*.f64 x x))))))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/ -1 (pow x 2))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(.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) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 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)))
(- (cos x) 1)
(+.f64 (cos.f64 x) #s(literal -1 binary64))
(- (cos x) 1)
(+.f64 (cos.f64 x) #s(literal -1 binary64))
(- (cos x) 1)
(+.f64 (cos.f64 x) #s(literal -1 binary64))
(- (cos x) 1)
(+.f64 (cos.f64 x) #s(literal -1 binary64))
(- (cos x) 1)
(+.f64 (cos.f64 x) #s(literal -1 binary64))
(- (cos x) 1)
(+.f64 (cos.f64 x) #s(literal -1 binary64))
(- (cos x) 1)
(+.f64 (cos.f64 x) #s(literal -1 binary64))
(- (cos x) 1)
(+.f64 (cos.f64 x) #s(literal -1 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) x)
(/.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) x)
(/.f64 (fma.f64 x (.f64 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))) #s(literal 1 binary64)) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) 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 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #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 x (.f64 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))) #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)
(* -1/24 x)
(*.f64 #s(literal -1/24 binary64) x)
(* x (- (* 1/720 (pow x 2)) 1/24))
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)))
(* x (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
(* x (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
(* -1/40320 (pow x 5))
(.f64 #s(literal -1/40320 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) x))
(* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) x))
(* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (+.f64 (/.f64 #s(literal 1/720 binary64) (.f64 x x)) (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x (.f64 x (*.f64 x x))) x))
(* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (+.f64 (/.f64 #s(literal 1/720 binary64) (.f64 x x)) (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x (.f64 x (*.f64 x x))) x))
(* -1/40320 (pow x 5))
(.f64 #s(literal -1/40320 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) x))
(* -1 (* (pow x 5) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))))
(.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) x))
(* -1 (* (pow x 5) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2))))))
(.f64 (+.f64 (/.f64 #s(literal 1/720 binary64) (.f64 x x)) (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x (.f64 x (*.f64 x x))) x))
(* -1 (* (pow x 5) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2))))))
(.f64 (+.f64 (/.f64 #s(literal 1/720 binary64) (.f64 x x)) (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x (.f64 x (*.f64 x x))) x))
1/720
#s(literal 1/720 binary64)
(+ 1/720 (* -1/40320 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))
(+ 1/720 (* -1/40320 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))
(+ 1/720 (* -1/40320 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))

rewrite346.0ms (3.2%)

Memory

7.8MiB live, 526.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 900×	`lower-/.f32`
4 886×	`lower-/.f64`
4 030×	`lower-*.f32`
4 016×	`lower-*.f64`
2 638×	`lower--.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	203
0	64	200
1	267	193
2	2260	193
0	8171	193

Stop Event

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

Counts

22 → 829

Calls

Call 1

Inputs
(.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (*.f64 x x)))
(sin.f64 x)
(/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 x x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (cos x) #s(literal 1 binary64))
(*.f64 x x)
(/.f64 #s(approx (* (/ -1 x) (+ -1 (cos x))) (.f64 x (fma.f64 x (.f64 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)))) x)
#s(approx (* (/ -1 x) (+ -1 (cos x))) (.f64 x (fma.f64 x (.f64 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))))
(.f64 x (fma.f64 x (.f64 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)))
(fma.f64 x (.f64 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))
(/.f64 (/.f64 #s(literal -1 binary64) x) x)
(*.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
(/.f64 #s(literal -1 binary64) x)
(+.f64 (cos.f64 x) #s(literal -1 binary64))
(fma.f64 (/.f64 (cos.f64 x) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (cos.f64 x) x)
(cos.f64 x)
(.f64 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)))
(fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))
(/.f64 #s(literal 1 binary64) (*.f64 x x))

Outputs
(/.f64 (sin.f64 x) (/.f64 (.f64 x x) (tan.f64 (.f64 x #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))))
(/.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (*.f64 x x))
(/.f64 (neg.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64))))) (neg.f64 (*.f64 x x)))
(/.f64 (.f64 (sin.f64 x) #s(literal 1 binary64)) (/.f64 (.f64 x x) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (.f64 (sin.f64 x) (neg.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))))) (neg.f64 (*.f64 x x)))
(/.f64 (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) x)) x)
(/.f64 (.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 (.f64 x x) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (.f64 (neg.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) (neg.f64 (*.f64 x x)))
(/.f64 (.f64 (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) x) (sin.f64 x)) x)
(/.f64 (/.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) x) x)
(/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (/.f64 (.f64 x x) (tan.f64 (.f64 x #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64)))))) (neg.f64 (neg.f64 (*.f64 x x))))
(/.f64 (neg.f64 (.f64 (sin.f64 x) #s(literal 1 binary64))) (neg.f64 (/.f64 (.f64 x x) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (.f64 (sin.f64 x) (neg.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))))) (neg.f64 (neg.f64 (*.f64 x x))))
(/.f64 (neg.f64 (.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) x))) (neg.f64 x))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (sin.f64 x))) (neg.f64 (/.f64 (.f64 x x) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (.f64 (neg.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))) (neg.f64 (neg.f64 (*.f64 x x))))
(/.f64 (neg.f64 (.f64 (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) x) (sin.f64 x))) (neg.f64 x))
(/.f64 (neg.f64 (/.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) x)) (neg.f64 x))
(pow.f64 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))) #s(literal -1 binary64))
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(/.f64 (neg.f64 (-.f64 #s(literal 1/518400 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1625702400 binary64)))) (neg.f64 (-.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x #s(literal -1/40320 binary64))))))
(pow.f64 (/.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1625702400 binary64) #s(literal 1/518400 binary64)) (.f64 (.f64 x x) #s(literal -1/29030400 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/65548320768000 binary64)) #s(literal 1/373248000 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal -1/720 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1625702400 binary64) #s(literal -1/518400 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/65548320768000 binary64)) #s(literal 1/373248000 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1625702400 binary64) #s(literal 1/518400 binary64)) (.f64 (*.f64 x x) #s(literal -1/29030400 binary64)))))
(.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1625702400 binary64) #s(literal -1/518400 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal -1/720 binary64))))
(exp.f64 (*.f64 #s(literal -2 binary64) (log.f64 x)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -2 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(neg.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (neg.f64 (.f64 x (.f64 x #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 x x)))
(/.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal -1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (neg.f64 (*.f64 x x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x))))
(/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x))
(/.f64 (/.f64 #s(literal 1 binary64) x) x)
(/.f64 (/.f64 #s(literal 1 binary64) x) (neg.f64 (neg.f64 x)))
(pow.f64 x #s(literal -2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal -2 binary64))
(pow.f64 (*.f64 x #s(literal -1 binary64)) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal -1/2 binary64))
(pow.f64 (.f64 (.f64 x #s(literal -1 binary64)) (neg.f64 x)) #s(literal -1 binary64))
(pow.f64 (.f64 (neg.f64 x) (.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))
(pow.f64 (neg.f64 (neg.f64 (*.f64 x x))) #s(literal -1 binary64))
(pow.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(pow.f64 (.f64 (.f64 x #s(literal -1 binary64)) (*.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) x))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal -1 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x))

eval152.0ms (1.4%)

Memory: 9.5MiB live, 305.5MiB allocated
Compiler: Compiled 25 874 to 2 348 computations (90.9% saved)

prune204.0ms (1.9%)

Memory

-15.1MiB live, 398.5MiB allocated

Pruning

48 alts after pruning (34 fresh and 14 done)

	Pruned	Kept	Total
New	1 213	9	1 222
Fresh	1	25	26
Picked	0	5	5
Done	0	9	9
Total	1 214	48	1 262

Accuracy

100.0%

Counts

1 262 → 48

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	47.5%	(fma.f64 (/.f64 (cos.f64 x) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
	4.3%	(fma.f64 (/.f64 #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x x)))
	20.0%	(fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	46.9%	(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (*.f64 x (neg.f64 x))))
	19.0%	(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x) #s(approx (/ (cos x) (* x (neg x))) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
✓	20.5%	(/.f64 (fma.f64 (/.f64 (cos.f64 x) x) (.f64 x (neg.f64 x)) x) (.f64 x (*.f64 x x)))
	3.9%	(/.f64 (fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x) (.f64 x (neg.f64 x)) x) (.f64 x (*.f64 x x)))
	20.4%	(/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) x) (.f64 x (*.f64 x x)))
	35.5%	(/.f64 (fma.f64 (neg.f64 (cos.f64 x)) x x) (.f64 x (.f64 x x)))
	14.7%	(/.f64 (fma.f64 x (neg.f64 x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x (.f64 x (*.f64 x (neg.f64 x)))))
	46.8%	(/.f64 (/.f64 (fma.f64 #s(literal 1 binary64) x (.f64 x (neg.f64 (cos.f64 x)))) (.f64 x x)) x)
	30.8%	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x x)) (*.f64 x x))
	48.6%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	48.6%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))) x)
	2.4%	(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 x x)) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 x x)))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 x x))))
	2.7%	(/.f64 (-.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (.f64 x x)) (.f64 (neg.f64 x) #s(approx (cos x) #s(literal 1 binary64)))) (.f64 (neg.f64 x) (*.f64 x x)))
	14.3%	(/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x (.f64 x (.f64 x x))))
	3.2%	(/.f64 (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x))) (.f64 x (*.f64 x x)))
	35.4%	(/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x (*.f64 x x)))
	19.1%	(/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x))) (.f64 x x))
✓	46.9%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
✓	18.6%	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
	48.1%	(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (fma.f64 (/.f64 (cos.f64 x) x) x #s(literal -1 binary64))) x)
	48.1%	(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal -1 binary64))) x)
✓	48.6%	(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal -1 binary64) (cos.f64 x))) x)
	32.8%	(/.f64 (.f64 (/.f64 #s(literal -1 binary64) x) #s(approx (+ -1 (cos x)) (.f64 (*.f64 x x) #s(literal -1/2 binary64)))) x)
	76.4%	(/.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (*.f64 x x))
	32.1%	(/.f64 (neg.f64 #s(approx (+ (cos x) -1) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) (.f64 x x))
✓	54.8%	(/.f64 #s(approx (* (/ -1 x) (+ -1 (cos x))) (.f64 x (fma.f64 x (.f64 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)))) x)
	14.4%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 (cos.f64 x) (.f64 x (neg.f64 x)) (*.f64 x x))))
	47.6%	(/.f64 #s(literal 1 binary64) (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
✓	47.3%	(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
✓	47.8%	(*.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
	30.9%	(.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) #s(approx (+ (cos x) -1) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
	48.5%	(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) (/.f64 #s(literal 1 binary64) x))
✓	76.6%	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
	46.9%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (cos.f64 x)))))
✓	46.9%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
	31.0%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))
	30.7%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))
	35.4%	(.f64 (-.f64 x (.f64 x (cos.f64 x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
✓	76.6%	(.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (*.f64 x x)))
	75.6%	(.f64 (sin.f64 x) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (tan.f64 (.f64 x #s(literal 1/2 binary64)))))
	55.8%	(.f64 (sin.f64 x) #s(approx (/ (tan ( x 1/2)) (* x x)) (/.f64 #s(literal 1/2 binary64) x)))
	54.8%	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
	55.1%	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
✓	54.5%	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
✓	55.3%	#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))

Compiler

Compiled 1 646 to 603 computations (63.4% saved)

regimes40.0ms (0.4%)

Memory

14.2MiB live, 90.2MiB allocated

Counts

66 → 2

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 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)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x))) (.f64 x x))
(.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) #s(approx (+ (cos x) -1) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) x) #s(approx (+ -1 (cos x)) (.f64 (*.f64 x x) #s(literal -1/2 binary64)))) x)
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x) #s(approx (/ (cos x) (* x (neg x))) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x) (.f64 x (neg.f64 x)) x) (.f64 x (*.f64 x x)))
(/.f64 #s(approx (* (/ -1 x) (+ -1 (cos x))) (.f64 x (fma.f64 x (.f64 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)))) x)
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x))) (.f64 x (*.f64 x x)))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (.f64 x x)) (.f64 (neg.f64 x) #s(approx (cos x) #s(literal 1 binary64)))) (.f64 (neg.f64 x) (*.f64 x x)))
(fma.f64 (/.f64 #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(/.f64 (neg.f64 #s(approx (+ (cos x) -1) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) (.f64 x x))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 x x)) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 x x)))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 x x))))
(.f64 (sin.f64 x) #s(approx (/ (tan ( x 1/2)) (* x x)) (/.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x) (neg.f64 x))
(/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x (*.f64 x x)))
(/.f64 (fma.f64 (neg.f64 (cos.f64 x)) x x) (.f64 x (.f64 x x)))
(*.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal -1 binary64) (cos.f64 x))) x)
(.f64 (-.f64 x (.f64 x (cos.f64 x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (/.f64 (cos.f64 x) x))) (.f64 x x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))) x)
(fma.f64 (cos.f64 x) (/.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(fma.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (cos.f64 x) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(/.f64 (/.f64 (fma.f64 #s(literal 1 binary64) x (.f64 x (neg.f64 (cos.f64 x)))) (.f64 x x)) x)
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (fma.f64 (/.f64 (cos.f64 x) x) x #s(literal -1 binary64))) x)
(/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x (.f64 x (.f64 x x))))
(fma.f64 (/.f64 (cos.f64 x) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (fma.f64 (/.f64 (cos.f64 x) x) (.f64 x (neg.f64 x)) x) (.f64 x (*.f64 x x)))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (cos.f64 x)))))
(/.f64 (fma.f64 x (neg.f64 x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x (.f64 x (*.f64 x (neg.f64 x)))))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (*.f64 x (neg.f64 x))))
(/.f64 (fma.f64 (/.f64 (cos.f64 x) x) x (/.f64 (neg.f64 x) x)) (*.f64 x (neg.f64 x)))
(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x x)) (*.f64 x x))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 (cos.f64 x) (.f64 x (neg.f64 x)) (*.f64 x x))))
(/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) x) (.f64 x (*.f64 x x)))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal -1 binary64))) x)
(.f64 (sin.f64 x) (/.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) (*.f64 x x)))
(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
(/.f64 (.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64)))) (*.f64 x x))
(.f64 (sin.f64 x) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (tan.f64 (.f64 x #s(literal 1/2 binary64)))))
(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 x x))
(/.f64 (+.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (neg.f64 (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
(.f64 (sin.f64 x) (/.f64 (sin.f64 x) (.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x))))))

Outputs

#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))

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

Calls

2 calls:

20.0ms	x
17.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Results

Accuracy	Segments	Branch
99.6%	2	`x`
98.7%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes35.0ms (0.3%)

Memory

-27.5MiB live, 17.7MiB allocated

Counts

41 → 2

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 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)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x))) (.f64 x x))
(.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) #s(approx (+ (cos x) -1) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) x) #s(approx (+ -1 (cos x)) (.f64 (*.f64 x x) #s(literal -1/2 binary64)))) x)
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x) #s(approx (/ (cos x) (* x (neg x))) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x) (.f64 x (neg.f64 x)) x) (.f64 x (*.f64 x x)))
(/.f64 #s(approx (* (/ -1 x) (+ -1 (cos x))) (.f64 x (fma.f64 x (.f64 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)))) x)
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x))) (.f64 x (*.f64 x x)))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (.f64 x x)) (.f64 (neg.f64 x) #s(approx (cos x) #s(literal 1 binary64)))) (.f64 (neg.f64 x) (*.f64 x x)))
(fma.f64 (/.f64 #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(/.f64 (neg.f64 #s(approx (+ (cos x) -1) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) (.f64 x x))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 x x)) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 x x)))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 x x))))
(.f64 (sin.f64 x) #s(approx (/ (tan ( x 1/2)) (* x x)) (/.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x) (neg.f64 x))
(/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x (*.f64 x x)))
(/.f64 (fma.f64 (neg.f64 (cos.f64 x)) x x) (.f64 x (.f64 x x)))
(*.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal -1 binary64) (cos.f64 x))) x)
(.f64 (-.f64 x (.f64 x (cos.f64 x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (/.f64 (cos.f64 x) x))) (.f64 x x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 x (/.f64 #s(literal 1 binary64) x)))

Outputs

#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))

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

Calls

1 calls:

11.0ms

Results

Accuracy	Segments	Branch
99.6%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes16.0ms (0.2%)

Memory

16.4MiB live, 16.4MiB allocated

Counts

28 → 2

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 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)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x))) (.f64 x x))
(.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) #s(approx (+ (cos x) -1) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) x) #s(approx (+ -1 (cos x)) (.f64 (*.f64 x x) #s(literal -1/2 binary64)))) x)
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x) #s(approx (/ (cos x) (* x (neg x))) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x) (.f64 x (neg.f64 x)) x) (.f64 x (*.f64 x x)))
(/.f64 #s(approx (* (/ -1 x) (+ -1 (cos x))) (.f64 x (fma.f64 x (.f64 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)))) x)
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x))) (.f64 x (*.f64 x x)))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (.f64 x x)) (.f64 (neg.f64 x) #s(approx (cos x) #s(literal 1 binary64)))) (.f64 (neg.f64 x) (*.f64 x x)))
(fma.f64 (/.f64 #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(/.f64 (neg.f64 #s(approx (+ (cos x) -1) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) (.f64 x x))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 x x)) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 x x)))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 x x))))
(.f64 (sin.f64 x) #s(approx (/ (tan ( x 1/2)) (* x x)) (/.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)

Outputs

#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))

(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))

Calls

2 calls:

8.0ms	x
7.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Results

Accuracy	Segments	Branch
83.8%	3	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`
98.7%	2	`x`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes9.0ms (0.1%)

Memory

9.1MiB live, 9.1MiB allocated

Counts

26 → 2

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 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)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x))) (.f64 x x))
(.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) #s(approx (+ (cos x) -1) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) x) #s(approx (+ -1 (cos x)) (.f64 (*.f64 x x) #s(literal -1/2 binary64)))) x)
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x) #s(approx (/ (cos x) (* x (neg x))) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x) (.f64 x (neg.f64 x)) x) (.f64 x (*.f64 x x)))
(/.f64 #s(approx (* (/ -1 x) (+ -1 (cos x))) (.f64 x (fma.f64 x (.f64 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)))) x)
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x))) (.f64 x (*.f64 x x)))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (.f64 x x)) (.f64 (neg.f64 x) #s(approx (cos x) #s(literal 1 binary64)))) (.f64 (neg.f64 x) (*.f64 x x)))
(fma.f64 (/.f64 #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(/.f64 (neg.f64 #s(approx (+ (cos x) -1) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) (.f64 x x))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 x x)) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 x x)))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 x x))))
(.f64 (sin.f64 x) #s(approx (/ (tan ( x 1/2)) (* x x)) (/.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Outputs

#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))

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

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
98.6%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes19.0ms (0.2%)

Memory

-23.0MiB live, 15.6MiB allocated

Counts

25 → 2

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 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)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x))) (.f64 x x))
(.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) #s(approx (+ (cos x) -1) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) x) #s(approx (+ -1 (cos x)) (.f64 (*.f64 x x) #s(literal -1/2 binary64)))) x)
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x) #s(approx (/ (cos x) (* x (neg x))) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x) (.f64 x (neg.f64 x)) x) (.f64 x (*.f64 x x)))
(/.f64 #s(approx (* (/ -1 x) (+ -1 (cos x))) (.f64 x (fma.f64 x (.f64 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)))) x)
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x))) (.f64 x (*.f64 x x)))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (.f64 x x)) (.f64 (neg.f64 x) #s(approx (cos x) #s(literal 1 binary64)))) (.f64 (neg.f64 x) (*.f64 x x)))
(fma.f64 (/.f64 #s(approx (cos x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(/.f64 (neg.f64 #s(approx (+ (cos x) -1) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) (.f64 x x))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 x x)) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 x x)))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) (.f64 x x))))
(.f64 (sin.f64 x) #s(approx (/ (tan ( x 1/2)) (* x x)) (/.f64 #s(literal 1/2 binary64) x)))

Outputs

#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 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)))

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

Calls

2 calls:

11.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
7.0ms	x

Results

Accuracy	Segments	Branch
55.8%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`
72.4%	2	`x`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes5.0ms (0%)

Memory

6.1MiB live, 6.1MiB allocated

Counts

14 → 2

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 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)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x))) (.f64 x x))
(.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) #s(approx (+ (cos x) -1) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) x) #s(approx (+ -1 (cos x)) (.f64 (*.f64 x x) #s(literal -1/2 binary64)))) x)
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x) #s(approx (/ (cos x) (* x (neg x))) (/.f64 #s(literal -1 binary64) (*.f64 x x))))

Outputs

#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 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)))

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
72.0%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Memory

7.7MiB live, 7.7MiB allocated

Counts

10 → 2

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 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)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64))) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/40320 binary64) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))

Outputs

#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 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)))

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
71.7%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Memory

6.3MiB live, 6.3MiB allocated

Counts

7 → 2

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(approx (+ (cos x) -1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))

Outputs

#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
71.7%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Memory

4.6MiB live, 4.6MiB allocated

Counts

4 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
71.3%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Memory

7.2MiB live, 7.2MiB allocated

Accuracy

Total -0.8b remaining (-2.8%)

Threshold costs -0.8b (-2.8%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
55.3%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`
55.3%	1	`x`

Compiler

Compiled 11 to 7 computations (36.4% saved)

bsearch12.0ms (0.1%)

Memory

-22.8MiB live, 15.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	0.006178343446038083	0.13028420349228442

Samples

7.0ms

112×

valid

Compiler

Compiled 194 to 122 computations (37.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-sub: 1.0ms (30.8% of total)

ival-div: 1.0ms (30.8% of total)

ival-cos: 1.0ms (30.8% of total)

ival-mult: 1.0ms (30.8% 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

1.5MiB live, 1.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.006178343446038083	0.13028420349228442

Compiler

Compiled 180 to 115 computations (36.1% saved)

bsearch1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.006178343446038083	0.13028420349228442

Compiler

Compiled 194 to 122 computations (37.1% saved)

bsearch1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.006178343446038083	0.13028420349228442

Compiler

Compiled 180 to 115 computations (36.1% saved)

bsearch15.0ms (0.1%)

Memory

21.9MiB live, 21.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	0.21224899097138283	4254.061804366628

Samples

9.0ms

128×

valid

Compiler

Compiled 284 to 178 computations (37.3% saved)

Precisions

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

ival-cos: 4.0ms (59.7% of total)

ival-sub: 1.0ms (14.9% of total)

ival-div: 1.0ms (14.9% of total)

ival-mult: 1.0ms (14.9% of total)

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

2.1MiB live, 2.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.21224899097138283	4254.061804366628

Compiler

Compiled 276 to 170 computations (38.4% saved)

bsearch3.0ms (0%)

Memory

-35.9MiB live, 2.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
3.0ms	0.21224899097138283	4254.061804366628

Compiler

Compiled 244 to 154 computations (36.9% saved)

bsearch22.0ms (0.2%)

Memory

1.1MiB live, 41.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
17.0ms	1.3372955215775695e+25	2.959411755585025e+39

Samples

11.0ms

160×

valid

Compiler

Compiled 252 to 150 computations (40.5% saved)

Precisions

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

ival-cos: 5.0ms (61% of total)

ival-sub: 1.0ms (12.2% of total)

ival-div: 1.0ms (12.2% of total)

ival-mult: 1.0ms (12.2% of total)

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

exact: 0.0ms (0% of total)

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

bsearch4.0ms (0%)

Memory

5.1MiB live, 5.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
4.0ms	0.21224899097138283	4254.061804366628

Samples

2.0ms

32×

valid

Compiler

Compiled 164 to 106 computations (35.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-cos: 1.0ms (62.5% of total)

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

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

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

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

exact: 0.0ms (0% of total)

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

simplify10.0ms (0.1%)

Memory

12.8MiB live, 12.8MiB allocated

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary64`
18×	`+-commutative_binary64`
16×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	331
1	79	331
2	95	331
3	107	331
4	113	331
5	114	331

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal 1062849512059437/36028797018963968 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))) x))
(if (<=.f64 x #s(literal 1062849512059437/36028797018963968 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x))
(if (<=.f64 x #s(literal 1062849512059437/36028797018963968 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) (.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (cos.f64 x) #s(literal -1 binary64))))
(if (<=.f64 x #s(literal 1062849512059437/36028797018963968 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x)))
(if (<=.f64 x #s(literal 9/2 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 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))) (fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x x))))
(if (<=.f64 x #s(literal 9/2 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 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))) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x))) (*.f64 x x)))
(if (<=.f64 x #s(literal 9/2 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 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))) (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (.f64 x x)))
(if (<=.f64 x #s(literal 560000000000000002504907756536655249408 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x)))
(if (<=.f64 x #s(literal 7/2 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (.f64 x x)))
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))

Outputs
(if (<=.f64 x #s(literal 1062849512059437/36028797018963968 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))) x))
(if (<=.f64 x #s(literal 1062849512059437/36028797018963968 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x))
(if (<=.f64 x #s(literal 1062849512059437/36028797018963968 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) (.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (cos.f64 x) #s(literal -1 binary64))))
(if (<=.f64 x #s(literal 1062849512059437/36028797018963968 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x)))
(if (<=.f64 x #s(literal 9/2 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 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))) (fma.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x x))))
(if (<=.f64 x #s(literal 9/2 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 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))) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (/.f64 #s(approx (cos x) #s(literal 1 binary64)) x))) (*.f64 x x)))
(if (<=.f64 x #s(literal 9/2 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 x (.f64 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))) (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (.f64 x x)))
(if (<=.f64 x #s(literal 560000000000000002504907756536655249408 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x)))
(if (<=.f64 x #s(literal 7/2 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (.f64 x x)))
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))

soundness1.9s (17.6%)

Memory

12.2MiB live, 882.3MiB allocated

Rules

16 752×	`lower-fma.f64`
16 752×	`lower-fma.f32`
11 662×	`lower-fma.f64`
11 662×	`lower-fma.f32`
4 900×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	109
0	47	97
1	187	94
2	1827	94
0	8878	94
0	42	284
1	105	284
2	258	284
3	609	284
4	1279	284
5	2001	284
6	2304	284
7	3158	284
8	4639	284
9	6288	284
10	7157	284
11	7373	284
12	7391	284
13	7393	284
14	7798	284
0	8007	266
0	36	203
0	64	200
1	267	193
2	2260	193
0	8171	193
0	43	179
0	76	173
1	296	169
2	2075	163
0	8255	161
0	6	17
0	10	17
1	40	17
2	268	17
3	2810	17
0	9656	17
0	163	2110
1	426	2102
2	1098	2096
3	3366	2096
4	5959	2096
0	8165	1986

Stop Event

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

Compiler

Compiled 462 to 178 computations (61.5% saved)

preprocess80.0ms (0.7%)

Memory: -4.4MiB live, 149.8MiB allocated
Compiler: Compiled 556 to 150 computations (73% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze3.0ms (0%)

sample2.0s (18.2%)

preprocess60.0ms (0.6%)

explain141.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify32.0ms (0.3%)

localize85.0ms (0.8%)

series3.0ms (0%)

simplify460.0ms (4.3%)

rewrite298.0ms (2.8%)

eval119.0ms (1.1%)

prune114.0ms (1.1%)

simplify92.0ms (0.8%)

localize186.0ms (1.7%)

series18.0ms (0.2%)

simplify359.0ms (3.3%)

rewrite268.0ms (2.5%)

eval377.0ms (3.5%)

prune263.0ms (2.4%)

simplify546.0ms (5%)

localize490.0ms (4.5%)

series16.0ms (0.1%)

simplify440.0ms (4.1%)

rewrite370.0ms (3.4%)

eval143.0ms (1.3%)

prune311.0ms (2.9%)

simplify187.0ms (1.7%)

localize196.0ms (1.8%)

series30.0ms (0.3%)

simplify347.0ms (3.2%)

rewrite346.0ms (3.2%)

eval152.0ms (1.4%)

prune204.0ms (1.9%)

regimes40.0ms (0.4%)

regimes35.0ms (0.3%)

regimes16.0ms (0.2%)

regimes9.0ms (0.1%)

regimes19.0ms (0.2%)

regimes5.0ms (0%)

regimes4.0ms (0%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes4.0ms (0%)

bsearch12.0ms (0.1%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch15.0ms (0.1%)

bsearch1.0ms (0%)

bsearch3.0ms (0%)

bsearch22.0ms (0.2%)

bsearch4.0ms (0%)

simplify10.0ms (0.1%)

soundness1.9s (17.6%)

preprocess80.0ms (0.7%)

end0.0ms (0%)

Profiling