Metrics for ENA, Section 1.4, Mentioned, A

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze3.0ms (0%)

Memory

6.4MiB live, 6.4MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	49.6%	50.4%	0%	0%	0%	0
0%	0%	49.6%	50.4%	0%	0%	0%	1
0%	0%	49.6%	50.4%	0%	0%	0%	2
50%	24.8%	24.8%	50.4%	0%	0%	0%	3
75%	37.2%	12.4%	50.4%	0%	0%	0%	4
87.5%	43.4%	6.2%	50.4%	0%	0%	0%	5
93.8%	46.5%	3.1%	50.4%	0%	0%	0%	6
96.9%	48.1%	1.6%	50.4%	0%	0%	0%	7
98.4%	48.8%	0.8%	50.4%	0%	0%	0%	8
99.2%	49.2%	0.4%	50.4%	0%	0%	0%	9
99.6%	49.4%	0.2%	50.4%	0%	0%	0%	10
99.8%	49.5%	0.1%	50.4%	0%	0%	0%	11
99.9%	49.6%	0%	50.4%	0%	0%	0%	12

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample2.8s (30.6%)

Memory

-114.4MiB live, 3 323.6MiB allocated

Samples

2.2s	5 679×	2	valid
310.0ms	2 477×	1	valid
7.0ms	100×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.9s

ival-cos: 1.1s (56.8% of total)

const: 389.0ms (20.6% of total)

adjust: 195.0ms (10.3% of total)

ival-sub: 140.0ms (7.4% of total)

ival-<=: 71.0ms (3.8% of total)

ival-and: 12.0ms (0.6% of total)

exact: 5.0ms (0.3% of total)

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

Bogosity

explain191.0ms (2.1%)

Memory

6.4MiB live, 259.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
133	-	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(cos.f64 x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	133	0

Confusion

	Predicted +	Predicted -
+	133	0
-	0	123

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	133	0	0
-	0	0	123

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	123
1	133

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

145.0ms	342×	2	valid
14.0ms	158×	1	valid
0.0ms	12×	0	valid

Compiler

Compiled 25 to 16 computations (36% saved)

Precisions

Click to see histograms. Total time spent on operations: 139.0ms

ival-cos: 101.0ms (72.7% of total)

ival-sub: 28.0ms (20.2% of total)

adjust: 9.0ms (6.5% of total)

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

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

exact: 0.0ms (0% of total)

preprocess53.0ms (0.6%)

Memory

-11.7MiB live, 30.8MiB allocated

Algorithm

1×	egg-herbie

Rules

24×	`lower-+.f64`
24×	`lower-+.f32`
20×	`sub-neg`
18×	`lower--.f32`
16×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	16	8
2	35	8
3	55	8
4	87	8
5	101	8
6	107	8
0	4	4
0	6	4
1	10	4
2	14	4
3	19	4
4	25	4
5	33	4
6	43	4
7	54	4
8	57	4
0	57	4

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 5 to 4 computations (20% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.3%	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Memory

12.4MiB live, 12.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

24×	`lower-+.f64`
24×	`lower-+.f32`
18×	`lower--.f32`
16×	`sub-neg`
16×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	10	8
2	14	8
3	19	8
4	25	8
5	33	8
6	43	8
7	54	8
8	57	8
0	57	8

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize70.0ms (0.8%)

Memory

1.3MiB live, 115.4MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(cos.f64 x)
accuracy	29.876071080808593	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Samples

56.0ms	171×	2	valid
7.0ms	79×	1	valid
0.0ms	6×	0	valid

Compiler

Compiled 10 to 6 computations (40% saved)

Precisions

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

ival-cos: 26.0ms (76.1% of total)

adjust: 4.0ms (11.7% of total)

ival-sub: 3.0ms (8.8% of total)

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

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

exact: 0.0ms (0% of total)

series1.0ms (0%)

Memory

2.4MiB live, 2.4MiB allocated

Counts

2 → 24

Calls

Call 1

Inputs
#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>) () ())

Inputs

#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>) () ())

Outputs
#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>) () ())) ())

Calls

6 calls:

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

simplify680.0ms (7.4%)

Memory

-25.2MiB live, 656.5MiB allocated

Algorithm

1×	egg-herbie

Rules

32 720×	`lower-fma.f64`
32 720×	`lower-fma.f32`
3 926×	`lower-*.f64`
3 926×	`lower-*.f32`
3 120×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	144
1	101	144
2	246	144
3	589	144
4	1230	144
5	1905	144
6	2165	144
7	2814	144
8	4054	144
9	5622	144
10	6523	144
11	6804	144
12	6843	144
13	6843	144
14	7276	144
15	7552	144
16	7593	144
17	7595	144
18	7595	144
19	7595	144
20	7595	144
21	7605	144
22	7605	144
23	7605	144
0	8510	132

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 24

Calls

Call 1

Inputs
(* 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)

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

rewrite304.0ms (3.3%)

Memory

14.1MiB live, 520.1MiB allocated

Rules

4 830×	`lower-*.f64`
4 830×	`lower-*.f32`
4 620×	`lower-/.f64`
4 620×	`lower-/.f32`
3 866×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
0	6	6
1	23	6
2	142	6
3	1153	6
0	9240	6

Stop Event

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

Counts

2 → 314

Calls

Call 1

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

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

eval41.0ms (0.4%)

Memory: 31.3MiB live, 108.0MiB allocated
Compiler: Compiled 10 777 to 911 computations (91.5% saved)

prune92.0ms (1%)

Memory

-19.5MiB live, 103.0MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	333	5	338
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	334	5	339

Accuracy

100.0%

Counts

339 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.6%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
▶	100.0%	#s(approx (- 1 (cos x)) (.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))))
▶	99.8%	#s(approx (- 1 (cos x)) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))))
▶	100.0%	#s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))))
▶	99.0%	#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))

Compiler

Compiled 126 to 68 computations (46% saved)

simplify44.0ms (0.5%)

Memory

24.7MiB live, 63.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(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))
cost-diff	0	(*.f64 x x)
cost-diff	0	(.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)))
cost-diff	0	#s(approx (- 1 (cos x)) (.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))))
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
cost-diff	0	(*.f64 x x)
cost-diff	0	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (- 1 (cos x)) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))))
cost-diff	0	(*.f64 x x)
cost-diff	0	(.f64 #s(literal 1/2 binary64) (.f64 x x))
cost-diff	0	#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.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	(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
cost-diff	0	(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
cost-diff	0	(.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))))

Rules

2 176×	`lower-fma.f32`
2 164×	`lower-fma.f64`
640×	`lower-*.f32`
624×	`lower-*.f64`
512×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	237
0	49	237
1	122	237
2	323	237
3	679	237
4	1117	237
5	1388	237
6	1426	237
7	1444	237
8	1448	237
0	1448	237

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize264.0ms (2.9%)

Memory

-15.1MiB live, 321.2MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0	#s(approx (- 1 (cos x)) (.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))))
accuracy	0.01171875	(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
accuracy	0.015625	(.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)))
accuracy	0.265625	(*.f64 x #s(literal 1/720 binary64))
accuracy	0	(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.01171875	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
accuracy	0.12538197299319515	#s(approx (- 1 (cos x)) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))))
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(.f64 #s(literal 1/2 binary64) (.f64 x x))
accuracy	0.60795238811281	#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
accuracy	0.6991393629556827	#s(approx (cos x) #s(literal 1 binary64))
accuracy	29.876071080808593	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
accuracy	0.00390625	(fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64))
accuracy	0.0078125	(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	0.0078125	(.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
accuracy	0.01171875	(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))

Samples

184.0ms	170×	2	valid
37.0ms	79×	1	valid
1.0ms	1×	3	valid
1.0ms	6×	0	valid

Compiler

Compiled 200 to 30 computations (85% saved)

Precisions

Click to see histograms. Total time spent on operations: 171.0ms

ival-mult: 48.0ms (28.2% of total)

ival-add: 41.0ms (24% of total)

ival-cos: 27.0ms (15.8% of total)

const: 26.0ms (15.2% of total)

adjust: 20.0ms (11.7% of total)

ival-sub: 8.0ms (4.7% of total)

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

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

exact: 0.0ms (0% of total)

series36.0ms (0.4%)

Memory

-32.2MiB live, 14.1MiB allocated

Counts

19 → 228

Calls

Call 1

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

Outputs
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt #s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))) (patch #s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))) (patch #s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) (taylor 0 x) (#s(alt #s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))) (patch #s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))) #<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 #s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))) (patch #s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))) (patch #s(approx (- 1 (cos x)) (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.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))) (patch (.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))) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor 0 x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/24 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #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 (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))) (taylor 0 x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (* 1/720 (pow x 4)) (taylor inf x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/720 (pow x 4)) (taylor -inf x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt -1/24 (taylor 0 x) (#s(alt (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 (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 (pow x 2)) 1/24) (taylor 0 x) (#s(alt (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 (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 (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24) (taylor 0 x) (#s(alt (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 (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 (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24) (taylor 0 x) (#s(alt (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 (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 (* -1/40320 (pow x 4)) (taylor inf x) (#s(alt (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 (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 (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320)) (taylor inf x) (#s(alt (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 (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 (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4))))) (taylor inf x) (#s(alt (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 (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 (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4))))) (taylor inf x) (#s(alt (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 (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 (* -1/40320 (pow x 4)) (taylor -inf x) (#s(alt (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 (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 (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320)) (taylor -inf x) (#s(alt (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 (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 (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4))))) (taylor -inf x) (#s(alt (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 (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 (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4))))) (taylor -inf x) (#s(alt (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 (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 (* 1/720 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/720 binary64)) (patch (.f64 x #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/720 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/720 binary64)) (patch (.f64 x #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/720 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/720 binary64)) (patch (.f64 x #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/720 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/720 binary64)) (patch (.f64 x #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/720 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/720 binary64)) (patch (.f64 x #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/720 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/720 binary64)) (patch (.f64 x #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/720 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/720 binary64)) (patch (.f64 x #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/720 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/720 binary64)) (patch (.f64 x #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/720 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/720 binary64)) (patch (.f64 x #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/720 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/720 binary64)) (patch (.f64 x #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/720 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/720 binary64)) (patch (.f64 x #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/720 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/720 binary64)) (patch (.f64 x #s(literal 1/720 binary64)) #<representation binary64>) () ())) ())
#s(alt -1/24 (taylor 0 x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (patch (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/720 (pow x 2)) 1/24) (taylor 0 x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (patch (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/720 (pow x 2)) 1/24) (taylor 0 x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (patch (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/720 (pow x 2)) 1/24) (taylor 0 x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (patch (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/720 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (patch (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (patch (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (patch (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (patch (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/720 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (patch (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (patch (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (patch (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (patch (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())

Calls

57 calls:

Time	Variable		Point	Expression
22.0ms	x	@	0	(* x (* x (+ (* (* x x) (+ (* (* x x) (+ (* x (* x -1/40320)) 1/720)) -1/24)) 1/2)))
1.0ms	x	@	inf	(* (* x x) (+ (* (* x x) -1/24) 1/2))
1.0ms	x	@	inf	(* x (* x (+ (* (* x x) (+ (* (* x x) (+ (* x (* x -1/40320)) 1/720)) -1/24)) 1/2)))
0.0ms	x	@	inf	(* (* x x) (+ (* (* x x) (+ (* x (* x 1/720)) -1/24)) 1/2))
0.0ms	x	@	0	(* 1/2 (* x x))

simplify253.0ms (2.7%)

Memory

24.7MiB live, 369.9MiB allocated

Algorithm

1×	egg-herbie

Rules

11 468×	`lower-fma.f64`
11 468×	`lower-fma.f32`
4 536×	`lower-*.f64`
4 536×	`lower-*.f32`
2 248×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	108	1830
1	274	1830
2	708	1830
3	1951	1830
4	5439	1822
0	8602	1695

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

Calls

Call 1

Inputs
(* 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))
(* 1/2 (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))))
(* -1/40320 (pow x 8))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 8) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/40320 (pow x 8))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 8) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* 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)))))
(* 1/2 (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)
(* 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))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (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)
(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))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
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))
(* 1/2 (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))
(* 1/2 (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) (- (* 1/720 (pow x 2)) 1/24))))
(* 1/720 (pow x 6))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* 1/720 (pow x 6))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 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) (- (* 1/720 (pow x 2)) 1/24)))
(* 1/720 (pow x 4))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* 1/720 (pow x 4))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
-1/24
(- (* 1/720 (pow x 2)) 1/24)
(- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)
(- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)
(* -1/40320 (pow x 4))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/40320 (pow x 4))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
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))
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
-1/24
(- (* 1/720 (pow x 2)) 1/24)
(- (* 1/720 (pow x 2)) 1/24)
(- (* 1/720 (pow x 2)) 1/24)
(* 1/720 (pow x 2))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* 1/720 (pow x 2))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))

Outputs
(* 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 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 x (.f64 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))))
(- 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))
(* 1/2 (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 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 x (.f64 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))))
(* -1/40320 (pow x 8))
(*.f64 #s(literal -1/40320 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (pow.f64 x #s(literal 8 binary64)) (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* (pow x 8) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 1/720 binary64) (.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 -1/2 binary64) (pow.f64 x #s(literal 6 binary64)))))))
(* -1/40320 (pow x 8))
(*.f64 #s(literal -1/40320 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (pow.f64 x #s(literal 8 binary64)) (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* (pow x 8) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 1/720 binary64) (.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 -1/2 binary64) (pow.f64 x #s(literal 6 binary64)))))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.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)))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 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)))
(* -1/40320 (pow x 7))
(*.f64 #s(literal -1/40320 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (+.f64 (/.f64 #s(literal 1/720 binary64) (.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 -1/2 binary64) (pow.f64 x #s(literal 6 binary64)))))) (pow.f64 x #s(literal 7 binary64)))
(* -1/40320 (pow x 7))
(*.f64 #s(literal -1/40320 binary64) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))))
(.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2))))))
(.f64 (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- (+ 1/40320 (/ 1/24 (pow x 4))) (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(.f64 (+.f64 (/.f64 #s(literal 1/720 binary64) (.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 -1/2 binary64) (pow.f64 x #s(literal 6 binary64)))))) (pow.f64 x #s(literal 7 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 (.f64 x x) (fma.f64 x (.f64 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))
(* -1/40320 (pow x 6))
(*.f64 #s(literal -1/40320 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(fma.f64 (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x))))) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/2 binary64))
(* -1/40320 (pow x 6))
(*.f64 #s(literal -1/40320 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (+.f64 (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal -1/720 binary64) (.f64 x x))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
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(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
-1/24
#s(literal -1/24 binary64)
(- (* 1/720 (pow x 2)) 1/24)
(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
(- (* 1/720 (pow x 2)) 1/24)
(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
(- (* 1/720 (pow x 2)) 1/24)
(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
(* 1/720 (pow x 2))
(.f64 x (.f64 x #s(literal 1/720 binary64)))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
(* 1/720 (pow x 2))
(.f64 x (.f64 x #s(literal 1/720 binary64)))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))

rewrite375.0ms (4.1%)

Memory

23.2MiB live, 609.1MiB allocated

Rules

4 964×	`lower-*.f32`
4 948×	`lower-*.f64`
4 326×	`lower-/.f64`
4 326×	`lower-/.f32`
3 972×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	210
0	49	210
1	219	210
2	1604	210
0	8149	210

Stop Event

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

Counts

19 → 498

Calls

Call 1

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

Outputs
#s(approx (- 1 (cos x)) (.f64 (.f64 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 x (.f64 x #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.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)))))
(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 (.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))) (.f64 x x)))
(+.f64 (.f64 x (.f64 (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)) (.f64 x (.f64 x x)))) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(+.f64 (.f64 (.f64 x x) (.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)))) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(+.f64 (.f64 (.f64 (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)) (.f64 x (.f64 x x))) x) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(+.f64 (.f64 (.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))) (.f64 x x)) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(fma.f64 x (.f64 (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)) (.f64 x (.f64 x x))) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 x (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 x x) (.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)))))
(fma.f64 x (.f64 x #s(literal 1/2 binary64)) (.f64 (.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))) (*.f64 x x)))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 (.f64 x x) (.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)))))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 (.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))) (*.f64 x x)))
(fma.f64 (.f64 x x) (.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))) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 (.f64 x x) (.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)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 (.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))) (*.f64 x x)))
(fma.f64 (.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))) (.f64 x x) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 (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)) (.f64 x (.f64 x x))) x (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 (.f64 x x) (.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)))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 (.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))) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (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)) (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 1/4 binary64)) (.f64 (.f64 x x) (.f64 (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 x x) (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (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)) (.f64 (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)) (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 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (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 x x) (fma.f64 (.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))) (.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 -1/4 binary64)))))
(/.f64 (.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (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)) (.f64 (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)) (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 1/8 binary64))) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (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)) (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 1/4 binary64)) (.f64 (.f64 x x) (.f64 (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 (.f64 x x) (fma.f64 (.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))) (.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 -1/4 binary64))) (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 (neg.f64 (.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (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)) (.f64 (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)) (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 1/8 binary64)))) (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (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)) (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 1/4 binary64)) (.f64 (.f64 x x) (.f64 (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 (neg.f64 (.f64 (.f64 x x) (fma.f64 (.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))) (.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 -1/4 binary64)))) (neg.f64 (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 (fma.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (pow.f64 (.f64 (.f64 x x) (.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 3 binary64))) (fma.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64))) (-.f64 (.f64 (.f64 (.f64 x x) (.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)))) (.f64 (.f64 x x) (.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))))) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.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))))))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (pow.f64 (.f64 (.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))) (.f64 x x)) #s(literal 3 binary64))) (fma.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64))) (-.f64 (.f64 (.f64 (.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))) (.f64 x x)) (.f64 (.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))) (.f64 x x))) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 (.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))) (*.f64 x x))))))
(/.f64 (+.f64 (pow.f64 (.f64 x (.f64 (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)) (.f64 x (.f64 x x)))) #s(literal 3 binary64)) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (fma.f64 (.f64 x (.f64 (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)) (.f64 x (.f64 x x)))) (.f64 x (.f64 (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)) (.f64 x (.f64 x x)))) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64)))) (.f64 (.f64 x (.f64 (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)) (.f64 x (.f64 x x)))) (.f64 x (.f64 x #s(literal 1/2 binary64)))))))
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eval169.0ms (1.8%)

Memory: -21.4MiB live, 305.3MiB allocated
Compiler: Compiled 27 565 to 2 068 computations (92.5% saved)

prune115.0ms (1.2%)

Memory

8.6MiB live, 322.9MiB allocated

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	831	3	834
Fresh	0	0	0
Picked	3	2	5
Done	0	0	0
Total	834	5	839

Accuracy

100.0%

Counts

839 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	51.6%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
▶	100.0%	#s(approx (- 1 (cos x)) (.f64 (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))) x))
▶	99.8%	#s(approx (- 1 (cos x)) (.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) x))
✓	100.0%	#s(approx (- 1 (cos x)) (.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))))
▶	99.1%	#s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x))

Compiler

Compiled 58 to 33 computations (43.1% saved)

simplify17.0ms (0.2%)

Memory

-3.3MiB live, 35.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))
cost-diff	0	(.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
cost-diff	0	(.f64 (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))) x)
cost-diff	0	#s(approx (- 1 (cos x)) (.f64 (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))) x))
cost-diff	0	(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
cost-diff	0	(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
cost-diff	0	(.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) x)
cost-diff	0	#s(approx (- 1 (cos x)) (.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) x))
cost-diff	0	(*.f64 x #s(literal 1/2 binary64))
cost-diff	0	(.f64 (.f64 x #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x))

Rules

420×	`lower-fma.f32`
414×	`lower-fma.f64`
250×	`lower-*.f32`
232×	`lower-*.f64`
138×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	145
0	37	145
1	78	145
2	139	145
3	233	145
4	381	145
5	468	145
6	486	145
7	498	145
8	501	145
0	501	145

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize249.0ms (2.7%)

Memory

14.0MiB live, 258.2MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
accuracy	0.01171875	(.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
accuracy	0.265625	(*.f64 x #s(literal 1/720 binary64))
accuracy	0.38671875	(.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
accuracy	0.0078125	(.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) x)
accuracy	0.01171875	(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
accuracy	0.12538197299319515	#s(approx (- 1 (cos x)) (.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) x))
accuracy	0.3828125	(*.f64 x #s(literal -1/24 binary64))
accuracy	0	(.f64 (.f64 x #s(literal 1/2 binary64)) x)
accuracy	0	(*.f64 x #s(literal 1/2 binary64))
accuracy	0.60795238811281	#s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x))

Samples

175.0ms	170×	2	valid
26.0ms	79×	1	valid
1.0ms	1×	3	valid
1.0ms	6×	0	valid

Compiler

Compiled 125 to 24 computations (80.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 176.0ms

ival-mult: 116.0ms (65.7% of total)

ival-cos: 26.0ms (14.7% of total)

adjust: 13.0ms (7.4% of total)

const: 11.0ms (6.2% of total)

ival-add: 6.0ms (3.4% of total)

ival-sub: 4.0ms (2.3% of total)

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

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

exact: 0.0ms (0% of total)

series19.0ms (0.2%)

Memory

-13.1MiB live, 26.5MiB allocated

Counts

15 → 180

Calls

Call 1

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

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

Calls

45 calls:

Time	Variable		Point	Expression
8.0ms	x	@	-inf	(* x (+ (* x (* x (+ (* x (* x 1/720)) -1/24))) 1/2))
1.0ms	x	@	inf	(* x -1/24)
0.0ms	x	@	-inf	(* x 1/2)
0.0ms	x	@	-inf	(* x -1/24)
0.0ms	x	@	0	(* x -1/24)

simplify430.0ms (4.7%)

Memory

10.4MiB live, 532.4MiB allocated

Algorithm

1×	egg-herbie

Rules

23 308×	`lower-fma.f64`
23 308×	`lower-fma.f32`
4 680×	`lower-*.f64`
4 680×	`lower-*.f32`
2 546×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	1292
1	201	1292
2	527	1292
3	1535	1292
4	4558	1292
0	8306	1204

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

Inputs
(* 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))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 (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))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* -1/24 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 3))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* -1/24 (pow x 2)))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 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))
(* 1/2 (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))
(* 1/2 (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) (- (* 1/720 (pow x 2)) 1/24))))
(* 1/720 (pow x 6))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* 1/720 (pow x 6))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 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) (- (* 1/720 (pow x 2)) 1/24))))
(* 1/720 (pow x 5))
(* (pow x 5) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* 1/720 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) 1/720)))
(* -1 (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4))))))
(* -1 (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4))))))
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) (- (* 1/720 (pow x 2)) 1/24)))
(* 1/720 (pow x 4))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* 1/720 (pow x 4))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* x (- (* 1/720 (pow x 2)) 1/24))
(* x (- (* 1/720 (pow x 2)) 1/24))
(* x (- (* 1/720 (pow x 2)) 1/24))
(* 1/720 (pow x 3))
(* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* 1/720 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720)))
(* -1 (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720)))
(* -1 (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720)))
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
-1/24
(- (* 1/720 (pow x 2)) 1/24)
(- (* 1/720 (pow x 2)) 1/24)
(- (* 1/720 (pow x 2)) 1/24)
(* 1/720 (pow x 2))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* 1/720 (pow x 2))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))

Outputs
(* 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 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 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) (+ 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 (*.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))
(-.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))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 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) (+ 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 (*.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))
(-.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))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* -1/24 (pow x 4))
(.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/24 binary64)))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* -1/24 (pow x 4))
(.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/24 binary64)))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* -1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/24 binary64))))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* -1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/24 binary64))))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(* -1/24 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(* -1/24 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(* 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 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 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) (+ 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 (*.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))
(-.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))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 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) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.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))))
(* 1/720 (pow x 6))
(*.f64 #s(literal 1/720 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 1/720 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x x))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 1/720 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/24 binary64) (*.f64 x x)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 1/720 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/24 binary64) (*.f64 x x)))))
(* 1/720 (pow x 6))
(*.f64 #s(literal 1/720 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 1/720 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x x))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 1/720 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/24 binary64) (*.f64 x x)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 1/720 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/24 binary64) (*.f64 x x)))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.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)))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.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)))
(* 1/720 (pow x 5))
(.f64 (.f64 (.f64 x x) #s(literal 1/720 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 5) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 1/720 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) x))
(* (pow x 5) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 1/720 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/24 binary64) (.f64 x x)))) (.f64 (.f64 x (.f64 x (*.f64 x x))) x))
(* (pow x 5) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 1/720 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/24 binary64) (.f64 x x)))) (.f64 (.f64 x (.f64 x (*.f64 x x))) x))
(* 1/720 (pow x 5))
(.f64 (.f64 (.f64 x x) #s(literal 1/720 binary64)) (.f64 x (*.f64 x x)))
(* -1 (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) 1/720)))
(.f64 (+.f64 #s(literal 1/720 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) x))
(* -1 (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4))))))
(.f64 (+.f64 #s(literal 1/720 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/24 binary64) (.f64 x x)))) (.f64 (.f64 x (.f64 x (*.f64 x x))) x))
(* -1 (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4))))))
(.f64 (+.f64 #s(literal 1/720 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/24 binary64) (.f64 x x)))) (.f64 (.f64 x (.f64 x (*.f64 x x))) x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(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))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(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))
(* 1/720 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/720 binary64)))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(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 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(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))
(* 1/720 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/720 binary64)))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(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 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(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))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* x (- (* 1/720 (pow x 2)) 1/24))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
(* x (- (* 1/720 (pow x 2)) 1/24))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
(* x (- (* 1/720 (pow x 2)) 1/24))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
(* 1/720 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/720 binary64)))
(* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
(* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
(* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
(* 1/720 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/720 binary64)))
(* -1 (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720)))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
(* -1 (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720)))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
(* -1 (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720)))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
-1/24
#s(literal -1/24 binary64)
(- (* 1/720 (pow x 2)) 1/24)
(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
(- (* 1/720 (pow x 2)) 1/24)
(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
(- (* 1/720 (pow x 2)) 1/24)
(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
(* 1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/720 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
(* 1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/720 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))

rewrite373.0ms (4%)

Memory

-5.5MiB live, 310.3MiB allocated

Rules

7 368×	`lower-fma.f32`
7 362×	`lower-fma.f64`
4 806×	`lower-*.f32`
4 788×	`lower-*.f64`
2 950×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	136
0	37	136
1	129	136
2	766	136
3	7093	136
0	8022	136

Stop Event

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

Counts

15 → 486

Calls

Call 1

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

Outputs
#s(approx (- 1 (cos x)) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
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(/.f64 (.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64))) #s(literal -1/576 binary64)) #s(literal 1 binary64)) (fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64)) #s(literal -1/13824 binary64)))) (neg.f64 (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/518400 binary64)) #s(literal -1/17280 binary64)) #s(literal 1/576 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64))) #s(literal -1/576 binary64)))) (neg.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/576 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64)))))) (neg.f64 (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64)))) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64)))) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64))) (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64)))) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64))) (fma.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64)))) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64)))) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64))) (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64)))) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64)))) (.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64))))) (fma.f64 x (/.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64))) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64))) (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/139314069504000000 binary64)) #s(literal -1/2641807540224 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/518400 binary64)) #s(literal -1/17280 binary64)) #s(literal 1/576 binary64)))) (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/139314069504000000 binary64) (-.f64 #s(literal 1/191102976 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1/5159780352000 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/139314069504000000 binary64) #s(literal -1/191102976 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/518400 binary64)) #s(literal -1/17280 binary64)) #s(literal 1/576 binary64)))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64)) #s(literal 1/13824 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/139314069504000000 binary64) #s(literal -1/191102976 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64)))) (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/268738560000 binary64) (fma.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/298598400 binary64) #s(literal 1/331776 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/268738560000 binary64) #s(literal -1/331776 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64)))) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64))) #s(literal 1/576 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64)) #s(literal -1/13824 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/518400 binary64)) #s(literal -1/17280 binary64)) #s(literal 1/576 binary64))))
(.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64))) #s(literal -1/576 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64)) #s(literal -1/13824 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/518400 binary64)) #s(literal -1/17280 binary64)) #s(literal 1/576 binary64)))))
(.f64 (neg.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64))) #s(literal -1/576 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/518400 binary64)) #s(literal -1/17280 binary64)) #s(literal 1/576 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/373248000 binary64)) #s(literal -1/13824 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64))) (fma.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 1/518400 binary64))) #s(literal -1/576 binary64)))
(.f64 (-.f64 #s(literal 1/576 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))
(.f64 (/.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64))) #s(literal -1/576 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64))) #s(literal -1/576 binary64))) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64)) #s(literal -1/13824 binary64)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/17280 binary64) #s(literal 1/576 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/17280 binary64) #s(literal 1/576 binary64)) (fma.f64 (.f64 x x) #s(literal 1/17280 binary64) #s(literal 1/576 binary64))) (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/139314069504000000 binary64)))) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/17280 binary64) #s(literal 1/576 binary64)) (-.f64 (fma.f64 (.f64 x x) #s(literal 1/17280 binary64) #s(literal 1/576 binary64)) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64))))) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/268738560000 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64)) #s(literal -1/13824 binary64)) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/518400 binary64)) #s(literal -1/17280 binary64)) #s(literal 1/576 binary64)) (+.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64))) #s(literal -1/576 binary64)) (.f64 (.f64 x x) #s(literal -1/17280 binary64))))) (+.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64))) #s(literal -1/576 binary64)) (.f64 (.f64 x x) #s(literal -1/17280 binary64))))
(.f64 (/.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64))) #s(literal -1/576 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64)) #s(literal 1/13824 binary64))) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64))) (fma.f64 x (*.f64 x #s(literal -1/17280 binary64)) #s(literal 1/576 binary64))))

eval87.0ms (0.9%)

Memory: 28.7MiB live, 214.4MiB allocated
Compiler: Compiled 21 716 to 1 954 computations (91% saved)

prune115.0ms (1.2%)

Memory

-28.3MiB live, 202.9MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	666	0	666
Fresh	0	0	0
Picked	0	3	3
Done	0	2	2
Total	666	5	671

Accuracy

100.0%

Counts

671 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	51.6%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
✓	100.0%	#s(approx (- 1 (cos x)) (.f64 (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))) x))
✓	99.8%	#s(approx (- 1 (cos x)) (.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) x))
✓	100.0%	#s(approx (- 1 (cos x)) (.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))))
✓	99.1%	#s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x))

Compiler

Compiled 154 to 66 computations (57.1% saved)

regimes11.0ms (0.1%)

Memory

-20.6MiB live, 20.9MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

5.0ms	(cos.f64 x)
3.0ms	x
2.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes6.0ms (0.1%)

Memory

16.3MiB live, 16.3MiB allocated

Counts

6 → 1

Calls

Call 1

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

Outputs
#s(approx (- 1 (cos x)) (.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))))

Calls

3 calls:

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

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes7.0ms (0.1%)

Memory

-23.6MiB live, 14.9MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
99.8%	1	`(cos.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes5.0ms (0.1%)

Memory

13.4MiB live, 13.4MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.8%	1	`(cos.f64 x)`
99.8%	1	`x`
99.8%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes5.0ms (0.1%)

Memory

12.4MiB live, 12.4MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.1%	1	`x`
99.1%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
99.1%	1	`(cos.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes5.0ms (0.1%)

Memory

-27.9MiB live, 10.7MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
99.0%	1	`(cos.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes3.0ms (0%)

Memory

9.5MiB live, 9.5MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
51.6%	1	`x`
51.6%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
51.6%	1	`(cos.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

simplify7.0ms (0.1%)

Memory

16.6MiB live, 16.7MiB allocated

Algorithm

1×	egg-herbie

Rules

26×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	96
1	50	96
2	54	96
3	56	96
4	57	96

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness2.3s (24.9%)

Memory

-13.5MiB live, 466.1MiB allocated

Rules

32 720×	`lower-fma.f64`
32 720×	`lower-fma.f32`
4 964×	`lower-*.f32`
4 948×	`lower-*.f64`
4 326×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	144
1	101	144
2	246	144
3	589	144
4	1230	144
5	1905	144
6	2165	144
7	2814	144
8	4054	144
9	5622	144
10	6523	144
11	6804	144
12	6843	144
13	6843	144
14	7276	144
15	7552	144
16	7593	144
17	7595	144
18	7595	144
19	7595	144
20	7595	144
21	7605	144
22	7605	144
23	7605	144
0	8510	132
0	28	210
0	49	210
1	219	210
2	1604	210
0	8149	210

Stop Event

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

Compiler

Compiled 177 to 84 computations (52.5% saved)

preprocess70.0ms (0.8%)

Memory: -6.5MiB live, 148.4MiB allocated
Remove: (abs x)
Compiler: Compiled 310 to 150 computations (51.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	6	9
1	16	8
2	35	8
3	55	8
4	87	8
5	101	8
6	107	8
0	4	4
0	6	4
1	10	4
2	14	4
3	19	4
4	25	4
5	33	4
6	43	4
7	54	4
8	57	4
0	57	4

Iter	Nodes	Cost
0	22	145
0	37	145
1	78	145
2	139	145
3	233	145
4	381	145
5	468	145
6	486	145
7	498	145
8	501	145
0	501	145

Iter	Nodes	Cost
0	6	9
1	16	8
2	35	8
3	55	8
4	87	8
5	101	8
6	107	8
0	4	4
0	6	4
1	10	4
2	14	4
3	19	4
4	25	4
5	33	4
6	43	4
7	54	4
8	57	4
0	57	4

Iter	Nodes	Cost
0	22	145
0	37	145
1	78	145
2	139	145
3	233	145
4	381	145
5	468	145
6	486	145
7	498	145
8	501	145
0	501	145

start0.0ms (0%)

analyze3.0ms (0%)

sample2.8s (30.6%)

explain191.0ms (2.1%)

preprocess53.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize70.0ms (0.8%)

series1.0ms (0%)

simplify680.0ms (7.4%)

rewrite304.0ms (3.3%)

eval41.0ms (0.4%)

prune92.0ms (1%)

simplify44.0ms (0.5%)

localize264.0ms (2.9%)

series36.0ms (0.4%)

simplify253.0ms (2.7%)

rewrite375.0ms (4.1%)

eval169.0ms (1.8%)

prune115.0ms (1.2%)

simplify17.0ms (0.2%)

localize249.0ms (2.7%)

series19.0ms (0.2%)

simplify430.0ms (4.7%)

rewrite373.0ms (4%)

eval87.0ms (0.9%)

prune115.0ms (1.2%)

regimes11.0ms (0.1%)

regimes6.0ms (0.1%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

regimes3.0ms (0%)

simplify7.0ms (0.1%)

soundness2.3s (24.9%)

preprocess70.0ms (0.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	6	9
1	16	8
2	35	8
3	55	8
4	87	8
5	101	8
6	107	8
0	4	4
0	6	4
1	10	4
2	14	4
3	19	4
4	25	4
5	33	4
6	43	4
7	54	4
8	57	4
0	57	4

Iter	Nodes	Cost
0	22	145
0	37	145
1	78	145
2	139	145
3	233	145
4	381	145
5	468	145
6	486	145
7	498	145
8	501	145
0	501	145