Metrics for ENA, Section 1.4, Mentioned, A

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze3.0ms (0%)

Memory

5.7MiB live, 5.7MiB 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)

sample3.0s (28.1%)

Memory

26.0MiB live, 3 073.6MiB allocated

Samples

2.2s	5 713×	2	valid
314.0ms	2 465×	1	valid
5.0ms	78×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 2.2s

ival-cos: 1.3s (58% of total)

const: 363.0ms (16.8% of total)

adjust: 218.0ms (10.1% of total)

ival-sub: 204.0ms (9.4% of total)

ival-<=: 106.0ms (4.9% of total)

ival-and: 11.0ms (0.5% of total)

exact: 4.0ms (0.2% of total)

ival-assert: 3.0ms (0.1% of total)

Bogosity

explain146.0ms (1.4%)

Memory

-5.2MiB live, 275.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
136	1	(7.636552920849174e-162)	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(cos.f64 x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	137	0

Confusion

	Predicted +	Predicted -
+	136	0
-	1	119

Precision

0.9927007299270073

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	136	0	0
-	1	0	119

Precision?

0.9927007299270073

Recall?

1.0

Freqs

test

number	freq
0	119
1	137

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

81.0ms	340×	2	valid
14.0ms	166×	1	valid
0.0ms	6×	0	valid

Compiler

Compiled 25 to 16 computations (36% saved)

Precisions

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

ival-cos: 52.0ms (73.2% of total)

adjust: 11.0ms (15.5% of total)

ival-sub: 7.0ms (9.9% of total)

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

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

exact: 0.0ms (0% of total)

preprocess46.0ms (0.4%)

Memory

2.0MiB live, 38.0MiB 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

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.2%	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0%)

Memory

7.8MiB live, 7.8MiB 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

localize83.0ms (0.8%)

Memory

2.4MiB live, 78.9MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(cos.f64 x)
accuracy	30.593554769293778	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Samples

70.0ms	170×	2	valid
7.0ms	83×	1	valid
0.0ms	3×	0	valid

Compiler

Compiled 10 to 6 computations (40% saved)

Precisions

Click to see histograms. Total time spent on operations: 67.0ms

ival-cos: 59.0ms (87.5% of total)

adjust: 4.0ms (5.9% of total)

ival-sub: 4.0ms (5.9% 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

2.1MiB live, 2.1MiB 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	@	-inf	(- 1 (cos x))
0.0ms	x	@	0	(cos x)
0.0ms	x	@	inf	(- 1 (cos x))
0.0ms	x	@	inf	(cos x)

simplify628.0ms (6%)

Memory

-22.7MiB live, 462.3MiB 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)

rewrite254.0ms (2.4%)

Memory

4.2MiB live, 401.3MiB 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))

eval51.0ms (0.5%)

Memory: -19.3MiB live, 92.5MiB allocated
Compiler: Compiled 10 777 to 911 computations (91.5% saved)

prune93.0ms (0.9%)

Memory

-2.7MiB live, 124.5MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	332	6	338
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	333	6	339

Accuracy

100.0%

Counts

339 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.1%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
▶	100.0%	(*.f64 (/.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 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))))
▶	99.9%	#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)))))
▶	99.5%	#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))

Compiler

Compiled 154 to 88 computations (42.9% saved)

simplify46.0ms (0.4%)

Memory

17.2MiB live, 55.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
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	(sin.f64 x)
cost-diff	0	(*.f64 (/.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
cost-diff	576	(/.f64 (sin.f64 x) #s(literal -1 binary64))
cost-diff	7104	(/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x)))

Rules

890×	`lower-fma.f32`
884×	`lower-fma.f64`
456×	`distribute-lft-in`
446×	`lower-*.f32`
434×	`lower-*.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	28	169
0	48	164
1	104	164
2	230	162
3	453	161
4	635	160
5	778	158
6	1315	158
7	1465	158
8	1621	158
9	1634	158
10	1635	158
0	1635	158

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize285.0ms (2.7%)

Memory

-7.6MiB live, 375.4MiB 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	0.00390625	(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	0.26953125	(*.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	0.015625	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
accuracy	0.05012770415158302	#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	0.0078125	(.f64 #s(literal 1/2 binary64) (.f64 x x))
accuracy	0.34199735011392574	#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
accuracy	0.41167327607070364	#s(approx (cos x) #s(literal 1 binary64))
accuracy	30.593554769293778	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
accuracy	0	(cos.f64 x)
accuracy	0.00390625	(/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
accuracy	0.00390625	(+.f64 #s(literal 1 binary64) (cos.f64 x))
accuracy	0.0078125	(*.f64 (/.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))))

Samples

185.0ms	168×	2	valid
38.0ms	84×	1	valid
1.0ms	4×	0	valid

Compiler

Compiled 141 to 27 computations (80.9% saved)

Precisions

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

ival-cos: 81.0ms (47.3% of total)

ival-mult: 40.0ms (23.4% of total)

adjust: 17.0ms (9.9% of total)

const: 10.0ms (5.8% of total)

ival-add: 10.0ms (5.8% of total)

ival-div: 6.0ms (3.5% of total)

ival-sub: 3.0ms (1.8% of total)

ival-sin: 2.0ms (1.2% of total)

ival-neg: 1.0ms (0.6% of total)

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

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

exact: 0.0ms (0% of total)

series22.0ms (0.2%)

Memory

7.6MiB live, 43.0MiB allocated

Counts

19 → 228

Calls

Call 1

Inputs
#s(alt (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (patch (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 x) #s(literal -1 binary64)) (patch (/.f64 (sin.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (patch (.f64 (/.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) #<representation binary64>) () ())
#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #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 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (+.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())
#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())
#s(alt (.f64 x #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 x) (taylor 0 x) (#s(alt (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (patch (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* x (- (* -1/24 (pow x 2)) 1/2)) (taylor 0 x) (#s(alt (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (patch (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* x (- (* (pow x 2) (- (* -1/240 (pow x 2)) 1/24)) 1/2)) (taylor 0 x) (#s(alt (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (patch (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -17/40320 (pow x 2)) 1/240)) 1/24)) 1/2)) (taylor 0 x) (#s(alt (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (patch (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (sin x) (+ 1 (cos x)))) (taylor inf x) (#s(alt (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (patch (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (sin x) (+ 1 (cos x)))) (taylor inf x) (#s(alt (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (patch (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (sin x) (+ 1 (cos x)))) (taylor inf x) (#s(alt (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (patch (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (sin x) (+ 1 (cos x)))) (taylor inf x) (#s(alt (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (patch (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (sin x) (+ 1 (cos x)))) (taylor -inf x) (#s(alt (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (patch (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (sin x) (+ 1 (cos x)))) (taylor -inf x) (#s(alt (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (patch (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (sin x) (+ 1 (cos x)))) (taylor -inf x) (#s(alt (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (patch (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (sin x) (+ 1 (cos x)))) (taylor -inf x) (#s(alt (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (patch (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (/.f64 (sin.f64 x) #s(literal -1 binary64)) (patch (/.f64 (sin.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/6 (pow x 2)) 1)) (taylor 0 x) (#s(alt (/.f64 (sin.f64 x) #s(literal -1 binary64)) (patch (/.f64 (sin.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)) (taylor 0 x) (#s(alt (/.f64 (sin.f64 x) #s(literal -1 binary64)) (patch (/.f64 (sin.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1)) (taylor 0 x) (#s(alt (/.f64 (sin.f64 x) #s(literal -1 binary64)) (patch (/.f64 (sin.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sin x)) (taylor inf x) (#s(alt (/.f64 (sin.f64 x) #s(literal -1 binary64)) (patch (/.f64 (sin.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sin x)) (taylor inf x) (#s(alt (/.f64 (sin.f64 x) #s(literal -1 binary64)) (patch (/.f64 (sin.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sin x)) (taylor inf x) (#s(alt (/.f64 (sin.f64 x) #s(literal -1 binary64)) (patch (/.f64 (sin.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sin x)) (taylor inf x) (#s(alt (/.f64 (sin.f64 x) #s(literal -1 binary64)) (patch (/.f64 (sin.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sin x)) (taylor -inf x) (#s(alt (/.f64 (sin.f64 x) #s(literal -1 binary64)) (patch (/.f64 (sin.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sin x)) (taylor -inf x) (#s(alt (/.f64 (sin.f64 x) #s(literal -1 binary64)) (patch (/.f64 (sin.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sin x)) (taylor -inf x) (#s(alt (/.f64 (sin.f64 x) #s(literal -1 binary64)) (patch (/.f64 (sin.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sin x)) (taylor -inf x) (#s(alt (/.f64 (sin.f64 x) #s(literal -1 binary64)) (patch (/.f64 (sin.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (/.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (patch (.f64 (/.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 x)) (+.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 (/.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (patch (.f64 (/.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 x)) (+.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 (/.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (patch (.f64 (/.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 x)) (+.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 (/.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (patch (.f64 (/.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (/ (pow (sin x) 2) (+ 1 (cos x))) (taylor inf x) (#s(alt (.f64 (/.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (patch (.f64 (/.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) #<representation binary64>) () ())) ())
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#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 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 (+ 2 (* -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 (+ 2 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) (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 (+ 2 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) (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 (+ 1 (cos x)) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (+.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (cos x)) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (+.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (cos x)) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (+.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (cos x)) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (+.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (cos x)) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (+.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (cos x)) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (+.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (cos x)) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (+.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (cos x)) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (+.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (* 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
2.0ms	x	@	inf	(* (* x x) (+ (* (* x x) (+ (* x (* x 1/720)) -1/24)) 1/2))
1.0ms	x	@	inf	(/ (neg (sin x)) (+ 1 (cos x)))
1.0ms	x	@	-inf	(/ (neg (sin x)) (+ 1 (cos x)))
1.0ms	x	@	-inf	(* (/ (sin x) -1) (/ (neg (sin x)) (+ 1 (cos x))))
1.0ms	x	@	inf	(* (/ (sin x) -1) (/ (neg (sin x)) (+ 1 (cos x))))

simplify273.0ms (2.6%)

Memory

14.8MiB live, 490.0MiB allocated

Algorithm

1×	egg-herbie

Rules

18 546×	`lower-fma.f64`
18 546×	`lower-fma.f32`
3 850×	`lower-+.f64`
3 850×	`lower-+.f32`
3 814×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	130	1547
1	309	1531
2	731	1511
3	2291	1511
4	4765	1511
5	7549	1511
0	8097	1401

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 227

Calls

Call 1

Inputs
(* -1/2 x)
(* x (- (* -1/24 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (- (* -1/240 (pow x 2)) 1/24)) 1/2))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -17/40320 (pow x 2)) 1/240)) 1/24)) 1/2))
(* -1 (/ (sin x) (+ 1 (cos x))))
(* -1 (/ (sin x) (+ 1 (cos x))))
(* -1 (/ (sin x) (+ 1 (cos x))))
(* -1 (/ (sin x) (+ 1 (cos x))))
(* -1 (/ (sin x) (+ 1 (cos x))))
(* -1 (/ (sin x) (+ 1 (cos x))))
(* -1 (/ (sin x) (+ 1 (cos x))))
(* -1 (/ (sin x) (+ 1 (cos x))))
(* -1 x)
(* x (- (* 1/6 (pow x 2)) 1))
(* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))
(* -1 (sin x))
(* -1 (sin x))
(* -1 (sin x))
(* -1 (sin x))
(* -1 (sin x))
(* -1 (sin x))
(* -1 (sin x))
(* -1 (sin x))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(/ (pow (sin x) 2) (+ 1 (cos x)))
(/ (pow (sin x) 2) (+ 1 (cos x)))
(/ (pow (sin x) 2) (+ 1 (cos x)))
(/ (pow (sin x) 2) (+ 1 (cos x)))
(/ (pow (sin x) 2) (+ 1 (cos x)))
(/ (pow (sin x) 2) (+ 1 (cos x)))
(/ (pow (sin x) 2) (+ 1 (cos x)))
(/ (pow (sin x) 2) (+ 1 (cos x)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(* 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)))))
2
(+ 2 (* -1/2 (pow x 2)))
(+ 2 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ 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)
(* 1/720 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 x)
(*.f64 #s(literal -1/2 binary64) x)
(* x (- (* -1/24 (pow x 2)) 1/2))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))
(* x (- (* (pow x 2) (- (* -1/240 (pow x 2)) 1/24)) 1/2))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -17/40320 (pow x 2)) 1/240)) 1/24)) 1/2))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -17/40320 binary64) #s(literal -1/240 binary64))) #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))
(* -1 (/ (sin x) (+ 1 (cos x))))
(tan.f64 (*.f64 #s(literal -1/2 binary64) x))
(* -1 (/ (sin x) (+ 1 (cos x))))
(tan.f64 (*.f64 #s(literal -1/2 binary64) x))
(* -1 (/ (sin x) (+ 1 (cos x))))
(tan.f64 (*.f64 #s(literal -1/2 binary64) x))
(* -1 (/ (sin x) (+ 1 (cos x))))
(tan.f64 (*.f64 #s(literal -1/2 binary64) x))
(* -1 (/ (sin x) (+ 1 (cos x))))
(tan.f64 (*.f64 #s(literal -1/2 binary64) x))
(* -1 (/ (sin x) (+ 1 (cos x))))
(tan.f64 (*.f64 #s(literal -1/2 binary64) x))
(* -1 (/ (sin x) (+ 1 (cos x))))
(tan.f64 (*.f64 #s(literal -1/2 binary64) x))
(* -1 (/ (sin x) (+ 1 (cos x))))
(tan.f64 (*.f64 #s(literal -1/2 binary64) x))
(* -1 x)
(neg.f64 x)
(* x (- (* 1/6 (pow x 2)) 1))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))
(* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))
(.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) #s(literal -1 binary64)))
(* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))) #s(literal 1/6 binary64)) #s(literal -1 binary64)))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
(* (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 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)))
(/ (pow (sin x) 2) (+ 1 (cos x)))
(.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (pow (sin x) 2) (+ 1 (cos x)))
(.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (pow (sin x) 2) (+ 1 (cos x)))
(.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (pow (sin x) 2) (+ 1 (cos x)))
(.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (pow (sin x) 2) (+ 1 (cos x)))
(.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (pow (sin x) 2) (+ 1 (cos x)))
(.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (pow (sin x) 2) (+ 1 (cos x)))
(.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (pow (sin x) 2) (+ 1 (cos x)))
(.f64 (sin.f64 x) (tan.f64 (.f64 x #s(literal 1/2 binary64))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 x (.f64 x (.f64 x #s(literal -1/6 binary64))) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
(* (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 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)))
(- 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 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
(* (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 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)))
(- 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 (.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
(* (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 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)))
(- 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 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(* -1/24 (pow x 4))
(.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(* -1/24 (pow x 4))
(.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(* -1/24 (pow x 2))
(.f64 #s(literal -1/24 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(* -1/24 (pow x 2))
(.f64 #s(literal -1/24 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
(* (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 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)))
(- 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 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
(* 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
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))
(* 1/720 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/720 binary64))))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (fma.f64 (*.f64 x 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 x (.f64 x (fma.f64 (.f64 x 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 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))
(* 1/720 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/720 binary64))))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (fma.f64 (*.f64 x 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 x (.f64 x (fma.f64 (.f64 x 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 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))
2
#s(literal 2 binary64)
(+ 2 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 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 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(* 1/720 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 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))
(- (* 1/720 (pow x 2)) 1/24)
(fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))
(- (* 1/720 (pow x 2)) 1/24)
(fma.f64 (*.f64 x 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 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x 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 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))

rewrite337.0ms (3.2%)

Memory

11.2MiB live, 491.8MiB allocated

Rules

4 192×	`lower-/.f32`
4 188×	`lower-/.f64`
3 966×	`lower-*.f32`
3 954×	`lower-*.f64`
2 974×	`lower-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	147
0	48	141
1	186	134
2	1266	133
0	8460	133

Stop Event

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

Counts

19 → 697

Calls

Call 1

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

Outputs
(+.f64 #s(literal 0 binary64) (tan.f64 (*.f64 x #s(literal -1/2 binary64))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal -1/2 binary64))))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
(tan.f64 (*.f64 x #s(literal -1/2 binary64)))
(neg.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
(/.f64 (sin.f64 x) (-.f64 #s(literal -1 binary64) (cos.f64 x)))
(/.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (neg.f64 (sin.f64 x)) (*.f64 (-.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x))) (-.f64 #s(literal -1 binary64) (cos.f64 x))))
(/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal -1 binary64) (cos.f64 x)) (neg.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (.f64 x #s(literal -1/2 binary64))) (sin.f64 (.f64 x #s(literal -1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (-.f64 #s(literal -1 binary64) (cos.f64 x))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x))) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 #s(literal -1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (neg.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (/.f64 #s(literal -1 binary64) (sin.f64 x))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal -1/2 binary64)))) #s(literal -1 binary64))))
(/.f64 (neg.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 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (-.f64 #s(literal -1 binary64) (cos.f64 x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64))))))
(/.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (cos.f64 x))) (/.f64 #s(literal -1 binary64) (sin.f64 x)))
(/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal -1/2 binary64))))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (sin.f64 x) (-.f64 #s(literal -1 binary64) (cos.f64 x))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (-.f64 #s(literal -1 binary64) (cos.f64 x)) (sin.f64 x)))
(/.f64 (sin.f64 (.f64 x #s(literal -1/2 binary64))) (cos.f64 (.f64 x #s(literal -1/2 binary64))))
(/.f64 (*.f64 (neg.f64 (sin.f64 x)) #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (cos.f64 x)))
(/.f64 (.f64 (neg.f64 (sin.f64 x)) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))
(/.f64 (-.f64 (sin.f64 #s(literal 0 binary64)) (sin.f64 x)) (+.f64 (cos.f64 #s(literal 0 binary64)) (cos.f64 x)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) (cos.f64 x))) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (neg.f64 (sin.f64 x)))) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (-.f64 #s(literal -1 binary64) (cos.f64 x))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64))))) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64))))))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)))
(/.f64 (.f64 (neg.f64 (sin.f64 x)) (neg.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) (cos.f64 x))))
(/.f64 (.f64 (neg.f64 (sin.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (.f64 (-.f64 #s(literal 1/2 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 (neg.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 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (.f64 (neg.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 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 (-.f64 #s(literal -1 binary64) (cos.f64 x)) #s(literal -1 binary64))))
(/.f64 (.f64 (neg.f64 (sin.f64 x)) (+.f64 (cos.f64 x) #s(literal -1 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 (neg.f64 (sin.f64 x)) (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (.f64 (-.f64 #s(literal 1/2 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 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 0 binary64)) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (.f64 (neg.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) (cos.f64 x))))
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(/.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64))) (-.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64)) #s(literal 1/576 binary64))) (.f64 (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 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64)))) #s(literal -1/2641807540224 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64))) (-.f64 #s(literal 1/191102976 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/5159780352000 binary64)))) (-.f64 (fma.f64 (.f64 (.f64 x x) (.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 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64))) #s(literal -1/191102976 binary64)) #s(literal 1 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 (fma.f64 (.f64 (.f64 x x) (.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 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64))) #s(literal -1/191102976 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (+.f64 #s(literal 1/331776 binary64) (.f64 (.f64 (.f64 (.f64 x x) (.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 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) #s(literal -1/331776 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 x x) (.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 (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 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal 1/576 binary64)) (.f64 (.f64 x x) #s(literal -1/17280 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal -1/576 binary64)))) (neg.f64 (neg.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)))) (neg.f64 (-.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.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 (.f64 (.f64 x x) (.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 (.f64 (.f64 x x) (.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 (.f64 (.f64 x x) (.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 (.f64 (.f64 x x) (.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 (.f64 (.f64 x x) (.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))))) (+.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.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)))))
(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) (-.f64 (fma.f64 (.f64 (.f64 x x) (.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 (.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) (+.f64 #s(literal 1/576 binary64) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (.f64 (.f64 x x) #s(literal -1/17280 binary64))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (.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 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal 1/576 binary64)) (.f64 (*.f64 x x) #s(literal -1/17280 binary64))))))
(.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal -1/576 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal 1/24 binary64)))))
(.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x #s(literal 1/720 binary64))))))

eval154.0ms (1.5%)

Memory: -1.9MiB live, 233.0MiB allocated
Compiler: Compiled 24 878 to 2 334 computations (90.6% saved)

prune259.0ms (2.5%)

Memory

-7.4MiB live, 293.6MiB allocated

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	1 018	3	1 021
Fresh	1	0	1
Picked	2	3	5
Done	0	0	0
Total	1 021	6	1 027

Accuracy

100.0%

Counts

1 027 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	51.1%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
▶	99.9%	#s(approx (- 1 (cos x)) (fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal -1/24 binary64)))))))
▶	99.9%	#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))))
✓	99.9%	#s(approx (- 1 (cos x)) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))))
▶	99.5%	#s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x))

Compiler

Compiled 69 to 38 computations (44.9% saved)

simplify22.0ms (0.2%)

Memory

-35.3MiB live, 9.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/24 binary64)))))
cost-diff	0	(*.f64 x #s(literal 1/2 binary64))
cost-diff	0	#s(approx (- 1 (cos x)) (fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal -1/24 binary64)))))))
cost-diff	640	(fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal -1/24 binary64))))))
cost-diff	0	(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
cost-diff	0	(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
cost-diff	0	(.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

84×	`lower-*.f32`
68×	`lower-*.f64`
60×	`lower-fma.f32`
56×	`lower-fma.f64`
36×	`lower-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	128
0	29	120
1	51	120
2	71	116
3	89	114
4	99	114
5	107	114
6	117	114
7	128	114
8	131	114
0	131	114

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

localize121.0ms (1.2%)

Memory

24.6MiB live, 217.8MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0.0703125	(.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/24 binary64)))))
accuracy	0.08203125	(.f64 x (.f64 x (*.f64 x #s(literal -1/24 binary64))))
accuracy	0.125	(.f64 x (.f64 x #s(literal -1/24 binary64)))
accuracy	0.265625	(*.f64 x #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	0.0078125	(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
accuracy	0.05012770415158302	#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	0.265625	(*.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	0.34199735011392574	#s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x))

Samples

77.0ms	169×	2	valid
21.0ms	83×	1	valid
1.0ms	1×	5	exit
0.0ms	3×	0	valid

Compiler

Compiled 102 to 18 computations (82.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 68.0ms

ival-cos: 28.0ms (41.3% of total)

ival-mult: 13.0ms (19.2% of total)

adjust: 12.0ms (17.7% of total)

ival-sub: 7.0ms (10.3% of total)

const: 4.0ms (5.9% of total)

ival-add: 3.0ms (4.4% of total)

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

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

exact: 0.0ms (0% of total)

series9.0ms (0.1%)

Memory

13.4MiB live, 13.4MiB allocated

Counts

13 → 156

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

Calls

39 calls:

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

simplify224.0ms (2.1%)

Memory

-36.7MiB live, 244.8MiB allocated

Algorithm

1×	egg-herbie

Rules

9 576×	`lower-fma.f64`
9 576×	`lower-fma.f32`
2 846×	`lower-*.f64`
2 846×	`lower-*.f32`
1 448×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	972
1	118	972
2	285	972
3	784	972
4	2245	972
5	5579	972
0	8100	918

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

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 (* -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 (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))
(* -1/24 (pow x 4))
(* -1/24 (pow x 4))
(* -1/24 (pow x 4))
(* -1/24 (pow x 4))
(* -1/24 (pow x 4))
(* -1/24 (pow x 4))
(* -1/24 (pow x 4))
(* -1/24 (pow x 4))
(* -1/24 (pow x 4))
(* -1/24 (pow x 4))
(* -1/24 (pow x 4))
(* -1/24 (pow x 4))
(* -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 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 3))
(* -1/24 (pow x 3))
(* -1/24 (pow x 3))
(* -1/24 (pow x 3))
(* -1/24 (pow x 3))
(* -1/24 (pow x 3))
(* -1/24 (pow x 3))
(* -1/24 (pow x 3))
(* -1/24 (pow x 3))
(* -1/24 (pow x 3))
(* -1/24 (pow x 3))
(* -1/24 (pow x 3))

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 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 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(* 1/2 (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 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 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(* 1/2 (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 x (*.f64 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 x (*.f64 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 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* -1/24 (pow x 4))
(.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (fma.f64 x (*.f64 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 x (*.f64 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 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* -1/24 (pow x 4))
(.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (fma.f64 x (*.f64 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 x (*.f64 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 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* -1/24 (pow x 3))
(.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (fma.f64 x (.f64 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 x (.f64 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 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* -1/24 (pow x 3))
(.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x x)))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* -1/24 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* -1/24 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 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 x (*.f64 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 x (*.f64 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 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* -1/24 (pow x 4))
(.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (fma.f64 x (*.f64 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 x (*.f64 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 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* -1/24 (pow x 4))
(.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (fma.f64 x (*.f64 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 x (*.f64 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 x (*.f64 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 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 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(* -1/24 (pow x 4))
(.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))
(* -1/24 (pow x 4))
(.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))
(* -1/24 (pow x 4))
(.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))
(* -1/24 (pow x 4))
(.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))
(* -1/24 (pow x 4))
(.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))
(* -1/24 (pow x 4))
(.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))
(* -1/24 (pow x 4))
(.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))
(* -1/24 (pow x 4))
(.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))
(* -1/24 (pow x 4))
(.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))
(* -1/24 (pow x 4))
(.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))
(* -1/24 (pow x 4))
(.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))
(* -1/24 (pow x 4))
(.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))
(* -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 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* -1/24 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* -1/24 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* -1/24 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* -1/24 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* -1/24 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* -1/24 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* -1/24 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* -1/24 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* -1/24 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* -1/24 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* -1/24 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* -1/24 (pow x 3))
(.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x x)))
(* -1/24 (pow x 3))
(.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x x)))
(* -1/24 (pow x 3))
(.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x x)))
(* -1/24 (pow x 3))
(.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x x)))
(* -1/24 (pow x 3))
(.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x x)))
(* -1/24 (pow x 3))
(.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x x)))
(* -1/24 (pow x 3))
(.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x x)))
(* -1/24 (pow x 3))
(.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x x)))
(* -1/24 (pow x 3))
(.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x x)))
(* -1/24 (pow x 3))
(.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x x)))
(* -1/24 (pow x 3))
(.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x x)))
(* -1/24 (pow x 3))
(.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x x)))

rewrite322.0ms (3.1%)

Memory

66.8MiB live, 517.9MiB allocated

Rules

8 500×	`lower-fma.f32`
8 496×	`lower-fma.f64`
5 868×	`lower-*.f32`
5 852×	`lower-*.f64`
1 976×	`lower-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	114
0	29	106
1	90	106
2	528	100
3	5101	100
0	8629	100

Stop Event

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

Counts

13 → 426

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

Outputs
#s(approx (- 1 (cos x)) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(exp.f64 (log.f64 (.f64 x (.f64 x #s(literal 1/2 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 x (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(pow.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 1/2 binary64)) x)
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 (.f64 x x) (exp.f64 (log.f64 #s(literal 1/2 binary64))))
(.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 (.f64 x #s(literal 1/2 binary64)))))
(.f64 (exp.f64 (log.f64 (.f64 x #s(literal 1/2 binary64)))) (exp.f64 (log.f64 x)))
(.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) (.f64 x x))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
#s(approx (- 1 (cos x)) (.f64 (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x)))
(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 (.f64 x #s(literal -1/24 binary64)) (.f64 x (.f64 x x))))
(+.f64 (.f64 (.f64 x #s(literal -1/24 binary64)) (.f64 x (.f64 x x))) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(+.f64 (/.f64 (.f64 x (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))) (neg.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))) #s(literal -1 binary64)))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))) (/.f64 (.f64 x (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))))
(fma.f64 x (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 x #s(literal -1/24 binary64)) (.f64 x (*.f64 x x))))
(fma.f64 x (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 x (/.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))) (neg.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 (.f64 x #s(literal -1/24 binary64)) (.f64 x (*.f64 x x))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 (.f64 x #s(literal -1/24 binary64)) (.f64 x (*.f64 x x))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) (/.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/2 binary64)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))) (neg.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))))))
(fma.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (/.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))) (neg.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))))))
(fma.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x #s(literal -1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) (.f64 x x) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))) x (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))) (neg.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))))))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 (.f64 x #s(literal -1/24 binary64)) (.f64 x (*.f64 x x))))
(fma.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/24 binary64))) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))) (neg.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))
(fma.f64 (.f64 x x) (exp.f64 (log.f64 #s(literal 1/2 binary64))) (.f64 (.f64 x #s(literal -1/24 binary64)) (.f64 x (*.f64 x x))))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal -1/24 binary64)) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x (.f64 x x)) (exp.f64 (log.f64 (.f64 x #s(literal -1/24 binary64)))) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))) (neg.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/24 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) (exp.f64 (log.f64 #s(literal -1/24 binary64))) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/2 binary64)))) (/.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))) (neg.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))))))
(fma.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x))) (/.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))) (neg.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))
(fma.f64 (/.f64 x x) (/.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))) (neg.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))))))
(fma.f64 (/.f64 (.f64 x #s(literal 1/2 binary64)) x) (/.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/2 binary64)))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))) (neg.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))
(fma.f64 (/.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x) (/.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))) (neg.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))
(fma.f64 (/.f64 (.f64 x x) x) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))) (neg.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))))))
(fma.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) x) (/.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))) (neg.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))))))
(fma.f64 (/.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/2 binary64)))) x) (/.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))) (neg.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))
(fma.f64 (/.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x))) x) (/.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))) (neg.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))))))
(fma.f64 (/.f64 (.f64 x (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))))) (.f64 (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x)) (neg.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))
(fma.f64 (/.f64 (.f64 x (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64))) (.f64 x (.f64 x x)))))) (fma.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x #s(literal -1/24 binary64)) (.f64 x (.f64 x x))) (.f64 (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))) (neg.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))))))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 (.f64 x #s(literal -1/24 binary64)) (.f64 x (*.f64 x x))))
(fma.f64 (exp.f64 (log.f64 (.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x))))) (exp.f64 (log.f64 x)) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
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(.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x x)))
(.f64 (.f64 x #s(literal -1/24 binary64)) (*.f64 x x))
(.f64 (.f64 x (*.f64 x #s(literal -1/24 binary64))) x)
(.f64 (.f64 x x) (*.f64 x #s(literal -1/24 binary64)))
(.f64 (.f64 x (*.f64 x x)) #s(literal -1/24 binary64))

eval98.0ms (0.9%)

Memory: -39.4MiB live, 205.1MiB allocated
Compiler: Compiled 19 456 to 941 computations (95.2% saved)

prune63.0ms (0.6%)

Memory

42.5MiB live, 150.8MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	609	1	610
Fresh	0	0	0
Picked	1	2	3
Done	0	3	3
Total	610	6	616

Accuracy

100.0%

Counts

616 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	51.1%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
▶	99.9%	#s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x))
✓	99.9%	#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))))
✓	99.9%	#s(approx (- 1 (cos x)) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))))
✓	99.5%	#s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x))

Compiler

Compiled 67 to 37 computations (44.8% saved)

simplify9.0ms (0.1%)

Memory

-25.7MiB live, 13.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

84×	`lower-*.f32`
76×	`lower-*.f64`
60×	`lower-fma.f32`
58×	`lower-fma.f64`
38×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	53
0	18	45
1	31	45
2	55	45
3	87	45
4	100	45
5	108	45
6	118	45
7	129	45
8	132	45
0	132	45

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize88.0ms (0.8%)

Memory

37.3MiB live, 193.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x #s(literal 1/2 binary64))
accuracy	0.0078125	(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x)
accuracy	0.05012770415158302	#s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x))
accuracy	0.08203125	(.f64 x (.f64 x x))

Samples

51.0ms	170×	2	valid
25.0ms	83×	1	valid
0.0ms	3×	0	valid

Compiler

Compiled 44 to 14 computations (68.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 63.0ms

ival-cos: 27.0ms (43% of total)

ival-add: 10.0ms (15.9% of total)

adjust: 8.0ms (12.7% of total)

ival-mult: 8.0ms (12.7% of total)

ival-sub: 5.0ms (8% of total)

const: 5.0ms (8% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

-26.4MiB live, 11.7MiB allocated

Counts

5 → 60

Calls

Call 1

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

Outputs
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/24 (pow x 3)) (taylor inf x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor inf x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor inf x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor inf x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/24 (pow x 3)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x)) (patch #s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.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 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x)) (patch #s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.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 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x)) (patch #s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.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 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x)) (patch #s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.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 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x)) (patch #s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.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 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x)) (patch #s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.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 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x)) (patch #s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.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 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x)) (patch #s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.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 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x)) (patch #s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.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 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x)) (patch #s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.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 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x)) (patch #s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.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 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x)) (patch #s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x) (patch (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.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 (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x) (patch (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.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 (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x) (patch (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.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 (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x) (patch (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1/24 (pow x 4)) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x) (patch (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x) (patch (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x) (patch (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x) (patch (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1/24 (pow x 4)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x) (patch (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x) (patch (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x) (patch (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x) (patch (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())

Calls

15 calls:

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

simplify182.0ms (1.7%)

Memory

-23.7MiB live, 351.3MiB allocated

Algorithm

1×	egg-herbie

Rules

11 926×	`lower-fma.f64`
11 926×	`lower-fma.f32`
2 650×	`lower-*.f64`
2 650×	`lower-*.f32`
1 620×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	368
1	114	368
2	281	368
3	785	368
4	2190	368
5	5141	368
0	8590	344

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

Inputs
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* -1/24 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 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 (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))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)

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

rewrite440.0ms (4.2%)

Memory

25.4MiB live, 342.2MiB allocated

Rules

7 244×	`lower-fma.f32`
7 242×	`lower-fma.f64`
6 550×	`lower-*.f32`
6 542×	`lower-*.f64`
2 584×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	47
0	18	39
1	57	39
2	376	39
3	3642	39
0	9941	39

Stop Event

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

Counts

5 → 177

Calls

Call 1

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

Outputs
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64)))
(+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64)) (.f64 x #s(literal 1/2 binary64)))
(+.f64 (.f64 x (/.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))) (neg.f64 (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))) #s(literal -1 binary64)))
(-.f64 (.f64 x (/.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))) (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64))))) (/.f64 (.f64 x (.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) x)) (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64))))))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/24 binary64)))
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/24 binary64)) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 x (/.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) (neg.f64 (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))))))
(fma.f64 x (/.f64 (.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) x) (.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))) (neg.f64 (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))))))
(fma.f64 x (exp.f64 (log.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)))) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 x (exp.f64 (log.f64 #s(literal 1/2 binary64))) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/24 binary64)))
(fma.f64 (.f64 x x) (.f64 x #s(literal -1/24 binary64)) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x x) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64)) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) (neg.f64 (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))))))
(fma.f64 (.f64 x x) (/.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))) (neg.f64 (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))))))
(fma.f64 (.f64 x x) (exp.f64 (log.f64 (.f64 x #s(literal -1/24 binary64)))) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))) (neg.f64 (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))))))
(fma.f64 (.f64 x (.f64 x x)) (exp.f64 (log.f64 #s(literal -1/24 binary64))) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/24 binary64) (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64)))) (.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))) (neg.f64 (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))))))
(fma.f64 #s(literal 1/2 binary64) x (.f64 (.f64 x (*.f64 x x)) #s(literal -1/24 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) x) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) (neg.f64 (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))))))
(fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64)) (/.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))) (neg.f64 (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))))))
(fma.f64 (.f64 x (.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) x)) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))) (neg.f64 (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))))))
(fma.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) x (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1/24 binary64)) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/576 binary64) (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))) (neg.f64 (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))))))
(fma.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64))) (/.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))) (neg.f64 (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))))))
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(/.f64 (.f64 x (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64)))))) (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (.f64 (neg.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64)) #s(literal 1/8 binary64)))) x) (neg.f64 (fma.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64))) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (.f64 x #s(literal 1/4 binary64))))))
(/.f64 (.f64 (neg.f64 (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) #s(literal 1/4 binary64)))) x) (.f64 (neg.f64 x) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))))
(/.f64 (.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))))) x) (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
(/.f64 (/.f64 (.f64 x (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) #s(literal 1/4 binary64)))) x) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) (.f64 x (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 (.f64 x (*.f64 x x)) #s(literal 1/576 binary64))) #s(literal 1/4 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64))) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (.f64 x #s(literal 1/4 binary64)))) (.f64 x (.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64)) #s(literal 1/8 binary64))))) #s(literal -1 binary64))
(.f64 x (.f64 x (fma.f64 x (*.f64 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 (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) x)
(.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))))
(.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64)) #s(literal 1/8 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64))) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (*.f64 x #s(literal 1/4 binary64))))) x))
(.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64)) #s(literal 1/8 binary64))) (/.f64 x (fma.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64))) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (.f64 x #s(literal 1/4 binary64))))))
(.f64 (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) #s(literal 1/4 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))) x))
(.f64 (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) #s(literal 1/4 binary64))) (/.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))))
(.f64 (.f64 x (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) #s(literal 1/4 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))))
(.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64)) #s(literal 1/8 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64))) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (*.f64 x #s(literal 1/4 binary64))))))
(.f64 (/.f64 (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) #s(literal 1/4 binary64))) x) (/.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))))
(.f64 (/.f64 (.f64 x (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) #s(literal 1/4 binary64)))) (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) #s(literal 1/4 binary64)))) (.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 (/.f64 (.f64 x (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) #s(literal 1/4 binary64)))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64))) #s(literal 1/8 binary64)))) (fma.f64 (.f64 x x) (fma.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64)) #s(literal 1/4 binary64)) (.f64 x (.f64 (.f64 x (*.f64 x x)) #s(literal -1/48 binary64)))))
(.f64 (/.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64)) #s(literal 1/8 binary64)))) (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))) (.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))) (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976 binary64)))))) (fma.f64 (.f64 x (-.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/48 binary64)))) (-.f64 (.f64 x (-.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/48 binary64)))) (.f64 x (.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) x))) (.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 1/331776 binary64))))
(.f64 (/.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64)) #s(literal 1/8 binary64)))) (.f64 (fma.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64))) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (.f64 x #s(literal 1/4 binary64)))) (fma.f64 (.f64 x x) (-.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) #s(literal 1/4 binary64)) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/48 binary64)))))) (fma.f64 (.f64 x x) (-.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) #s(literal 1/4 binary64)) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/48 binary64)))))
(exp.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 3/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 3/2 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 3/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 3/2 binary64) (*.f64 (log.f64 x) #s(literal 3/2 binary64))))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 3 binary64)) (log.f64 x))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 x) #s(literal 3 binary64)))
(exp.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 x (exp.f64 (log.f64 #s(literal 1/2 binary64))))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) x)

eval46.0ms (0.4%)

Memory: 7.4MiB live, 45.1MiB allocated
Compiler: Compiled 7 022 to 593 computations (91.6% saved)

prune77.0ms (0.7%)

Memory

-5.5MiB live, 70.4MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	237	0	237
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	237	6	243

Accuracy

100.0%

Counts

243 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	51.1%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
✓	99.9%	#s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #s(literal 1/2 binary64))) x))
✓	99.9%	#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))))
✓	99.9%	#s(approx (- 1 (cos x)) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))))
✓	99.5%	#s(approx (- 1 (cos x)) (.f64 (.f64 x #s(literal 1/2 binary64)) x))

Compiler

Compiled 188 to 80 computations (57.4% saved)

regimes55.0ms (0.5%)

Memory

-41.4MiB live, 34.6MiB allocated

Counts

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

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

Calls

3 calls:

48.0ms	x
3.0ms	(cos.f64 x)
3.0ms	(-.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)

regimes9.0ms (0.1%)

Memory

17.5MiB live, 17.5MiB allocated

Counts

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

Calls

3 calls:

3.0ms	x
3.0ms	(cos.f64 x)
3.0ms	(-.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)

regimes35.0ms (0.3%)

Memory

-19.7MiB live, 15.7MiB allocated

Counts

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

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:

28.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))
3.0ms	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)

regimes8.0ms (0.1%)

Memory

15.1MiB live, 15.1MiB allocated

Counts

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
99.9%	1	`(cos.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes7.0ms (0.1%)

Memory

12.2MiB live, 12.2MiB 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 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/24 binary64) (.f64 x #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	x
2.0ms	(cos.f64 x)
2.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
99.9%	1	`(cos.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes16.0ms (0.2%)

Memory

-27.7MiB live, 10.6MiB 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:

12.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))
2.0ms	x
2.0ms	(cos.f64 x)

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
99.9%	1	`(cos.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes5.0ms (0%)

Memory

7.8MiB live, 7.8MiB 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
99.5%	1	`x`
99.5%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
99.5%	1	`(cos.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes4.0ms (0%)

Memory

7.0MiB live, 7.0MiB 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:

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

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
99.5%	1	`(cos.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes3.0ms (0%)

Memory

6.2MiB live, 6.2MiB 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
51.1%	1	`x`
51.1%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
51.1%	1	`(cos.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

simplify9.0ms (0.1%)

Memory

12.4MiB live, 12.4MiB allocated

Algorithm

1×	egg-herbie

Rules

50×	`*-commutative_binary64`
20×	`+-commutative_binary64`
20×	`sub-neg_binary64`
20×	`neg-sub0_binary64`
20×	`neg-mul-1_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	49	133
1	75	133
2	88	133
3	106	133
4	123	132
5	137	132
6	140	132
7	141	132

Stop Event

1×

saturated

Calls

Call 1

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

soundness3.0s (28.1%)

Memory

-39.4MiB live, 604.4MiB allocated

Rules

32 720×	`lower-fma.f64`
32 720×	`lower-fma.f32`
4 830×	`lower-*.f64`
4 830×	`lower-*.f32`
4 620×	`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	4	6
0	6	6
1	23	6
2	142	6
3	1153	6
0	9240	6
0	28	147
0	48	141
1	186	134
2	1266	133
0	8460	133

Stop Event

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

Compiler

Compiled 218 to 104 computations (52.3% saved)

preprocess69.0ms (0.7%)

Memory: 22.5MiB live, 209.6MiB allocated
Remove: (abs x)
Compiler: Compiled 368 to 178 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	19	128
0	29	120
1	51	120
2	71	116
3	89	114
4	99	114
5	107	114
6	117	114
7	128	114
8	131	114
0	131	114

Iter	Nodes	Cost
0	12	53
0	18	45
1	31	45
2	55	45
3	87	45
4	100	45
5	108	45
6	118	45
7	129	45
8	132	45
0	132	45

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	19	128
0	29	120
1	51	120
2	71	116
3	89	114
4	99	114
5	107	114
6	117	114
7	128	114
8	131	114
0	131	114

Iter	Nodes	Cost
0	12	53
0	18	45
1	31	45
2	55	45
3	87	45
4	100	45
5	108	45
6	118	45
7	129	45
8	132	45
0	132	45

start0.0ms (0%)

analyze3.0ms (0%)

sample3.0s (28.1%)

explain146.0ms (1.4%)

preprocess46.0ms (0.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0%)

localize83.0ms (0.8%)

series1.0ms (0%)

simplify628.0ms (6%)

rewrite254.0ms (2.4%)

eval51.0ms (0.5%)

prune93.0ms (0.9%)

simplify46.0ms (0.4%)

localize285.0ms (2.7%)

series22.0ms (0.2%)

simplify273.0ms (2.6%)

rewrite337.0ms (3.2%)

eval154.0ms (1.5%)

prune259.0ms (2.5%)

simplify22.0ms (0.2%)

localize121.0ms (1.2%)

series9.0ms (0.1%)

simplify224.0ms (2.1%)

rewrite322.0ms (3.1%)

eval98.0ms (0.9%)

prune63.0ms (0.6%)

simplify9.0ms (0.1%)

localize88.0ms (0.8%)

series6.0ms (0.1%)

simplify182.0ms (1.7%)

rewrite440.0ms (4.2%)

eval46.0ms (0.4%)

prune77.0ms (0.7%)

regimes55.0ms (0.5%)

regimes9.0ms (0.1%)

regimes35.0ms (0.3%)

regimes8.0ms (0.1%)

regimes7.0ms (0.1%)

regimes16.0ms (0.2%)

regimes5.0ms (0%)

regimes4.0ms (0%)

regimes3.0ms (0%)

simplify9.0ms (0.1%)

soundness3.0s (28.1%)

preprocess69.0ms (0.7%)

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	19	128
0	29	120
1	51	120
2	71	116
3	89	114
4	99	114
5	107	114
6	117	114
7	128	114
8	131	114
0	131	114

Iter	Nodes	Cost
0	12	53
0	18	45
1	31	45
2	55	45
3	87	45
4	100	45
5	108	45
6	118	45
7	129	45
8	132	45
0	132	45