Metrics for Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, A

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze171.0ms (1.7%)

Memory

18.3MiB live, 378.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample1.7s (17.6%)

Memory

14.0MiB live, 1 949.7MiB allocated

Samples

1.4s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.1s

ival-sin: 741.0ms (70.1% of total)

ival-mult: 173.0ms (16.4% of total)

ival-div: 122.0ms (11.5% of total)

exact: 11.0ms (1% of total)

ival-true: 7.0ms (0.7% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

explain130.0ms (1.3%)

Memory

14.4MiB live, 289.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
65	0	-	3	(-1.3440810208745528e-158)	`(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))`
0	0	-	0	-	`(.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64))))`
0	124	(-5.571022353677027e+86)	0	-	`(sin.f64 (*.f64 x #s(literal 1/2 binary64)))`
0	0	-	0	-	`#s(literal 8 binary64)`
0	0	-	0	-	`#s(literal 3 binary64)`
0	0	-	0	-	`(*.f64 x #s(literal 1/2 binary64))`
0	0	-	0	-	`(.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64))))`
0	0	-	0	-	`(/.f64 #s(literal 8 binary64) #s(literal 3 binary64))`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`#s(literal 1/2 binary64)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sin.f64`	`(sin.f64 (*.f64 x #s(literal 1/2 binary64)))`	sensitivity	124	0
`/.f64`	`(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))`	u/n	62	0
↳	`(.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64))))`	underflow	62

Confusion

	Predicted +	Predicted -
+	62	3
-	124	67

Precision

0.3333333333333333

Recall

0.9538461538461539

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	62	0	3
-	124	0	67

Precision?

0.3333333333333333

Recall?

0.9538461538461539

Freqs

test

number	freq
0	70
1	186

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

58.0ms

512×

valid

Compiler

Compiled 126 to 37 computations (70.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-sin: 25.0ms (58.6% of total)

ival-mult: 9.0ms (21.1% of total)

ival-div: 7.0ms (16.4% of total)

exact: 1.0ms (2.3% of total)

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

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

preprocess56.0ms (0.6%)

Memory

-5.7MiB live, 37.1MiB allocated

Algorithm

1×	egg-herbie

Rules

586×	`times-frac`
414×	`associate-*r/`
412×	`associate-r`
284×	`associate-l`
270×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	35
1	35	29
2	95	28
3	296	28
4	900	28
5	1747	28
6	1848	28
7	1878	28
8	1906	28
9	1918	28
10	1990	28
11	2425	28
0	11	14
0	19	14
1	26	14
2	36	14
3	45	14
4	48	14
0	48	14

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))

Outputs

(/.f64 (*.f64 (*.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (*.f64 x #s(literal 1/2 binary64)))) (sin.f64 (*.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))

(*.f64 (*.f64 (/.f64 #s(literal 8/3 binary64) (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) x)))

Symmetry

(negabs x)

Compiler

Compiled 16 to 11 computations (31.3% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	76.4%	(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))

Compiler

Compiled 16 to 11 computations (31.3% saved)

simplify4.0ms (0%)

Memory

7.1MiB live, 7.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
cost-diff	0	(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))
cost-diff	704	(/.f64 #s(literal 8 binary64) #s(literal 3 binary64))

Rules

46×	`lower-*.f32`
40×	`lower-*.f64`
20×	`*-commutative`
10×	`associate-/l*`
10×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	45
0	19	45
1	26	45
2	36	45
3	45	45
4	48	45
0	48	45

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))
(.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(/.f64 #s(literal 8 binary64) #s(literal 3 binary64))
#s(literal 8 binary64)
#s(literal 3 binary64)
(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
(sin.f64 x)

Outputs
(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))
(.f64 (.f64 (/.f64 #s(literal 8/3 binary64) (sin.f64 x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 8/3 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 8/3 binary64))
(/.f64 #s(literal 8 binary64) #s(literal 3 binary64))
#s(literal 8/3 binary64)
#s(literal 8 binary64)
#s(literal 3 binary64)
(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
x
#s(literal 1/2 binary64)
(sin.f64 x)

localize38.0ms (0.4%)

Memory

-16.0MiB live, 61.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(sin.f64 x)
accuracy	0.19140625	(.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
accuracy	0.375	(.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
accuracy	14.935009939409168	(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))

Samples

30.0ms

256×

valid

Compiler

Compiled 55 to 13 computations (76.4% saved)

Precisions

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

ival-sin: 11.0ms (53.5% of total)

ival-div: 5.0ms (24.3% of total)

ival-mult: 4.0ms (19.5% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

10.6MiB live, 10.6MiB allocated

Counts

5 → 48

Calls

Call 1

Inputs
#s(alt (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (patch (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) (patch (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())

Outputs
#s(alt (* 2/3 x) (taylor 0 x) (#s(alt (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) (patch (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2/3 (* 1/18 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) (patch (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2)))))) (taylor 0 x) (#s(alt (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) (patch (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2)))))))) (taylor 0 x) (#s(alt (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) (patch (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 2/3 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 2/3 (* -1/18 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18)))) (taylor 0 x) (#s(alt (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 2/3 (* (pow x 2) (- (* (pow x 2) (+ 1/540 (* -1/30240 (pow x 2)))) 1/18)))) (taylor 0 x) (#s(alt (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 4/3 x) (taylor 0 x) (#s(alt (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 4/3 (* -1/18 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 4/3 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/18)))) (taylor 0 x) (#s(alt (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 4/3 (* (pow x 2) (- (* (pow x 2) (+ 1/1440 (* -1/241920 (pow x 2)))) 1/18)))) (taylor 0 x) (#s(alt (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/6 (pow x 2)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x))) (taylor inf x) (#s(alt (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) (patch (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x))) (taylor inf x) (#s(alt (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) (patch (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x))) (taylor inf x) (#s(alt (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) (patch (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x))) (taylor inf x) (#s(alt (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) (patch (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (pow (sin (* 1/2 x)) 2)) (taylor inf x) (#s(alt (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (pow (sin (* 1/2 x)) 2)) (taylor inf x) (#s(alt (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (pow (sin (* 1/2 x)) 2)) (taylor inf x) (#s(alt (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (pow (sin (* 1/2 x)) 2)) (taylor inf x) (#s(alt (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (sin (* 1/2 x))) (taylor inf x) (#s(alt (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (sin (* 1/2 x))) (taylor inf x) (#s(alt (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (sin (* 1/2 x))) (taylor inf x) (#s(alt (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (sin (* 1/2 x))) (taylor inf x) (#s(alt (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x))) (taylor -inf x) (#s(alt (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) (patch (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x))) (taylor -inf x) (#s(alt (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) (patch (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x))) (taylor -inf x) (#s(alt (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) (patch (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x))) (taylor -inf x) (#s(alt (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) (patch (/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (pow (sin (* 1/2 x)) 2)) (taylor -inf x) (#s(alt (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (pow (sin (* 1/2 x)) 2)) (taylor -inf x) (#s(alt (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (pow (sin (* 1/2 x)) 2)) (taylor -inf x) (#s(alt (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (pow (sin (* 1/2 x)) 2)) (taylor -inf x) (#s(alt (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (sin (* 1/2 x))) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (sin (* 1/2 x))) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (sin (* 1/2 x))) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (sin (* 1/2 x))) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (patch (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((/ 8 3) (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (* (/ 8 3) (sin (* x 1/2))) (sin x))
1.0ms	x	@	inf	((/ 8 3) (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (* (/ 8 3) (sin (* x 1/2))) (sin x))
1.0ms	x	@	0	((/ 8 3) (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (* (/ 8 3) (sin (* x 1/2))) (sin x))

Time

Variable

Point

Expression

2.0ms

-inf

((/ 8 3) (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (* (/ 8 3) (sin (* x 1/2))) (sin x))

1.0ms

inf

((/ 8 3) (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (* (/ 8 3) (sin (* x 1/2))) (sin x))

1.0ms

((/ 8 3) (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (* (/ 8 3) (sin (* x 1/2))) (sin x))

simplify200.0ms (2%)

Memory

8.2MiB live, 196.8MiB allocated

Algorithm

1×	egg-herbie

Rules

18 506×	`lower-fma.f64`
18 506×	`lower-fma.f32`
4 370×	`lower-+.f64`
4 370×	`lower-+.f32`
3 662×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	90	414
1	252	414
2	600	408
3	1793	408
4	3345	408
5	4708	408
6	5020	408
7	5315	408
8	5937	408
9	7802	408
0	8069	384

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 47

Calls

Call 1

Inputs
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 2/3 (pow x 2))
(* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* (pow x 2) (+ 1/540 (* -1/30240 (pow x 2)))) 1/18))))
(* 4/3 x)
(* x (+ 4/3 (* -1/18 (pow x 2))))
(* x (+ 4/3 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/18))))
(* x (+ 4/3 (* (pow x 2) (- (* (pow x 2) (+ 1/1440 (* -1/241920 (pow x 2)))) 1/18))))
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))))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(sin x)
(sin x)
(sin x)
(sin x)
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(sin x)
(sin x)
(sin x)
(sin x)

Outputs
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x)
(* 2/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* (pow x 2) (+ 1/540 (* -1/30240 (pow x 2)))) 1/18))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/30240 binary64) (.f64 x x) #s(literal 1/540 binary64)) (.f64 x x) #s(literal -1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x) x)
(* 4/3 x)
(*.f64 #s(literal 4/3 binary64) x)
(* x (+ 4/3 (* -1/18 (pow x 2))))
(.f64 (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 4/3 binary64)) x)
(* x (+ 4/3 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/18))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/1440 binary64) (.f64 x x) #s(literal -1/18 binary64)) (*.f64 x x) #s(literal 4/3 binary64)) x)
(* x (+ 4/3 (* (pow x 2) (- (* (pow x 2) (+ 1/1440 (* -1/241920 (pow x 2)))) 1/18))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/241920 binary64) (.f64 x x) #s(literal 1/1440 binary64)) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 4/3 binary64)) x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) x)
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 (/.f64 #s(literal 8/3 binary64) (sin.f64 x)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 (/.f64 #s(literal 8/3 binary64) (sin.f64 x)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 (/.f64 #s(literal 8/3 binary64) (sin.f64 x)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 (/.f64 #s(literal 8/3 binary64) (sin.f64 x)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(literal 8/3 binary64))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(literal 8/3 binary64))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(literal 8/3 binary64))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(literal 8/3 binary64))
(* 8/3 (sin (* 1/2 x)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 8/3 binary64))
(* 8/3 (sin (* 1/2 x)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 8/3 binary64))
(* 8/3 (sin (* 1/2 x)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 8/3 binary64))
(* 8/3 (sin (* 1/2 x)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 8/3 binary64))
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 (/.f64 #s(literal 8/3 binary64) (sin.f64 x)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 (/.f64 #s(literal 8/3 binary64) (sin.f64 x)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 (/.f64 #s(literal 8/3 binary64) (sin.f64 x)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 (/.f64 #s(literal 8/3 binary64) (sin.f64 x)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(literal 8/3 binary64))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(literal 8/3 binary64))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(literal 8/3 binary64))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(literal 8/3 binary64))
(* 8/3 (sin (* 1/2 x)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 8/3 binary64))
(* 8/3 (sin (* 1/2 x)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 8/3 binary64))
(* 8/3 (sin (* 1/2 x)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 8/3 binary64))
(* 8/3 (sin (* 1/2 x)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 8/3 binary64))
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)

rewrite137.0ms (1.4%)

Memory

20.7MiB live, 138.0MiB allocated

Rules

2 420×	`lower-*.f32`
2 414×	`lower-*.f64`
2 008×	`lower-/.f32`
2 006×	`lower-/.f64`
534×	`lower-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	34
0	19	34
1	34	28
2	115	28
3	628	24
0	4915	24

Stop Event

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

Counts

5 → 286

Calls

Call 1

Inputs
(/.f64 #s(literal 8 binary64) #s(literal 3 binary64))
(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))
(.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(sin.f64 x)

Outputs
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eval51.0ms (0.5%)

Memory: -1.3MiB live, 82.3MiB allocated
Compiler: Compiled 5 206 to 753 computations (85.5% saved)

prune32.0ms (0.3%)

Memory

-7.8MiB live, 68.0MiB allocated

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	307	26	333
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	308	26	334

Accuracy

100.0%

Counts

334 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
	52.0%	(/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) #s(literal 1/2 binary64)) (*.f64 #s(literal 3/8 binary64) (sin.f64 x)))
	52.0%	(/.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) #s(literal 1/2 binary64)) (sin.f64 x)) #s(literal 3/8 binary64))
▶	51.9%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) (sin.f64 x))
	51.6%	(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (.f64 (*.f64 #s(literal 3/8 binary64) (sin.f64 x)) (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
	51.8%	(/.f64 (+.f64 #s(literal 4/3 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 8/3 binary64))) (sin.f64 x))
	51.5%	(/.f64 (.f64 (/.f64 #s(literal 8/3 binary64) (sin.f64 x)) (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
	51.9%	(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)) (sin.f64 x))
	76.4%	(/.f64 #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(literal 8/3 binary64))) (sin.f64 x))
	27.4%	(/.f64 #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/30240 binary64) (.f64 x x) #s(literal 1/540 binary64)) (.f64 x x) #s(literal -1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x))
▶	28.9%	(/.f64 #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x))
	27.4%	(/.f64 #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x))
	29.1%	(/.f64 #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 x x) #s(literal 2/3 binary64))) (sin.f64 x))
	51.9%	(/.f64 #s(literal 8/3 binary64) (/.f64 (sin.f64 x) (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) #s(literal 1/2 binary64))))
	51.9%	(/.f64 #s(literal 8/3 binary64) (*.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x)))
	51.9%	(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))))
	51.9%	(*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 8/3 binary64) (sin.f64 x)))
	51.9%	(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) #s(literal 4/3 binary64))
	99.2%	(.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 #s(literal 3/8 binary64) (sin.f64 x))) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
▶	99.5%	(.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64)))
▶	51.9%	(.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x))))
	99.2%	(.f64 (.f64 (/.f64 #s(literal 8/3 binary64) (sin.f64 x)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
	50.7%	#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x))
	50.7%	#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x))
	50.7%	#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x))
	76.4%	#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (.f64 (/.f64 #s(literal 8/3 binary64) (sin.f64 x)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64))))
▶	51.0%	#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 x #s(literal 2/3 binary64)))

Compiler

Compiled 662 to 506 computations (23.6% saved)

simplify338.0ms (3.4%)

Memory

-35.1MiB live, 110.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	128	(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64))
cost-diff	192	(/.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))
cost-diff	1216	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64))))
cost-diff	6464	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) (sin.f64 x))
cost-diff	0	(cos.f64 x)
cost-diff	0	(-.f64 #s(literal 1 binary64) (cos.f64 x))
cost-diff	320	(/.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 3/8 binary64) (sin.f64 x)))
cost-diff	6592	(.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x))))
cost-diff	0	(.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
cost-diff	0	(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)
cost-diff	0	#s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x))
cost-diff	0	(/.f64 #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x))
cost-diff	0	(*.f64 x #s(literal 2/3 binary64))
cost-diff	0	#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 x #s(literal 2/3 binary64)))
cost-diff	0	(*.f64 x #s(literal 1/2 binary64))
cost-diff	0	(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
cost-diff	0	(/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) (sin.f64 x))
cost-diff	384	(.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64)))

Rules

12 358×	`lower-fma.f32`
12 354×	`lower-fma.f64`
2 444×	`lower-*.f32`
2 426×	`lower-*.f64`
1 348×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	255
0	67	245
1	108	241
2	194	235
3	412	235
4	853	235
5	1595	235
6	2853	235
7	4194	235
8	5105	235
9	5888	235
10	6909	235
11	7400	235
12	7465	235
13	7531	235
0	8052	233

Stop Event

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

Calls

Call 1

Inputs
(.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64)))
(/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) (sin.f64 x))
(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
(sin.f64 x)
(/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64))
#s(literal 3/8 binary64)
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 x #s(literal 2/3 binary64)))
(*.f64 x #s(literal 2/3 binary64))
x
#s(literal 2/3 binary64)
(/.f64 #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x))
#s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)
(.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64))
(fma.f64 #s(literal 1/540 binary64) (*.f64 x x) #s(literal -1/18 binary64))
#s(literal 1/540 binary64)
(*.f64 x x)
x
#s(literal -1/18 binary64)
#s(literal 2/3 binary64)
(sin.f64 x)
(.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x))))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(/.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 3/8 binary64) (sin.f64 x)))
#s(literal 1/2 binary64)
(*.f64 #s(literal 3/8 binary64) (sin.f64 x))
#s(literal 3/8 binary64)
(sin.f64 x)
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) (sin.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64))))
#s(literal 1 binary64)
(/.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))
#s(literal 2 binary64)
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
x
#s(literal 8/3 binary64)
(sin.f64 x)

Outputs
(.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64)))
(.f64 (.f64 (/.f64 #s(literal 8/3 binary64) (sin.f64 x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) x)) (sin.f64 x))
(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
x
#s(literal 1/2 binary64)
(sin.f64 x)
(/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64))
(/.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 3/8 binary64))
#s(literal 3/8 binary64)
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 x #s(literal 2/3 binary64)))
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 #s(literal 2/3 binary64) x))
(*.f64 x #s(literal 2/3 binary64))
(*.f64 #s(literal 2/3 binary64) x)
x
#s(literal 2/3 binary64)
(/.f64 #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x))
(/.f64 #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/540 binary64) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x))
#s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x))
#s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/540 binary64) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)
(.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/540 binary64) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)
(.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/540 binary64) #s(literal -1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/540 binary64) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64))
(fma.f64 #s(literal 1/540 binary64) (*.f64 x x) #s(literal -1/18 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/540 binary64) #s(literal -1/18 binary64))
#s(literal 1/540 binary64)
(*.f64 x x)
x
#s(literal -1/18 binary64)
#s(literal 2/3 binary64)
(sin.f64 x)
(.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x))))
(*.f64 #s(literal -4/3 binary64) (tan.f64 (/.f64 x #s(literal -2 binary64))))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(/.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 3/8 binary64) (sin.f64 x)))
(/.f64 #s(literal 4/3 binary64) (sin.f64 x))
#s(literal 1/2 binary64)
(*.f64 #s(literal 3/8 binary64) (sin.f64 x))
#s(literal 3/8 binary64)
(sin.f64 x)
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) (sin.f64 x))
(*.f64 #s(literal -4/3 binary64) (tan.f64 (/.f64 x #s(literal -2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64))))
(fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))
#s(literal 1 binary64)
(/.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))
(/.f64 #s(literal 3/4 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
#s(literal 2 binary64)
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64))
(fma.f64 #s(literal -8/3 binary64) (cos.f64 x) #s(literal 8/3 binary64))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
x
#s(literal 8/3 binary64)
(sin.f64 x)

localize519.0ms (5.3%)

Memory

10.8MiB live, 327.5MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.3046875	(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64))
accuracy	0.5491115806186344	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64))))
accuracy	14.935009939409168	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) (sin.f64 x))
accuracy	15.681067201600388	(-.f64 #s(literal 1 binary64) (cos.f64 x))
accuracy	0.19140625	(*.f64 #s(literal 3/8 binary64) (sin.f64 x))
accuracy	0.296875	(/.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 3/8 binary64) (sin.f64 x)))
accuracy	14.947129605796523	(.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x))))
accuracy	15.681067201600388	(-.f64 #s(literal 1 binary64) (cos.f64 x))
accuracy	0.22265625	(.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
accuracy	0.3030649583020021	(fma.f64 #s(literal 1/540 binary64) (*.f64 x x) #s(literal -1/18 binary64))
accuracy	14.935009939409168	(/.f64 #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x))
accuracy	30.740214876098612	#s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x))
accuracy	0.328125	(*.f64 x #s(literal 2/3 binary64))
accuracy	31.163838776788044	#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 x #s(literal 2/3 binary64)))
accuracy	0	(sin.f64 x)
accuracy	0.1171875	(/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64))
accuracy	0.13671875	(/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) (sin.f64 x))
accuracy	0.203125	(.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64)))

Samples

87.0ms	130×	0	valid
82.0ms	58×	2	valid
55.0ms	46×	1	valid
30.0ms	22×	3	valid

Compiler

Compiled 234 to 40 computations (82.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 225.0ms

const: 53.0ms (23.6% of total)

ival-div: 50.0ms (22.2% of total)

ival-sin: 36.0ms (16% of total)

ival-mult: 28.0ms (12.5% of total)

ival-cos: 22.0ms (9.8% of total)

ival-sub: 22.0ms (9.8% of total)

adjust: 9.0ms (4% of total)

ival-add: 3.0ms (1.3% of total)

exact: 1.0ms (0.4% of total)

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

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

series28.0ms (0.3%)

Memory

9.0MiB live, 45.4MiB allocated

Counts

22 → 264

Calls

Call 1

Inputs
#s(alt (.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64))) (patch (.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (patch (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())
#s(alt (sin.f64 (.f64 x #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (.f64 x #s(literal 2/3 binary64))) (patch #s(approx (/ ( (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 x #s(literal 2/3 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 2/3 binary64)) (patch (.f64 x #s(literal 2/3 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x)) (patch (/.f64 #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x)) #<representation binary64>) () ())
#s(alt #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)) (patch #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x)))) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x))) (patch (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 x)) (patch (-.f64 #s(literal 1 binary64) (cos.f64 x)) #<representation binary64>) () ())
#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) (sin.f64 x)) (patch (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) (sin.f64 x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64))) (patch (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64)) (patch (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64)) #<representation binary64>) () ())
#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (patch (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 3/8 binary64) (sin.f64 x)) (patch (.f64 #s(literal 3/8 binary64) (sin.f64 x)) #<representation binary64>) () ())

Outputs
#s(alt (* 2/3 x) (taylor 0 x) (#s(alt (.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64))) (patch (.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2/3 (* 1/18 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64))) (patch (.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2)))))) (taylor 0 x) (#s(alt (.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64))) (patch (.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2)))))))) (taylor 0 x) (#s(alt (.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64))) (patch (.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64))) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor 0 x) (#s(alt (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (patch (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/16 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (patch (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (+ 1/16 (* 5/768 (pow x 2))))) (taylor 0 x) (#s(alt (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (patch (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (+ 1/16 (* (pow x 2) (+ 5/768 (* 61/92160 (pow x 2))))))) (taylor 0 x) (#s(alt (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (patch (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (sin.f64 (.f64 x #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/48 (pow x 2)))) (taylor 0 x) (#s(alt (sin.f64 (.f64 x #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48)))) (taylor 0 x) (#s(alt (sin.f64 (.f64 x #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48)))) (taylor 0 x) (#s(alt (sin.f64 (.f64 x #s(literal 1/2 binary64))) (patch (sin.f64 (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/3 x) (taylor 0 x) (#s(alt #s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (.f64 x #s(literal 2/3 binary64))) (patch #s(approx (/ ( (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 x #s(literal 2/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2/3 (* 1/18 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (.f64 x #s(literal 2/3 binary64))) (patch #s(approx (/ ( (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 x #s(literal 2/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (.f64 x #s(literal 2/3 binary64))) (patch #s(approx (/ ( (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 x #s(literal 2/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (.f64 x #s(literal 2/3 binary64))) (patch #s(approx (/ ( (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 x #s(literal 2/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2/3 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2/3 binary64)) (patch (.f64 x #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/3 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2/3 binary64)) (patch (.f64 x #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2/3 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2/3 binary64)) (patch (.f64 x #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* 8/3 (pow (sin (* 1/2 x)) 2)) (taylor -inf x) (#s(alt #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)) (patch #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (pow (sin (* 1/2 x)) 2)) (taylor -inf x) (#s(alt #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)) (patch #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/540 (pow x 6)) (taylor -inf x) (#s(alt (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (- 1/540 (* 1/18 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (- (+ 1/540 (/ 2/3 (pow x 4))) (* 1/18 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 6) (- (+ 1/540 (/ 2/3 (pow x 4))) (* 1/18 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* 1/540 (pow x 5)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* (pow x 5) (- (* 1/18 (/ 1 (pow x 2))) (+ 1/540 (/ 2/3 (pow x 4)))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) #<representation binary64>) () ())) ())
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#s(alt (* 4/3 (/ (- 1 (cos x)) (sin x))) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x)))) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (/ (- 1 (cos x)) (sin x))) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x)))) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (/ (- 1 (cos x)) (sin x))) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x)))) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (/ (- 1 (cos x)) (sin x))) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x)))) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (/ 4/3 (sin x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x))) (patch (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ 4/3 (sin x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x))) (patch (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ 4/3 (sin x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x))) (patch (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ 4/3 (sin x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x))) (patch (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.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 (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 (* 4/3 (/ (- 1 (cos x)) (sin x))) (taylor -inf x) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) (sin.f64 x)) (patch (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) (sin.f64 x)) #<representation binary64>) () ())) ())
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#s(alt (* 4/3 (/ (- 1 (cos x)) (sin x))) (taylor -inf x) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) (sin.f64 x)) (patch (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (/ (- 1 (cos x)) (sin x))) (taylor -inf x) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) (sin.f64 x)) (patch (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (- 1 (cos x))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (- 1 (cos x))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (- 1 (cos x))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (- 1 (cos x))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 3/4 (- 1 (cos x))) (taylor -inf x) (#s(alt (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64))) (patch (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 3/4 (- 1 (cos x))) (taylor -inf x) (#s(alt (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64))) (patch (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 3/4 (- 1 (cos x))) (taylor -inf x) (#s(alt (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64))) (patch (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 3/4 (- 1 (cos x))) (taylor -inf x) (#s(alt (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64))) (patch (/.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (- 1 (cos x))) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (- 1 (cos x))) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (- 1 (cos x))) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* 8/3 (sin (* 1/2 x))) (taylor -inf x) (#s(alt (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64)) (patch (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (sin (* 1/2 x))) (taylor -inf x) (#s(alt (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64)) (patch (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (sin (* 1/2 x))) (taylor -inf x) (#s(alt (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64)) (patch (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 8/3 (sin (* 1/2 x))) (taylor -inf x) (#s(alt (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64)) (patch (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* 1/540 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (patch (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/540 (* 1/18 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (patch (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/540 (* 1/18 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (patch (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/540 (* 1/18 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (patch (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 3/8 (sin x)) (taylor -inf x) (#s(alt (.f64 #s(literal 3/8 binary64) (sin.f64 x)) (patch (.f64 #s(literal 3/8 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 3/8 (sin x)) (taylor -inf x) (#s(alt (.f64 #s(literal 3/8 binary64) (sin.f64 x)) (patch (.f64 #s(literal 3/8 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 3/8 (sin x)) (taylor -inf x) (#s(alt (.f64 #s(literal 3/8 binary64) (sin.f64 x)) (patch (.f64 #s(literal 3/8 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 3/8 (sin x)) (taylor -inf x) (#s(alt (.f64 #s(literal 3/8 binary64) (sin.f64 x)) (patch (.f64 #s(literal 3/8 binary64) (sin.f64 x)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

8.0ms

inf

((* (/ (sin (* x 1/2)) (sin x)) (/ (sin (* x 1/2)) 3/8)) (/ (sin (* x 1/2)) (sin x)) (sin (* x 1/2)) (* x 1/2) (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (* x 2/3) (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (* (* (+ (* (+ (* 1/540 (* x x)) -1/18) (* x x)) 2/3) x) x) (* (+ (* (+ (* 1/540 (* x x)) -1/18) (* x x)) 2/3) x) (* (- 1 (cos x)) (/ 1/2 (* 3/8 (sin x)))) (/ 1/2 (* 3/8 (sin x))) (- 1 (cos x)) (cos x) (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (/ 2 (* (- 1 (cos x)) 8/3)) (* (- 1 (cos x)) 8/3) (/ (sin (* x 1/2)) 3/8) (sin x) (+ (* 1/540 (* x x)) -1/18) (* 3/8 (sin x)))

7.0ms

-inf

((* (/ (sin (* x 1/2)) (sin x)) (/ (sin (* x 1/2)) 3/8)) (/ (sin (* x 1/2)) (sin x)) (sin (* x 1/2)) (* x 1/2) (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (* x 2/3) (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (* (* (+ (* (+ (* 1/540 (* x x)) -1/18) (* x x)) 2/3) x) x) (* (+ (* (+ (* 1/540 (* x x)) -1/18) (* x x)) 2/3) x) (* (- 1 (cos x)) (/ 1/2 (* 3/8 (sin x)))) (/ 1/2 (* 3/8 (sin x))) (- 1 (cos x)) (cos x) (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (/ 2 (* (- 1 (cos x)) 8/3)) (* (- 1 (cos x)) 8/3) (/ (sin (* x 1/2)) 3/8) (sin x) (+ (* 1/540 (* x x)) -1/18) (* 3/8 (sin x)))

4.0ms

((* (/ (sin (* x 1/2)) (sin x)) (/ (sin (* x 1/2)) 3/8)) (/ (sin (* x 1/2)) (sin x)) (sin (* x 1/2)) (* x 1/2) (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (* x 2/3) (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (* (* (+ (* (+ (* 1/540 (* x x)) -1/18) (* x x)) 2/3) x) x) (* (+ (* (+ (* 1/540 (* x x)) -1/18) (* x x)) 2/3) x) (* (- 1 (cos x)) (/ 1/2 (* 3/8 (sin x)))) (/ 1/2 (* 3/8 (sin x))) (- 1 (cos x)) (cos x) (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (/ 2 (* (- 1 (cos x)) 8/3)) (* (- 1 (cos x)) 8/3) (/ (sin (* x 1/2)) 3/8) (sin x) (+ (* 1/540 (* x x)) -1/18) (* 3/8 (sin x)))

simplify207.0ms (2.1%)

Memory

2.3MiB live, 190.5MiB allocated

Algorithm

1×	egg-herbie

Rules

12 558×	`lower-fma.f64`
12 558×	`lower-fma.f32`
5 306×	`lower-+.f64`
5 306×	`lower-+.f32`
4 290×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	276	2108
1	740	2108
2	1815	2102
3	3189	2102
4	5298	2102
5	7155	2102
0	8178	1965

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 263

Calls

Call 1

Inputs
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
1/2
(+ 1/2 (* 1/16 (pow x 2)))
(+ 1/2 (* (pow x 2) (+ 1/16 (* 5/768 (pow x 2)))))
(+ 1/2 (* (pow x 2) (+ 1/16 (* (pow x 2) (+ 5/768 (* 61/92160 (pow x 2)))))))
(* 1/2 x)
(* x (+ 1/2 (* -1/48 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 2/3 (pow x 2))
(* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* (pow x 2) (+ 1/540 (* -1/30240 (pow x 2)))) 1/18))))
(* 2/3 (pow x 2))
(* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))
(* 2/3 x)
(* x (+ 2/3 (* -1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))
(* x (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(/ 4/3 x)
(/ (+ 4/3 (* 2/9 (pow x 2))) x)
(/ (+ 4/3 (* (pow x 2) (+ 2/9 (* 7/270 (pow x 2))))) x)
(/ (+ 4/3 (* (pow x 2) (+ 2/9 (* (pow x 2) (+ 7/270 (* 31/11340 (pow x 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
(+ 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)))
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 2/3 (pow x 2))
(* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* (pow x 2) (+ 1/540 (* -1/30240 (pow x 2)))) 1/18))))
(/ 3/2 (pow x 2))
(/ (+ 3/2 (* 1/8 (pow x 2))) (pow x 2))
(/ (+ 3/2 (* (pow x 2) (+ 1/8 (* 1/160 (pow x 2))))) (pow x 2))
(/ (+ 3/2 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 1/160 (* 1/4032 (pow x 2))))))) (pow x 2))
(* 4/3 (pow x 2))
(* (pow x 2) (+ 4/3 (* -1/9 (pow x 2))))
(* (pow x 2) (+ 4/3 (* (pow x 2) (- (* 1/270 (pow x 2)) 1/9))))
(* (pow x 2) (+ 4/3 (* (pow x 2) (- (* (pow x 2) (+ 1/270 (* -1/15120 (pow x 2)))) 1/9))))
(* 4/3 x)
(* x (+ 4/3 (* -1/18 (pow x 2))))
(* x (+ 4/3 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/18))))
(* x (+ 4/3 (* (pow x 2) (- (* (pow x 2) (+ 1/1440 (* -1/241920 (pow x 2)))) 1/18))))
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))))
-1/18
(- (* 1/540 (pow x 2)) 1/18)
(- (* 1/540 (pow x 2)) 1/18)
(- (* 1/540 (pow x 2)) 1/18)
(* 3/8 x)
(* x (+ 3/8 (* -1/16 (pow x 2))))
(* x (+ 3/8 (* (pow x 2) (- (* 1/320 (pow x 2)) 1/16))))
(* x (+ 3/8 (* (pow x 2) (- (* (pow x 2) (+ 1/320 (* -1/13440 (pow x 2)))) 1/16))))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(/ (sin (* 1/2 x)) (sin x))
(/ (sin (* 1/2 x)) (sin x))
(/ (sin (* 1/2 x)) (sin x))
(/ (sin (* 1/2 x)) (sin x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 1/540 (pow x 6))
(* (pow x 6) (- 1/540 (* 1/18 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/540 (/ 2/3 (pow x 4))) (* 1/18 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/540 (/ 2/3 (pow x 4))) (* 1/18 (/ 1 (pow x 2)))))
(* 1/540 (pow x 5))
(* (pow x 5) (- 1/540 (* 1/18 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 1/540 (/ 2/3 (pow x 4))) (* 1/18 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 1/540 (/ 2/3 (pow x 4))) (* 1/18 (/ 1 (pow x 2)))))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(/ 4/3 (sin x))
(/ 4/3 (sin x))
(/ 4/3 (sin x))
(/ 4/3 (sin x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(/ 3/4 (- 1 (cos x)))
(/ 3/4 (- 1 (cos x)))
(/ 3/4 (- 1 (cos x)))
(/ 3/4 (- 1 (cos x)))
(* 8/3 (- 1 (cos x)))
(* 8/3 (- 1 (cos x)))
(* 8/3 (- 1 (cos x)))
(* 8/3 (- 1 (cos x)))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(sin x)
(sin x)
(sin x)
(sin x)
(* 1/540 (pow x 2))
(* (pow x 2) (- 1/540 (* 1/18 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/540 (* 1/18 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/540 (* 1/18 (/ 1 (pow x 2)))))
(* 3/8 (sin x))
(* 3/8 (sin x))
(* 3/8 (sin x))
(* 3/8 (sin x))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(/ (sin (* 1/2 x)) (sin x))
(/ (sin (* 1/2 x)) (sin x))
(/ (sin (* 1/2 x)) (sin x))
(/ (sin (* 1/2 x)) (sin x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 1/540 (pow x 6))
(* (pow x 6) (- 1/540 (* 1/18 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/540 (/ 2/3 (pow x 4))) (* 1/18 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/540 (/ 2/3 (pow x 4))) (* 1/18 (/ 1 (pow x 2)))))
(* 1/540 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/18 (/ 1 (pow x 2))) 1/540)))
(* -1 (* (pow x 5) (- (* 1/18 (/ 1 (pow x 2))) (+ 1/540 (/ 2/3 (pow x 4))))))
(* -1 (* (pow x 5) (- (* 1/18 (/ 1 (pow x 2))) (+ 1/540 (/ 2/3 (pow x 4))))))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(/ 4/3 (sin x))
(/ 4/3 (sin x))
(/ 4/3 (sin x))
(/ 4/3 (sin x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(/ 3/4 (- 1 (cos x)))
(/ 3/4 (- 1 (cos x)))
(/ 3/4 (- 1 (cos x)))
(/ 3/4 (- 1 (cos x)))
(* 8/3 (- 1 (cos x)))
(* 8/3 (- 1 (cos x)))
(* 8/3 (- 1 (cos x)))
(* 8/3 (- 1 (cos x)))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(sin x)
(sin x)
(sin x)
(sin x)
(* 1/540 (pow x 2))
(* (pow x 2) (- 1/540 (* 1/18 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/540 (* 1/18 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/540 (* 1/18 (/ 1 (pow x 2)))))
(* 3/8 (sin x))
(* 3/8 (sin x))
(* 3/8 (sin x))
(* 3/8 (sin x))

Outputs
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/16 (pow x 2)))
(fma.f64 #s(literal 1/16 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (+ 1/16 (* 5/768 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 5/768 binary64) (.f64 x x) #s(literal 1/16 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (+ 1/16 (* (pow x 2) (+ 5/768 (* 61/92160 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 61/92160 binary64) (.f64 x x) #s(literal 5/768 binary64)) (.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/48 (pow x 2))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 x x) #s(literal -1/48 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 x x) #s(literal 1/3840 binary64)) (.f64 x x) #s(literal -1/48 binary64)) (.f64 x x) #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)
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x)
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x)
(* 2/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* (pow x 2) (+ 1/540 (* -1/30240 (pow x 2)))) 1/18))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/30240 binary64) (.f64 x x) #s(literal 1/540 binary64)) (.f64 x x) #s(literal -1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x) x)
(* 2/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* -1/18 (pow x 2))))
(.f64 (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
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(/.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) x)) (sin.f64 x))
(/ (sin (* 1/2 x)) (sin x))
(/.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) x)) (sin.f64 x))
(/ (sin (* 1/2 x)) (sin x))
(/.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) x)) (sin.f64 x))
(/ (sin (* 1/2 x)) (sin x))
(/.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) x)) (sin.f64 x))
(sin (* 1/2 x))
(sin.f64 (*.f64 #s(literal 1/2 binary64) x))
(sin (* 1/2 x))
(sin.f64 (*.f64 #s(literal 1/2 binary64) x))
(sin (* 1/2 x))
(sin.f64 (*.f64 #s(literal 1/2 binary64) x))
(sin (* 1/2 x))
(sin.f64 (*.f64 #s(literal 1/2 binary64) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 (/.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (sin.f64 x)) #s(literal 8/3 binary64))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 (/.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (sin.f64 x)) #s(literal 8/3 binary64))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 (/.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (sin.f64 x)) #s(literal 8/3 binary64))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 (/.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (sin.f64 x)) #s(literal 8/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 (/.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (sin.f64 x)) #s(literal 8/3 binary64))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 (/.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (sin.f64 x)) #s(literal 8/3 binary64))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 (/.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (sin.f64 x)) #s(literal 8/3 binary64))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 (/.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (sin.f64 x)) #s(literal 8/3 binary64))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(literal 8/3 binary64))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(literal 8/3 binary64))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(literal 8/3 binary64))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(literal 8/3 binary64))
(* 1/540 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/540 binary64))
(* (pow x 6) (- 1/540 (* 1/18 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 1/540 binary64) (/.f64 #s(literal 1/18 binary64) (.f64 x x))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (+ 1/540 (/ 2/3 (pow x 4))) (* 1/18 (/ 1 (pow x 2)))))
(.f64 (-.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/18 binary64) (.f64 x x)) #s(literal 1/540 binary64))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (+ 1/540 (/ 2/3 (pow x 4))) (* 1/18 (/ 1 (pow x 2)))))
(.f64 (-.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/18 binary64) (.f64 x x)) #s(literal 1/540 binary64))) (pow.f64 x #s(literal 6 binary64)))
(* 1/540 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/540 binary64))
(* -1 (* (pow x 5) (- (* 1/18 (/ 1 (pow x 2))) 1/540)))
(.f64 (pow.f64 x #s(literal 5 binary64)) (-.f64 #s(literal 1/540 binary64) (/.f64 #s(literal 1/18 binary64) (.f64 x x))))
(* -1 (* (pow x 5) (- (* 1/18 (/ 1 (pow x 2))) (+ 1/540 (/ 2/3 (pow x 4))))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (-.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/18 binary64) (.f64 x x)) #s(literal 1/540 binary64))))
(* -1 (* (pow x 5) (- (* 1/18 (/ 1 (pow x 2))) (+ 1/540 (/ 2/3 (pow x 4))))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (-.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/18 binary64) (.f64 x x)) #s(literal 1/540 binary64))))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(/ 4/3 (sin x))
(/.f64 #s(literal 4/3 binary64) (sin.f64 x))
(/ 4/3 (sin x))
(/.f64 #s(literal 4/3 binary64) (sin.f64 x))
(/ 4/3 (sin x))
(/.f64 #s(literal 4/3 binary64) (sin.f64 x))
(/ 4/3 (sin x))
(/.f64 #s(literal 4/3 binary64) (sin.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))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (- 1 (cos x)))
(fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))
(* 4/3 (- 1 (cos x)))
(fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))
(* 4/3 (- 1 (cos x)))
(fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))
(* 4/3 (- 1 (cos x)))
(fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))
(/ 3/4 (- 1 (cos x)))
(/.f64 #s(literal 3/4 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(/ 3/4 (- 1 (cos x)))
(/.f64 #s(literal 3/4 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(/ 3/4 (- 1 (cos x)))
(/.f64 #s(literal 3/4 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(/ 3/4 (- 1 (cos x)))
(/.f64 #s(literal 3/4 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(* 8/3 (- 1 (cos x)))
(fma.f64 #s(literal -8/3 binary64) (cos.f64 x) #s(literal 8/3 binary64))
(* 8/3 (- 1 (cos x)))
(fma.f64 #s(literal -8/3 binary64) (cos.f64 x) #s(literal 8/3 binary64))
(* 8/3 (- 1 (cos x)))
(fma.f64 #s(literal -8/3 binary64) (cos.f64 x) #s(literal 8/3 binary64))
(* 8/3 (- 1 (cos x)))
(fma.f64 #s(literal -8/3 binary64) (cos.f64 x) #s(literal 8/3 binary64))
(* 8/3 (sin (* 1/2 x)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 8/3 binary64))
(* 8/3 (sin (* 1/2 x)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 8/3 binary64))
(* 8/3 (sin (* 1/2 x)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 8/3 binary64))
(* 8/3 (sin (* 1/2 x)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 8/3 binary64))
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(* 1/540 (pow x 2))
(.f64 #s(literal 1/540 binary64) (.f64 x x))
(* (pow x 2) (- 1/540 (* 1/18 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/540 binary64) (*.f64 x x) #s(literal -1/18 binary64))
(* (pow x 2) (- 1/540 (* 1/18 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/540 binary64) (*.f64 x x) #s(literal -1/18 binary64))
(* (pow x 2) (- 1/540 (* 1/18 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/540 binary64) (*.f64 x x) #s(literal -1/18 binary64))
(* 3/8 (sin x))
(*.f64 (sin.f64 x) #s(literal 3/8 binary64))
(* 3/8 (sin x))
(*.f64 (sin.f64 x) #s(literal 3/8 binary64))
(* 3/8 (sin x))
(*.f64 (sin.f64 x) #s(literal 3/8 binary64))
(* 3/8 (sin x))
(*.f64 (sin.f64 x) #s(literal 3/8 binary64))

rewrite238.0ms (2.4%)

Memory

-0.8MiB live, 248.3MiB allocated

Rules

5 448×	`lower-*.f32`
5 430×	`lower-*.f64`
5 038×	`lower-fma.f32`
5 034×	`lower-fma.f64`
3 510×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	212
0	67	202
1	204	186
2	1139	180
0	8644	179

Stop Event

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

Counts

22 → 1 254

Calls

Call 1

Inputs
(.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64)))
(/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) (sin.f64 x))
(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 x #s(literal 2/3 binary64)))
(*.f64 x #s(literal 2/3 binary64))
(/.f64 #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x))
#s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)
(.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
(.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x))))
(/.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 3/8 binary64) (sin.f64 x)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) (sin.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64))))
(/.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64))
(/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64))
(sin.f64 x)
(fma.f64 #s(literal 1/540 binary64) (*.f64 x x) #s(literal -1/18 binary64))
(*.f64 #s(literal 3/8 binary64) (sin.f64 x))

Outputs
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eval340.0ms (3.5%)

Memory: 20.0MiB live, 392.4MiB allocated
Compiler: Compiled 29 445 to 3 323 computations (88.7% saved)

prune76.0ms (0.8%)

Memory

7.0MiB live, 141.9MiB allocated

Pruning

22 alts after pruning (19 fresh and 3 done)

	Pruned	Kept	Total
New	1 665	17	1 682
Fresh	19	2	21
Picked	2	3	5
Done	0	0	0
Total	1 686	22	1 708

Accuracy

100.0%

Counts

1 708 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	52.0%	(fma.f64 (/.f64 #s(literal 4/3 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x)) (/.f64 #s(literal 4/3 binary64) (sin.f64 x)))
	76.5%	(/.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (.f64 #s(literal 3/8 binary64) (sin.f64 x)))
	76.1%	(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (.f64 (sin.f64 x) #s(literal 3/4 binary64))))
	52.0%	(/.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) #s(literal 1/2 binary64)) (sin.f64 x)) #s(literal 3/8 binary64))
	76.6%	(/.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (sin.f64 x)) #s(literal 3/8 binary64))
▶	52.0%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (sin.f64 x) #s(literal 3/4 binary64)))
	52.0%	(/.f64 #s(approx (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))) (sin.f64 x))
▶	27.4%	(/.f64 #s(approx (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x))
▶	51.9%	(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))))
	99.3%	(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 4/3 binary64))))
	51.9%	(*.f64 (fma.f64 #s(literal -8/3 binary64) (cos.f64 x) #s(literal 8/3 binary64)) (/.f64 #s(literal 1/2 binary64) (sin.f64 x)))
	76.4%	(.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (/.f64 #s(literal 8/3 binary64) (sin.f64 x)))
	51.9%	(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -3/8 binary64)) (/.f64 #s(literal -1/2 binary64) (sin.f64 x)))
✓	99.5%	(.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64)))
	51.9%	(*.f64 (/.f64 #s(literal 4/3 binary64) (sin.f64 x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
✓	51.9%	(.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x))))
	56.4%	(.f64 #s(approx (/ (sin ( x 1/2)) (sin x)) #s(literal 1/2 binary64)) (/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64)))
	50.7%	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x))
	50.7%	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x))
▶	50.7%	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x))
▶	99.4%	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)))
✓	51.0%	#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 x #s(literal 2/3 binary64)))

Compiler

Compiled 449 to 363 computations (19.2% saved)

simplify440.0ms (4.5%)

Memory

-12.9MiB live, 105.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f64 x)
cost-diff	0	(/.f64 (sin.f64 x) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)))
cost-diff	128	(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))
cost-diff	7552	(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))))
cost-diff	0	(*.f64 (sin.f64 x) #s(literal 3/4 binary64))
cost-diff	0	(cos.f64 x)
cost-diff	0	(-.f64 #s(literal 1 binary64) (cos.f64 x))
cost-diff	6976	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (sin.f64 x) #s(literal 3/4 binary64)))
cost-diff	0	(.f64 (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x)
cost-diff	0	(.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)
cost-diff	0	#s(approx (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x))
cost-diff	0	(/.f64 #s(approx (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64))
cost-diff	0	(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
cost-diff	0	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
cost-diff	0	(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
cost-diff	0	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)))

Rules

2 400×	`lower-fma.f32`
2 396×	`lower-fma.f64`
1 756×	`lower-*.f32`
1 740×	`lower-*.f64`
1 182×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	216
0	58	206
1	94	192
2	174	186
3	390	186
4	856	186
5	1588	186
6	2774	186
7	3817	186
8	4354	186
9	5422	186
10	6019	186
11	6264	186
12	6319	186
13	6348	186
14	6370	186
15	6642	186
16	6959	186
17	7008	186
18	7008	186
19	7014	186
20	7070	186
21	7214	186
22	7305	186
23	7511	186
24	7511	186
25	7511	186
26	7512	186
27	7513	186
0	7513	182

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(literal 4/3 binary64)
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64))
(*.f64 x x)
x
#s(literal 1/18 binary64)
#s(literal 2/3 binary64)
(/.f64 #s(approx (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x))
#s(approx (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x))
(.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)
(.f64 (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x)
(fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))
#s(literal -1/18 binary64)
(*.f64 x x)
x
#s(literal 2/3 binary64)
(sin.f64 x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (sin.f64 x) #s(literal 3/4 binary64)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(*.f64 (sin.f64 x) #s(literal 3/4 binary64))
(sin.f64 x)
#s(literal 3/4 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))))
#s(literal 1 binary64)
(/.f64 (sin.f64 x) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)))
(sin.f64 x)
x
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
#s(literal 4/3 binary64)

Outputs
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 #s(literal 4/3 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(.f64 #s(literal 4/3 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(literal 4/3 binary64)
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 #s(literal 1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(.f64 (fma.f64 #s(literal 1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64))
(fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))
(*.f64 x x)
x
#s(literal 1/18 binary64)
#s(literal 2/3 binary64)
(/.f64 #s(approx (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x))
#s(approx (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x))
(.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)
(.f64 (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x)
(fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))
#s(literal -1/18 binary64)
(*.f64 x x)
x
#s(literal 2/3 binary64)
(sin.f64 x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (sin.f64 x) #s(literal 3/4 binary64)))
(.f64 (tan.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal -4/3 binary64))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(*.f64 (sin.f64 x) #s(literal 3/4 binary64))
(*.f64 #s(literal 3/4 binary64) (sin.f64 x))
(sin.f64 x)
#s(literal 3/4 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))))
(.f64 (tan.f64 (.f64 #s(literal -1/2 binary64) x)) #s(literal -4/3 binary64))
#s(literal 1 binary64)
(/.f64 (sin.f64 x) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)))
(/.f64 (sin.f64 x) (fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64)))
(sin.f64 x)
x
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))
(fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
#s(literal 4/3 binary64)

localize343.0ms (3.5%)

Memory

5.8MiB live, 382.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.28515625	(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))))
accuracy	0.3046875	(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))
accuracy	14.939519841004017	(/.f64 (sin.f64 x) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)))
accuracy	15.681067201600388	(-.f64 #s(literal 1 binary64) (cos.f64 x))
accuracy	0	(cos.f64 x)
accuracy	0.19140625	(*.f64 (sin.f64 x) #s(literal 3/4 binary64))
accuracy	14.95789088510185	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (sin.f64 x) #s(literal 3/4 binary64)))
accuracy	15.681067201600388	(-.f64 #s(literal 1 binary64) (cos.f64 x))
accuracy	0.24609375	(.f64 (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x)
accuracy	0.33268199132746407	(fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))
accuracy	14.935009939409168	(/.f64 #s(approx (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x))
accuracy	31.68212994066581	#s(approx (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x))
accuracy	0	(*.f64 x x)
accuracy	0.24609375	(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
accuracy	0.34830699132746407	(fma.f64 (*.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64))
accuracy	31.337552390867344	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x))
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
accuracy	0	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)))
accuracy	0.375	(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))

Samples

107.0ms	58×	2	valid
51.0ms	130×	0	valid
28.0ms	22×	3	valid
21.0ms	46×	1	valid

Compiler

Compiled 185 to 35 computations (81.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 179.0ms

const: 62.0ms (34.7% of total)

ival-cos: 29.0ms (16.2% of total)

adjust: 25.0ms (14% of total)

ival-mult: 23.0ms (12.9% of total)

ival-sin: 15.0ms (8.4% of total)

ival-div: 14.0ms (7.8% of total)

ival-tan: 5.0ms (2.8% of total)

ival-sub: 3.0ms (1.7% of total)

ival-add: 3.0ms (1.7% of total)

exact: 1.0ms (0.6% of total)

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

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

series29.0ms (0.3%)

Memory

-27.8MiB live, 39.8MiB allocated

Counts

21 → 252

Calls

Call 1

Inputs
#s(alt #s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))) (patch #s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)) (patch (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)) #<representation binary64>) () ())
#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())
#s(alt #s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)) (patch #s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x)) (patch (/.f64 #s(approx (/ 1 (/ 2 ( (- 1 (cos x)) 8/3))) (.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x)) #<representation binary64>) () ())
#s(alt #s(approx (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x) x)) (patch #s(approx (/ 1 (/ 2 ( (- 1 (cos x)) 8/3))) (.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x) x) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x) (patch (.f64 (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 (sin.f64 x) #s(literal 3/4 binary64))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 (sin.f64 x) #s(literal 3/4 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 (sin.f64 x) #s(literal 3/4 binary64)) (patch (.f64 (sin.f64 x) #s(literal 3/4 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 x) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))) (patch (/.f64 (sin.f64 x) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))) #<representation binary64>) () ())
#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) (patch (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* 2/3 x) (taylor 0 x) (#s(alt #s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))) (patch #s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2/3 (* 1/18 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))) (patch #s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))) (patch #s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))) (patch #s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2/3 x) (taylor 0 x) (#s(alt (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)) (patch (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2/3 (* 1/18 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)) (patch (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2)))))) (taylor 0 x) (#s(alt (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)) (patch (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2)))))))) (taylor 0 x) (#s(alt (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)) (patch (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))) (taylor 0 x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))) (taylor 0 x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
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#s(alt (* 4/3 (/ (- 1 (cos x)) (sin x))) (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 (sin.f64 x) #s(literal 3/4 binary64))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 (sin.f64 x) #s(literal 3/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (/ (- 1 (cos x)) (sin x))) (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 (sin.f64 x) #s(literal 3/4 binary64))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 (sin.f64 x) #s(literal 3/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (/ (- 1 (cos x)) (sin x))) (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 (sin.f64 x) #s(literal 3/4 binary64))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 (sin.f64 x) #s(literal 3/4 binary64))) #<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 (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 (* 3/4 (sin x)) (taylor -inf x) (#s(alt (.f64 (sin.f64 x) #s(literal 3/4 binary64)) (patch (.f64 (sin.f64 x) #s(literal 3/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 3/4 (sin x)) (taylor -inf x) (#s(alt (.f64 (sin.f64 x) #s(literal 3/4 binary64)) (patch (.f64 (sin.f64 x) #s(literal 3/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 3/4 (sin x)) (taylor -inf x) (#s(alt (.f64 (sin.f64 x) #s(literal 3/4 binary64)) (patch (.f64 (sin.f64 x) #s(literal 3/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 3/4 (sin x)) (taylor -inf x) (#s(alt (.f64 (sin.f64 x) #s(literal 3/4 binary64)) (patch (.f64 (sin.f64 x) #s(literal 3/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (/ (- 1 (cos x)) (sin x))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (/ (- 1 (cos x)) (sin x))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (/ (- 1 (cos x)) (sin x))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (/ (- 1 (cos x)) (sin x))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (- 1 (cos x))) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (- 1 (cos x))) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (- 1 (cos x))) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (- 1 (cos x))) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 3/4 (/ (sin x) (- 1 (cos x)))) (taylor -inf x) (#s(alt (/.f64 (sin.f64 x) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))) (patch (/.f64 (sin.f64 x) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 3/4 (/ (sin x) (- 1 (cos x)))) (taylor -inf x) (#s(alt (/.f64 (sin.f64 x) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))) (patch (/.f64 (sin.f64 x) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 3/4 (/ (sin x) (- 1 (cos x)))) (taylor -inf x) (#s(alt (/.f64 (sin.f64 x) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))) (patch (/.f64 (sin.f64 x) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 3/4 (/ (sin x) (- 1 (cos x)))) (taylor -inf x) (#s(alt (/.f64 (sin.f64 x) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))) (patch (/.f64 (sin.f64 x) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1/18 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) (patch (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 2/3 (/ 1 (pow x 2))) 1/18)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) (patch (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 2/3 (/ 1 (pow x 2))) 1/18)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) (patch (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 2/3 (/ 1 (pow x 2))) 1/18)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) (patch (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

16.0ms

-inf

((/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (* (tan (* 1/2 x)) 4/3) (tan (* 1/2 x)) (* 1/2 x) (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (* (+ (* (* x x) 1/18) 2/3) x) (+ (* (* x x) 1/18) 2/3) (* x x) (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (* (* (+ (* -1/18 (* x x)) 2/3) x) x) (* (+ (* -1/18 (* x x)) 2/3) x) (/ (- 1 (cos x)) (* (sin x) 3/4)) (- 1 (cos x)) (cos x) (* (sin x) 3/4) (/ 1 (/ (sin x) (* (- 1 (cos x)) 4/3))) (* (- 1 (cos x)) 4/3) (/ (sin x) (* (- 1 (cos x)) 4/3)) (sin x) (+ (* -1/18 (* x x)) 2/3))

4.0ms

inf

((/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (* (tan (* 1/2 x)) 4/3) (tan (* 1/2 x)) (* 1/2 x) (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (* (+ (* (* x x) 1/18) 2/3) x) (+ (* (* x x) 1/18) 2/3) (* x x) (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (* (* (+ (* -1/18 (* x x)) 2/3) x) x) (* (+ (* -1/18 (* x x)) 2/3) x) (/ (- 1 (cos x)) (* (sin x) 3/4)) (- 1 (cos x)) (cos x) (* (sin x) 3/4) (/ 1 (/ (sin x) (* (- 1 (cos x)) 4/3))) (* (- 1 (cos x)) 4/3) (/ (sin x) (* (- 1 (cos x)) 4/3)) (sin x) (+ (* -1/18 (* x x)) 2/3))

2.0ms

((/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (* (tan (* 1/2 x)) 4/3) (tan (* 1/2 x)) (* 1/2 x) (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (* (+ (* (* x x) 1/18) 2/3) x) (+ (* (* x x) 1/18) 2/3) (* x x) (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (* (* (+ (* -1/18 (* x x)) 2/3) x) x) (* (+ (* -1/18 (* x x)) 2/3) x) (/ (- 1 (cos x)) (* (sin x) 3/4)) (- 1 (cos x)) (cos x) (* (sin x) 3/4) (/ 1 (/ (sin x) (* (- 1 (cos x)) 4/3))) (* (- 1 (cos x)) 4/3) (/ (sin x) (* (- 1 (cos x)) 4/3)) (sin x) (+ (* -1/18 (* x x)) 2/3))

simplify226.0ms (2.3%)

Memory

26.9MiB live, 183.4MiB allocated

Algorithm

1×	egg-herbie

Rules

15 094×	`lower-fma.f64`
15 094×	`lower-fma.f32`
5 058×	`lower-*.f64`
5 058×	`lower-*.f32`
2 858×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	189	1872
1	517	1866
2	1276	1866
3	3878	1866
4	6407	1866
0	8100	1727

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 251

Calls

Call 1

Inputs
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* 1/18 (pow x 2))))
2/3
(+ 2/3 (* 1/18 (pow x 2)))
(+ 2/3 (* 1/18 (pow x 2)))
(+ 2/3 (* 1/18 (pow x 2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 2/3 (pow x 2))
(* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* (pow x 2) (+ 1/540 (* -1/30240 (pow x 2)))) 1/18))))
(* 2/3 (pow x 2))
(* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))
(* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))
(* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))
(* 2/3 x)
(* x (+ 2/3 (* -1/18 (pow x 2))))
(* x (+ 2/3 (* -1/18 (pow x 2))))
(* x (+ 2/3 (* -1/18 (pow x 2))))
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (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
(+ 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)))
(* 3/4 x)
(* x (+ 3/4 (* -1/8 (pow x 2))))
(* x (+ 3/4 (* (pow x 2) (- (* 1/160 (pow x 2)) 1/8))))
(* x (+ 3/4 (* (pow x 2) (- (* (pow x 2) (+ 1/160 (* -1/6720 (pow x 2)))) 1/8))))
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 2/3 (pow x 2))
(* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* (pow x 2) (+ 1/540 (* -1/30240 (pow x 2)))) 1/18))))
(/ 3/2 x)
(/ (+ 3/2 (* -1/8 (pow x 2))) x)
(/ (+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))) x)
(/ (+ 3/2 (* (pow x 2) (- (* (pow x 2) (- (* -1/20160 (pow x 2)) 1/480)) 1/8))) 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))))
2/3
(+ 2/3 (* -1/18 (pow x 2)))
(+ 2/3 (* -1/18 (pow x 2)))
(+ 2/3 (* -1/18 (pow x 2)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 1/18 (pow x 3))
(* (pow x 3) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(* 1/18 (pow x 2))
(* (pow x 2) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(* -1/18 (pow x 4))
(* (pow x 4) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(* (pow x 4) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(* (pow x 4) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(* -1/18 (pow x 3))
(* (pow x 3) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(* (pow x 3) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(* (pow x 3) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(* 3/4 (sin x))
(* 3/4 (sin x))
(* 3/4 (sin x))
(* 3/4 (sin x))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(sin x)
(sin x)
(sin x)
(sin x)
(* -1/18 (pow x 2))
(* (pow x 2) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(* (pow x 2) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(* (pow x 2) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 1/18 (pow x 3))
(* (pow x 3) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(* 1/18 (pow x 2))
(* (pow x 2) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(* -1/18 (pow x 4))
(* (pow x 4) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(* (pow x 4) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(* (pow x 4) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(* -1/18 (pow x 3))
(* -1 (* (pow x 3) (- 1/18 (* 2/3 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/18 (* 2/3 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/18 (* 2/3 (/ 1 (pow x 2))))))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(* 3/4 (sin x))
(* 3/4 (sin x))
(* 3/4 (sin x))
(* 3/4 (sin x))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(sin x)
(sin x)
(sin x)
(sin x)
(* -1/18 (pow x 2))
(* (pow x 2) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(* (pow x 2) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(* (pow x 2) (- (* 2/3 (/ 1 (pow x 2))) 1/18))

Outputs
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x)
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #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)
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x)
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
2/3
#s(literal 2/3 binary64)
(+ 2/3 (* 1/18 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64))
(+ 2/3 (* 1/18 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64))
(+ 2/3 (* 1/18 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 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)
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x)
(* 2/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* (pow x 2) (+ 1/540 (* -1/30240 (pow x 2)))) 1/18))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/30240 binary64) (.f64 x x) #s(literal 1/540 binary64)) (.f64 x x) #s(literal -1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x) x)
(* 2/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)
(* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)
(* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* -1/18 (pow x 2))))
(.f64 (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* -1/18 (pow x 2))))
(.f64 (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* -1/18 (pow x 2))))
(.f64 (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x)
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x)
(* 1/2 (pow x 2))
(.f64 (.f64 #s(literal 1/2 binary64) x) x)
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) (.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) 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 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(* 3/4 x)
(*.f64 #s(literal 3/4 binary64) x)
(* x (+ 3/4 (* -1/8 (pow x 2))))
(.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 x x) #s(literal 3/4 binary64)) x)
(* x (+ 3/4 (* (pow x 2) (- (* 1/160 (pow x 2)) 1/8))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/160 binary64) (.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 3/4 binary64)) x)
(* x (+ 3/4 (* (pow x 2) (- (* (pow x 2) (+ 1/160 (* -1/6720 (pow x 2)))) 1/8))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6720 binary64) (.f64 x x) #s(literal 1/160 binary64)) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/4 binary64)) x)
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x)
(* 2/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* (pow x 2) (+ 1/540 (* -1/30240 (pow x 2)))) 1/18))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/30240 binary64) (.f64 x x) #s(literal 1/540 binary64)) (.f64 x x) #s(literal -1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x) x)
(/ 3/2 x)
(/.f64 #s(literal 3/2 binary64) x)
(/ (+ 3/2 (* -1/8 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 3/2 binary64)) x)
(/ (+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))) x)
(/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x)
(/ (+ 3/2 (* (pow x 2) (- (* (pow x 2) (- (* -1/20160 (pow x 2)) 1/480)) 1/8))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/20160 binary64) (.f64 x x) #s(literal -1/480 binary64)) (.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 3/2 binary64)) x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) x)
2/3
#s(literal 2/3 binary64)
(+ 2/3 (* -1/18 (pow x 2)))
(fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))
(+ 2/3 (* -1/18 (pow x 2)))
(fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))
(+ 2/3 (* -1/18 (pow x 2)))
(fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))) #s(literal 4/3 binary64))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))) #s(literal 4/3 binary64))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))) #s(literal 4/3 binary64))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))) #s(literal 4/3 binary64))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(* 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)
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 1/18 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/18 binary64))
(* (pow x 3) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* (pow x 3) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* (pow x 3) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* 1/18 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/18 binary64))
(* (pow x 2) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64))
(* (pow x 2) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64))
(* (pow x 2) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 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)
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (- 1 (cos x)))
(fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))
(* 4/3 (- 1 (cos x)))
(fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))
(* 4/3 (- 1 (cos x)))
(fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))
(* 4/3 (- 1 (cos x)))
(fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))
(* -1/18 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/18 binary64))
(* (pow x 4) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 2/3 binary64) (.f64 x x)) #s(literal 1/18 binary64)))
(* (pow x 4) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 2/3 binary64) (.f64 x x)) #s(literal 1/18 binary64)))
(* (pow x 4) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 2/3 binary64) (.f64 x x)) #s(literal 1/18 binary64)))
(* -1/18 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/18 binary64))
(* (pow x 3) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(.f64 (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x)
(* (pow x 3) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(.f64 (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x)
(* (pow x 3) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(.f64 (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x)
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 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))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(* 3/4 (sin x))
(*.f64 (sin.f64 x) #s(literal 3/4 binary64))
(* 3/4 (sin x))
(*.f64 (sin.f64 x) #s(literal 3/4 binary64))
(* 3/4 (sin x))
(*.f64 (sin.f64 x) #s(literal 3/4 binary64))
(* 3/4 (sin x))
(*.f64 (sin.f64 x) #s(literal 3/4 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (- 1 (cos x)))
(fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))
(* 4/3 (- 1 (cos x)))
(fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))
(* 4/3 (- 1 (cos x)))
(fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))
(* 4/3 (- 1 (cos x)))
(fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(*.f64 (/.f64 #s(literal 3/4 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(*.f64 (/.f64 #s(literal 3/4 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(*.f64 (/.f64 #s(literal 3/4 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(*.f64 (/.f64 #s(literal 3/4 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x))
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(* -1/18 (pow x 2))
(.f64 #s(literal -1/18 binary64) (.f64 x x))
(* (pow x 2) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))
(* (pow x 2) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))
(* (pow x 2) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))) #s(literal 4/3 binary64))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))) #s(literal 4/3 binary64))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))) #s(literal 4/3 binary64))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))) #s(literal 4/3 binary64))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(* 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)
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 1/18 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/18 binary64))
(* (pow x 3) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* (pow x 3) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* (pow x 3) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* 1/18 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/18 binary64))
(* (pow x 2) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64))
(* (pow x 2) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64))
(* (pow x 2) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 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)
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (- 1 (cos x)))
(fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))
(* 4/3 (- 1 (cos x)))
(fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))
(* 4/3 (- 1 (cos x)))
(fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))
(* 4/3 (- 1 (cos x)))
(fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))
(* -1/18 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/18 binary64))
(* (pow x 4) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 2/3 binary64) (.f64 x x)) #s(literal 1/18 binary64)))
(* (pow x 4) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 2/3 binary64) (.f64 x x)) #s(literal 1/18 binary64)))
(* (pow x 4) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 2/3 binary64) (.f64 x x)) #s(literal 1/18 binary64)))
(* -1/18 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/18 binary64))
(* -1 (* (pow x 3) (- 1/18 (* 2/3 (/ 1 (pow x 2))))))
(.f64 (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x)
(* -1 (* (pow x 3) (- 1/18 (* 2/3 (/ 1 (pow x 2))))))
(.f64 (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x)
(* -1 (* (pow x 3) (- 1/18 (* 2/3 (/ 1 (pow x 2))))))
(.f64 (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x)
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 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))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(* 3/4 (sin x))
(*.f64 (sin.f64 x) #s(literal 3/4 binary64))
(* 3/4 (sin x))
(*.f64 (sin.f64 x) #s(literal 3/4 binary64))
(* 3/4 (sin x))
(*.f64 (sin.f64 x) #s(literal 3/4 binary64))
(* 3/4 (sin x))
(*.f64 (sin.f64 x) #s(literal 3/4 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(* 4/3 (- 1 (cos x)))
(fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))
(* 4/3 (- 1 (cos x)))
(fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))
(* 4/3 (- 1 (cos x)))
(fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))
(* 4/3 (- 1 (cos x)))
(fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(*.f64 (/.f64 #s(literal 3/4 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(*.f64 (/.f64 #s(literal 3/4 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(*.f64 (/.f64 #s(literal 3/4 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(*.f64 (/.f64 #s(literal 3/4 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x))
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(* -1/18 (pow x 2))
(.f64 #s(literal -1/18 binary64) (.f64 x x))
(* (pow x 2) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))
(* (pow x 2) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))
(* (pow x 2) (- (* 2/3 (/ 1 (pow x 2))) 1/18))
(fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))

rewrite256.0ms (2.6%)

Memory

5.9MiB live, 318.8MiB allocated

Rules

5 172×	`lower-*.f32`
5 156×	`lower-*.f64`
4 910×	`lower-fma.f32`
4 906×	`lower-fma.f64`
4 202×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	188
0	58	172
1	180	157
2	1056	155
0	8796	152

Stop Event

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

Counts

21 → 2 048

Calls

Call 1

Inputs
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)))
(.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64))
(*.f64 x x)
(/.f64 #s(approx (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x))
#s(approx (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x))
(.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)
(.f64 (fma.f64 #s(literal -1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (sin.f64 x) #s(literal 3/4 binary64)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
(*.f64 (sin.f64 x) #s(literal 3/4 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))))
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))
(/.f64 (sin.f64 x) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)))
(sin.f64 x)
(fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))

Outputs
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eval858.0ms (8.7%)

Memory: -13.0MiB live, 778.3MiB allocated
Compiler: Compiled 43 459 to 4 966 computations (88.6% saved)

prune272.0ms (2.8%)

Memory

2.6MiB live, 278.6MiB allocated

Pruning

23 alts after pruning (19 fresh and 4 done)

	Pruned	Kept	Total
New	2 440	14	2 454
Fresh	9	5	14
Picked	2	3	5
Done	2	1	3
Total	2 453	23	2 476

Accuracy

100.0%

Counts

2 476 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	76.1%	(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (.f64 (sin.f64 x) #s(literal 3/4 binary64))))
✓	52.0%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (sin.f64 x) #s(literal 3/4 binary64)))
	99.3%	(/.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)) (cos.f64 (*.f64 #s(literal 1/2 binary64) x)))
▶	99.8%	(/.f64 (tan.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 3/4 binary64))
	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/4 binary64) (tan.f64 (*.f64 #s(literal 1/2 binary64) x))))
▶	99.4%	(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64)))
	51.8%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/20160 binary64) (.f64 x x) #s(literal -1/480 binary64)) (.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 3/2 binary64)) x)))
▶	51.8%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x)))
	52.1%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 3/2 binary64)) x)))
	51.1%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 #s(literal 3/2 binary64) x)))
	99.3%	(/.f64 #s(literal -4/3 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 (*.f64 #s(literal 1/2 binary64) x))))
	51.9%	(*.f64 (fma.f64 #s(literal -8/3 binary64) (cos.f64 x) #s(literal 8/3 binary64)) (/.f64 #s(literal 1/2 binary64) (sin.f64 x)))
	51.9%	(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -3/8 binary64)) (/.f64 #s(literal -1/2 binary64) (sin.f64 x)))
	50.7%	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/18 binary64) x) (*.f64 x #s(literal 2/3 binary64))))
▶	51.0%	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)))))
	50.7%	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x))
	50.7%	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x))
✓	50.7%	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x))
	99.3%	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (.f64 (neg.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x))))) #s(literal 4/3 binary64)))
✓	99.4%	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)))
	50.7%	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64)))
▶	50.7%	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64)))
✓	51.0%	#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 x #s(literal 2/3 binary64)))

Compiler

Compiled 503 to 392 computations (22.1% saved)

simplify154.0ms (1.6%)

Memory

32.8MiB live, 151.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
cost-diff	0	(/.f64 #s(literal -1 binary64) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
cost-diff	320	(.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64))
cost-diff	1088	(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64)))
cost-diff	0	(fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64))
cost-diff	0	(/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x)
cost-diff	0	#s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x)))
cost-diff	0	(fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))
cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)))
cost-diff	0	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)))))
cost-diff	1088	(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))))
cost-diff	0	(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (tan (* 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
cost-diff	0	(.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64))
cost-diff	0	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64)))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
cost-diff	384	(/.f64 (tan.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 3/4 binary64))

Rules

8 944×	`lower-fma.f32`
8 936×	`lower-fma.f64`
2 318×	`lower-*.f32`
2 308×	`lower-*.f64`
1 420×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	271
0	68	261
1	108	253
2	189	253
3	363	247
4	598	247
5	1007	247
6	2114	247
7	3626	247
8	4575	247
9	5193	247
10	6159	247
11	6952	247
12	7430	247
13	7637	247
0	8256	245

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (tan.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 3/4 binary64))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(literal 3/4 binary64)
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64)))
(.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64))
#s(approx (tan (* 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
#s(literal 1/24 binary64)
(*.f64 x x)
x
#s(literal 1/2 binary64)
#s(literal 4/3 binary64)
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)))))
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))))
x
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)))
#s(literal 1 binary64)
(fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))
#s(literal 1/18 binary64)
(*.f64 x x)
#s(literal 2/3 binary64)
(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x)))
#s(literal 1 binary64)
#s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x))
(/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64))
(fma.f64 #s(literal -1/480 binary64) (*.f64 x x) #s(literal -1/8 binary64))
#s(literal -1/480 binary64)
(*.f64 x x)
x
#s(literal -1/8 binary64)
#s(literal 3/2 binary64)
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64)))
#s(literal 1 binary64)
(.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64))
(/.f64 #s(literal -1 binary64) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
#s(literal -1 binary64)
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(literal -3/4 binary64)

Outputs
(/.f64 (tan.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 3/4 binary64))
(.f64 #s(literal 4/3 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64))))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
#s(literal 3/4 binary64)
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64)))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 #s(literal 4/3 binary64) #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))))
(.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64))
(.f64 #s(literal 4/3 binary64) #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)))
#s(approx (tan (* 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (tan (* 1/2 x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
#s(literal 1/24 binary64)
(*.f64 x x)
x
#s(literal 1/2 binary64)
#s(literal 4/3 binary64)
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)))))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 #s(literal 1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x))
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))))
(.f64 (fma.f64 #s(literal 1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) x)
x
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)))
#s(literal 1 binary64)
(fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))
#s(literal 1/18 binary64)
(*.f64 x x)
#s(literal 2/3 binary64)
(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x)))
#s(literal 1 binary64)
#s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x))
(/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64))
(fma.f64 #s(literal -1/480 binary64) (*.f64 x x) #s(literal -1/8 binary64))
#s(literal -1/480 binary64)
(*.f64 x x)
x
#s(literal -1/8 binary64)
#s(literal 3/2 binary64)
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64)))
(.f64 #s(literal 4/3 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64))
(/.f64 #s(literal 3/4 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
(/.f64 #s(literal -1 binary64) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 #s(literal -1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
#s(literal -1 binary64)
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
#s(literal -3/4 binary64)

localize251.0ms (2.6%)

Memory

-12.3MiB live, 285.5MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
accuracy	0.140625	(/.f64 #s(literal -1 binary64) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
accuracy	0.28515625	(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64)))
accuracy	0.3046875	(.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64))
accuracy	0.28515625	(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x)))
accuracy	0.29513361737428045	(fma.f64 #s(literal -1/480 binary64) (*.f64 x x) #s(literal -1/8 binary64))
accuracy	3.0067694237467326	(/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x)
accuracy	30.930831144954432	#s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x))
accuracy	0.046875	(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))))
accuracy	0.0703125	(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)))
accuracy	0.34830699132746407	(fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))
accuracy	31.337552390867344	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)))))
accuracy	0.046875	(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
accuracy	0.29558851795670427	(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
accuracy	0.375	(.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64))
accuracy	31.33590837736428	#s(approx (tan (* 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
accuracy	0.109375	(/.f64 (tan.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 3/4 binary64))

Samples

92.0ms	130×	0	valid
80.0ms	66×	2	valid
27.0ms	14×	3	valid
24.0ms	46×	1	valid

Compiler

Compiled 210 to 47 computations (77.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 155.0ms

ival-div: 31.0ms (20% of total)

adjust: 24.0ms (15.5% of total)

const: 22.0ms (14.2% of total)

ival-cos: 22.0ms (14.2% of total)

ival-mult: 19.0ms (12.3% of total)

ival-sin: 14.0ms (9% of total)

ival-tan: 13.0ms (8.4% of total)

ival-add: 5.0ms (3.2% of total)

ival-sub: 3.0ms (1.9% of total)

exact: 1.0ms (0.6% of total)

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

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

series65.0ms (0.7%)

Memory

1.5MiB live, 39.4MiB allocated

Counts

20 → 240

Calls

Call 1

Inputs
#s(alt (/.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 3/4 binary64)) (patch (/.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 3/4 binary64)) #<representation binary64>) () ())
#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())
#s(alt #s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64))) (patch #s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64)) (patch (.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (tan (* 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (tan (* 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())
#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (.f64 x x) #s(literal 2/3 binary64))))) (patch #s(approx (/ (/ 1 (/ 2 ( (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (.f64 x x) #s(literal 2/3 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (.f64 x x) #s(literal 2/3 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) (patch (fma.f64 #s(literal 1/18 binary64) (.f64 x x) #s(literal 2/3 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x))) #<representation binary64>) () ())
#s(alt #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x)) (patch #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x)) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x) (patch (/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64))) (patch (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64)) (patch (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) (patch (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (patch (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* 2/3 x) (taylor 0 x) (#s(alt (/.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 3/4 binary64)) (patch (/.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 3/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2/3 (* 1/18 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 3/4 binary64)) (patch (/.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 3/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2)))))) (taylor 0 x) (#s(alt (/.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 3/4 binary64)) (patch (/.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 3/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2)))))))) (taylor 0 x) (#s(alt (/.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 3/4 binary64)) (patch (/.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 3/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))) (taylor 0 x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
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#s(alt (* -1/480 (pow x 4)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 4) (+ 1/480 (* 1/8 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (/ 3/2 (pow x 4)) (+ 1/480 (* 1/8 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (/ 3/2 (pow x 4)) (+ 1/480 (* 1/8 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64))) (patch (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64))) (patch (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64))) (patch (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64))) (patch (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x)))) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64)) (patch (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x)))) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64)) (patch (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x)))) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64)) (patch (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x)))) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64)) (patch (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (cos (* 1/2 x)) (sin (* 1/2 x)))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) (patch (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (cos (* 1/2 x)) (sin (* 1/2 x)))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) (patch (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (cos (* 1/2 x)) (sin (* 1/2 x)))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) (patch (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (cos (* 1/2 x)) (sin (* 1/2 x)))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) (patch (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/480 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (patch (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 2) (+ 1/480 (* 1/8 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (patch (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 2) (+ 1/480 (* 1/8 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (patch (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 2) (+ 1/480 (* 1/8 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (patch (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

4.0ms

inf

((/ (tan (* 1/2 x)) 3/4) (tan (* 1/2 x)) (* 1/2 x) (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (* (tan (* 1/2 x)) 4/3) (tan (* 1/2 x)) (* (+ (* 1/24 (* x x)) 1/2) x) (/ x (/ 1 (+ (* 1/18 (* x x)) 2/3))) (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/ 1 (+ (* 1/18 (* x x)) 2/3)) (+ (* 1/18 (* x x)) 2/3) (/ 1 (/ (sin x) (* (- 1 (cos x)) 4/3))) (/ (sin x) (* (- 1 (cos x)) 4/3)) (/ (+ (* (+ (* -1/480 (* x x)) -1/8) (* x x)) 3/2) x) (+ (* (+ (* -1/480 (* x x)) -1/8) (* x x)) 3/2) (/ 1 (* (/ -1 (tan (* 1/2 x))) -3/4)) (* (/ -1 (tan (* 1/2 x))) -3/4) (/ -1 (tan (* 1/2 x))) (+ (* 1/24 (* x x)) 1/2) (+ (* -1/480 (* x x)) -1/8))

4.0ms

-inf

((/ (tan (* 1/2 x)) 3/4) (tan (* 1/2 x)) (* 1/2 x) (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (* (tan (* 1/2 x)) 4/3) (tan (* 1/2 x)) (* (+ (* 1/24 (* x x)) 1/2) x) (/ x (/ 1 (+ (* 1/18 (* x x)) 2/3))) (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/ 1 (+ (* 1/18 (* x x)) 2/3)) (+ (* 1/18 (* x x)) 2/3) (/ 1 (/ (sin x) (* (- 1 (cos x)) 4/3))) (/ (sin x) (* (- 1 (cos x)) 4/3)) (/ (+ (* (+ (* -1/480 (* x x)) -1/8) (* x x)) 3/2) x) (+ (* (+ (* -1/480 (* x x)) -1/8) (* x x)) 3/2) (/ 1 (* (/ -1 (tan (* 1/2 x))) -3/4)) (* (/ -1 (tan (* 1/2 x))) -3/4) (/ -1 (tan (* 1/2 x))) (+ (* 1/24 (* x x)) 1/2) (+ (* -1/480 (* x x)) -1/8))

2.0ms

((/ (tan (* 1/2 x)) 3/4) (tan (* 1/2 x)) (* 1/2 x) (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (* (tan (* 1/2 x)) 4/3) (tan (* 1/2 x)) (* (+ (* 1/24 (* x x)) 1/2) x) (/ x (/ 1 (+ (* 1/18 (* x x)) 2/3))) (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/ 1 (+ (* 1/18 (* x x)) 2/3)) (+ (* 1/18 (* x x)) 2/3) (/ 1 (/ (sin x) (* (- 1 (cos x)) 4/3))) (/ (sin x) (* (- 1 (cos x)) 4/3)) (/ (+ (* (+ (* -1/480 (* x x)) -1/8) (* x x)) 3/2) x) (+ (* (+ (* -1/480 (* x x)) -1/8) (* x x)) 3/2) (/ 1 (* (/ -1 (tan (* 1/2 x))) -3/4)) (* (/ -1 (tan (* 1/2 x))) -3/4) (/ -1 (tan (* 1/2 x))) (+ (* 1/24 (* x x)) 1/2) (+ (* -1/480 (* x x)) -1/8))

simplify218.0ms (2.2%)

Memory

-14.8MiB live, 251.5MiB allocated

Algorithm

1×	egg-herbie

Rules

15 756×	`lower-fma.f64`
15 756×	`lower-fma.f32`
3 734×	`lower-*.f64`
3 734×	`lower-*.f32`
2 758×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	166	2182
1	466	2182
2	1330	2166
3	3518	2160
4	7019	2160
0	8152	2013

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

Inputs
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 1/2 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))))
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
3/2
(+ 3/2 (* -1/8 (pow x 2)))
(+ 3/2 (* (pow x 2) (- (* 1/96 (pow x 2)) 1/8)))
(+ 3/2 (* (pow x 2) (- (* (pow x 2) (+ 1/96 (* -1/1152 (pow x 2)))) 1/8)))
2/3
(+ 2/3 (* 1/18 (pow x 2)))
(+ 2/3 (* 1/18 (pow x 2)))
(+ 2/3 (* 1/18 (pow x 2)))
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(/ 3/2 x)
(/ (+ 3/2 (* -1/8 (pow x 2))) x)
(/ (+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))) x)
(/ (+ 3/2 (* (pow x 2) (- (* (pow x 2) (- (* -1/20160 (pow x 2)) 1/480)) 1/8))) x)
(/ 3/2 x)
(/ (+ 3/2 (* -1/8 (pow x 2))) x)
(/ (+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))) x)
(/ (+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))) x)
3/2
(+ 3/2 (* -1/8 (pow x 2)))
(+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8)))
(+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8)))
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(/ 3/2 x)
(/ (+ 3/2 (* -1/8 (pow x 2))) x)
(/ (+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))) x)
(/ (+ 3/2 (* (pow x 2) (- (* (pow x 2) (- (* -1/20160 (pow x 2)) 1/480)) 1/8))) x)
(/ -2 x)
(/ (- (* 1/6 (pow x 2)) 2) x)
(/ (- (* (pow x 2) (+ 1/6 (* 1/360 (pow x 2)))) 2) x)
(/ (- (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/360 (* 1/15120 (pow x 2)))))) 2) x)
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* 1/24 (pow x 2)))
-1/8
(- (* -1/480 (pow x 2)) 1/8)
(- (* -1/480 (pow x 2)) 1/8)
(- (* -1/480 (pow x 2)) 1/8)
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/18 (pow x 3))
(* (pow x 3) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(/ 18 (pow x 2))
(/ (- 18 (* 216 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 18 (/ 2592 (pow x 4))) (* 216 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 18 (/ 2592 (pow x 4))) (+ (* 216 (/ 1 (pow x 2))) (* 31104 (/ 1 (pow x 6))))) (pow x 2))
(* 1/18 (pow x 2))
(* (pow x 2) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(* -1/480 (pow x 3))
(* -1 (* (pow x 3) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* (pow x 3) (- (/ 3/2 (pow x 4)) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* (pow x 3) (- (/ 3/2 (pow x 4)) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* -1/480 (pow x 4))
(* -1 (* (pow x 4) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 3/2 (pow x 4)) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 3/2 (pow x 4)) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* -1 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* -1 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* -1 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* -1 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* -1/480 (pow x 2))
(* -1 (* (pow x 2) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 2) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 2) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/18 (pow x 3))
(* (pow x 3) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(/ 18 (pow x 2))
(/ (- 18 (* 216 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 18 (/ 2592 (pow x 4))) (* 216 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 18 (/ 2592 (pow x 4))) (+ (* 216 (/ 1 (pow x 2))) (* 31104 (/ 1 (pow x 6))))) (pow x 2))
(* 1/18 (pow x 2))
(* (pow x 2) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/18 (* 2/3 (/ 1 (pow x 2)))))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(* -1/480 (pow x 3))
(* -1 (* (pow x 3) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- (+ 1/480 (* 1/8 (/ 1 (pow x 2)))) (/ 3/2 (pow x 4)))))
(* -1 (* (pow x 3) (- (+ 1/480 (* 1/8 (/ 1 (pow x 2)))) (/ 3/2 (pow x 4)))))
(* -1/480 (pow x 4))
(* -1 (* (pow x 4) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 3/2 (pow x 4)) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 3/2 (pow x 4)) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* -1 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* -1 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* -1 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* -1 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* -1/480 (pow x 2))
(* -1 (* (pow x 2) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 2) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 2) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))

Outputs
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #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)
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x)
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x)
3/2
#s(literal 3/2 binary64)
(+ 3/2 (* -1/8 (pow x 2)))
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 3/2 binary64))
(+ 3/2 (* (pow x 2) (- (* 1/96 (pow x 2)) 1/8)))
(fma.f64 (fma.f64 #s(literal 1/96 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64))
(+ 3/2 (* (pow x 2) (- (* (pow x 2) (+ 1/96 (* -1/1152 (pow x 2)))) 1/8)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/1152 binary64) (.f64 x x) #s(literal 1/96 binary64)) (.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 3/2 binary64))
2/3
#s(literal 2/3 binary64)
(+ 2/3 (* 1/18 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64))
(+ 2/3 (* 1/18 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64))
(+ 2/3 (* 1/18 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x)
(/ 3/2 x)
(/.f64 #s(literal 3/2 binary64) x)
(/ (+ 3/2 (* -1/8 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 3/2 binary64)) x)
(/ (+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))) x)
(/.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/480 binary64) #s(literal 3/2 binary64))) x)
(/ (+ 3/2 (* (pow x 2) (- (* (pow x 2) (- (* -1/20160 (pow x 2)) 1/480)) 1/8))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/20160 binary64) (.f64 x x) #s(literal -1/480 binary64)) (.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 3/2 binary64)) x)
(/ 3/2 x)
(/.f64 #s(literal 3/2 binary64) x)
(/ (+ 3/2 (* -1/8 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 3/2 binary64)) x)
(/ (+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))) x)
(/.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/480 binary64) #s(literal 3/2 binary64))) x)
(/ (+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))) x)
(/.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/480 binary64) #s(literal 3/2 binary64))) x)
3/2
#s(literal 3/2 binary64)
(+ 3/2 (* -1/8 (pow x 2)))
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 3/2 binary64))
(+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8)))
(fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/480 binary64) #s(literal 3/2 binary64)))
(+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8)))
(fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/480 binary64) #s(literal 3/2 binary64)))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x)
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x)
(/ 3/2 x)
(/.f64 #s(literal 3/2 binary64) x)
(/ (+ 3/2 (* -1/8 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 3/2 binary64)) x)
(/ (+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))) x)
(/.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) x) x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/480 binary64) #s(literal 3/2 binary64))) x)
(/ (+ 3/2 (* (pow x 2) (- (* (pow x 2) (- (* -1/20160 (pow x 2)) 1/480)) 1/8))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/20160 binary64) (.f64 x x) #s(literal -1/480 binary64)) (.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 3/2 binary64)) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ (- (* 1/6 (pow x 2)) 2) x)
(fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -2 binary64) x))
(/ (- (* (pow x 2) (+ 1/6 (* 1/360 (pow x 2)))) 2) x)
(fma.f64 (fma.f64 #s(literal 1/360 binary64) (*.f64 x x) #s(literal 1/6 binary64)) x (/.f64 #s(literal -2 binary64) x))
(/ (- (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/360 (* 1/15120 (pow x 2)))))) 2) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/15120 binary64) (.f64 x x) #s(literal 1/360 binary64)) (.f64 x x) #s(literal 1/6 binary64)) x (/.f64 #s(literal -2 binary64) 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 (* 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))
-1/8
#s(literal -1/8 binary64)
(- (* -1/480 (pow x 2)) 1/8)
(fma.f64 #s(literal -1/480 binary64) (*.f64 x x) #s(literal -1/8 binary64))
(- (* -1/480 (pow x 2)) 1/8)
(fma.f64 #s(literal -1/480 binary64) (*.f64 x x) #s(literal -1/8 binary64))
(- (* -1/480 (pow x 2)) 1/8)
(fma.f64 #s(literal -1/480 binary64) (*.f64 x x) #s(literal -1/8 binary64))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))) #s(literal 4/3 binary64))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))) #s(literal 4/3 binary64))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))) #s(literal 4/3 binary64))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))) #s(literal 4/3 binary64))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(* 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)
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 4/3 binary64))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 4/3 binary64))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))) #s(literal 4/3 binary64))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))) #s(literal 4/3 binary64))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))) #s(literal 4/3 binary64))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(.f64 (/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))) #s(literal 4/3 binary64))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
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(.f64 (/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) x))) #s(literal 3/4 binary64))
(* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(.f64 (/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) x))) #s(literal 3/4 binary64))
(* -1 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(/.f64 (neg.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(* -1 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(/.f64 (neg.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(* -1 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(/.f64 (neg.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(* -1 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(/.f64 (neg.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(* -1/480 (pow x 2))
(.f64 #s(literal -1/480 binary64) (.f64 x x))
(* -1 (* (pow x 2) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(fma.f64 #s(literal -1/480 binary64) (*.f64 x x) #s(literal -1/8 binary64))
(* -1 (* (pow x 2) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(fma.f64 #s(literal -1/480 binary64) (*.f64 x x) #s(literal -1/8 binary64))
(* -1 (* (pow x 2) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(fma.f64 #s(literal -1/480 binary64) (*.f64 x x) #s(literal -1/8 binary64))

rewrite148.0ms (1.5%)

Memory

12.4MiB live, 246.0MiB allocated

Rules

4 608×	`lower-*.f32`
4 598×	`lower-*.f64`
4 278×	`lower-/.f32`
4 264×	`lower-/.f64`
4 096×	`lower-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	47	234
0	68	224
1	252	216
2	1474	208
0	8454	208

Stop Event

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

Counts

20 → 630

Calls

Call 1

Inputs
(/.f64 (tan.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 3/4 binary64))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64)))
(.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64))
#s(approx (tan (* 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)))))
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)))
(fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x)))
#s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x))
(/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64))
(/.f64 #s(literal -1 binary64) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/480 binary64) (*.f64 x x) #s(literal -1/8 binary64))

Outputs
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eval147.0ms (1.5%)

Memory: -15.9MiB live, 265.9MiB allocated
Compiler: Compiled 18 259 to 3 034 computations (83.4% saved)

prune50.0ms (0.5%)

Memory

9.9MiB live, 132.5MiB allocated

Pruning

25 alts after pruning (17 fresh and 8 done)

	Pruned	Kept	Total
New	903	11	914
Fresh	8	6	14
Picked	1	4	5
Done	0	4	4
Total	912	25	937

Accuracy

100.0%

Counts

937 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	76.1%	(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (.f64 (sin.f64 x) #s(literal 3/4 binary64))))
✓	52.0%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (sin.f64 x) #s(literal 3/4 binary64)))
	99.3%	(/.f64 (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 4/3 binary64)) (cos.f64 (*.f64 x #s(literal 1/2 binary64))))
✓	99.8%	(/.f64 (tan.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 3/4 binary64))
	99.7%	(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 #s(literal 3/4 binary64) (cos.f64 (*.f64 x #s(literal 1/2 binary64)))))
	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/4 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
✓	99.4%	(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64)))
	51.7%	(/.f64 #s(literal 1 binary64) (.f64 #s(approx (/ -1 (tan ( 1/2 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/15120 binary64) (.f64 x x) #s(literal 1/360 binary64)) (.f64 x x) #s(literal 1/6 binary64)) x (/.f64 #s(literal -2 binary64) x))) #s(literal -3/4 binary64)))
	52.1%	(/.f64 #s(literal 1 binary64) (.f64 #s(approx (/ -1 (tan ( 1/2 x))) (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -2 binary64) x))) #s(literal -3/4 binary64)))
	51.0%	(/.f64 #s(literal 1 binary64) (.f64 #s(approx (/ -1 (tan ( 1/2 x))) (/.f64 #s(literal -2 binary64) x)) #s(literal -3/4 binary64)))
✓	51.8%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x)))
	51.1%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 #s(approx (+ (* (+ (* -1/480 (* x x)) -1/8) (* x x)) 3/2) #s(literal 3/2 binary64)) x)))
	99.3%	(/.f64 #s(literal -4/3 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
	51.9%	(*.f64 (fma.f64 #s(literal -8/3 binary64) (cos.f64 x) #s(literal 8/3 binary64)) (/.f64 #s(literal 1/2 binary64) (sin.f64 x)))
	99.3%	(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 3/4 binary64) (cos.f64 (.f64 x #s(literal 1/2 binary64))))))
	50.7%	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/18 binary64) x) (*.f64 x #s(literal 2/3 binary64))))
	52.3%	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x #s(approx (/ 1 (+ (* 1/18 (* x x)) 2/3)) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 3/2 binary64)))))
	51.3%	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x #s(approx (/ 1 (+ (* 1/18 (* x x)) 2/3)) #s(literal 3/2 binary64))))
	50.7%	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x))
	50.7%	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x))
✓	50.7%	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x))
✓	99.4%	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)))
	50.7%	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64)))
✓	50.7%	#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64)))
✓	51.0%	#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 x #s(literal 2/3 binary64)))

Compiler

Compiled 1 094 to 478 computations (56.3% saved)

regimes71.0ms (0.7%)

Memory

18.5MiB live, 90.8MiB allocated

Counts

69 → 1

Calls

Call 1

Inputs
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 x #s(literal 2/3 binary64)))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x #s(approx (/ 1 (+ (* 1/18 (* x x)) 2/3)) #s(literal 3/2 binary64))))
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64)))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/18 binary64) x) (*.f64 x #s(literal 2/3 binary64))))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x #s(approx (/ 1 (+ (* 1/18 (* x x)) 2/3)) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 #s(literal 3/2 binary64) x)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 #s(approx (+ (* (+ (* -1/480 (* x x)) -1/8) (* x x)) 3/2) #s(literal 3/2 binary64)) x)))
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (/ -1 (tan ( 1/2 x))) (/.f64 #s(literal -2 binary64) x)) #s(literal -3/4 binary64)))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 3/2 binary64)) x)))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (/ -1 (tan ( 1/2 x))) (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -2 binary64) x))) #s(literal -3/4 binary64)))
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/20160 binary64) (.f64 x x) #s(literal -1/480 binary64)) (.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 3/2 binary64)) x)))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (/ -1 (tan ( 1/2 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/15120 binary64) (.f64 x x) #s(literal 1/360 binary64)) (.f64 x x) #s(literal 1/6 binary64)) x (/.f64 #s(literal -2 binary64) x))) #s(literal -3/4 binary64)))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)))
(/.f64 (tan.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 3/4 binary64))
(.f64 #s(approx (/ (sin ( x 1/2)) (sin x)) #s(literal 1/2 binary64)) (/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64)))
(/.f64 #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 x x) #s(literal 2/3 binary64))) (sin.f64 x))
(/.f64 #s(literal -4/3 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 (*.f64 #s(literal 1/2 binary64) x))))
(/.f64 #s(literal -4/3 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/4 binary64) (tan.f64 (*.f64 #s(literal 1/2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/4 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #s(literal -3/4 binary64)))
(/.f64 #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x))
(/.f64 #s(approx (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (.f64 (.f64 (fma.f64 #s(literal -1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 4/3 binary64))))
(/.f64 #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/540 binary64) (.f64 x x) #s(literal -1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x))
(/.f64 #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/30240 binary64) (.f64 x x) #s(literal 1/540 binary64)) (.f64 x x) #s(literal -1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x) x)) (sin.f64 x))
(/.f64 #s(approx (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (fma.f64 #s(literal -4/3 binary64) (cos.f64 x) #s(literal 4/3 binary64))) (sin.f64 x))
(*.f64 (/.f64 #s(literal 4/3 binary64) (sin.f64 x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) #s(literal 4/3 binary64))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)) (sin.f64 x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (sin.f64 x) #s(literal 3/4 binary64)))
(*.f64 (fma.f64 #s(literal -8/3 binary64) (cos.f64 x) #s(literal 8/3 binary64)) (/.f64 #s(literal 1/2 binary64) (sin.f64 x)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 8/3 binary64) (sin.f64 x)))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) #s(literal 1/2 binary64)) (*.f64 #s(literal 3/8 binary64) (sin.f64 x)))
(.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/8 binary64) (sin.f64 x))))
(/.f64 (+.f64 #s(literal 4/3 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 8/3 binary64))) (sin.f64 x))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 #s(literal 3/4 binary64) (cos.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)) (cos.f64 (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 4/3 binary64)) (cos.f64 (*.f64 x #s(literal 1/2 binary64))))
(/.f64 #s(literal 8/3 binary64) (/.f64 (sin.f64 x) (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) #s(literal 1/2 binary64))))
(/.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) #s(literal 1/2 binary64)) (sin.f64 x)) #s(literal 3/8 binary64))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -3/8 binary64)) (/.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64))))
(/.f64 #s(literal 8/3 binary64) (*.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x)))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 3/4 binary64) (cos.f64 (.f64 x #s(literal 1/2 binary64))))))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (.f64 (neg.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x))))) #s(literal 4/3 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 8/3 binary64)))) (sin.f64 x))
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (.f64 (/.f64 #s(literal 8/3 binary64) (sin.f64 x)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64))))
(.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (/.f64 #s(literal 8/3 binary64) (sin.f64 x)))
(/.f64 #s(approx (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) #s(literal 8/3 binary64))) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (.f64 #s(literal 3/8 binary64) (sin.f64 x)))
(/.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (sin.f64 x)) #s(literal 3/8 binary64))
(fma.f64 (/.f64 #s(literal 4/3 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x)) (/.f64 #s(literal 4/3 binary64) (sin.f64 x)))
(.f64 (.f64 (/.f64 #s(literal 8/3 binary64) (sin.f64 x)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 #s(literal 3/8 binary64) (sin.f64 x))) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(.f64 (/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 x)) (/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/8 binary64)))
(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (.f64 (sin.f64 x) #s(literal 3/4 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (.f64 (*.f64 #s(literal 3/8 binary64) (sin.f64 x)) (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 (.f64 (/.f64 #s(literal 8/3 binary64) (sin.f64 x)) (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))

Outputs
(/.f64 (tan.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 3/4 binary64))

Calls

2 calls:

42.0ms	(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))
26.0ms	x

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))`

Compiler

Compiled 17 to 12 computations (29.4% saved)

regimes29.0ms (0.3%)

Memory

-5.7MiB live, 32.2MiB allocated

Counts

22 → 1

Calls

Call 1

Inputs
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 x #s(literal 2/3 binary64)))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x #s(approx (/ 1 (+ (* 1/18 (* x x)) 2/3)) #s(literal 3/2 binary64))))
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64)))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/18 binary64) x) (*.f64 x #s(literal 2/3 binary64))))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x #s(approx (/ 1 (+ (* 1/18 (* x x)) 2/3)) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 #s(literal 3/2 binary64) x)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 #s(approx (+ (* (+ (* -1/480 (* x x)) -1/8) (* x x)) 3/2) #s(literal 3/2 binary64)) x)))
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (/ -1 (tan ( 1/2 x))) (/.f64 #s(literal -2 binary64) x)) #s(literal -3/4 binary64)))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 3/2 binary64)) x)))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (/ -1 (tan ( 1/2 x))) (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -2 binary64) x))) #s(literal -3/4 binary64)))
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/20160 binary64) (.f64 x x) #s(literal -1/480 binary64)) (.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 3/2 binary64)) x)))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (/ -1 (tan ( 1/2 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/15120 binary64) (.f64 x x) #s(literal 1/360 binary64)) (.f64 x x) #s(literal 1/6 binary64)) x (/.f64 #s(literal -2 binary64) x))) #s(literal -3/4 binary64)))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)))

Outputs
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)))

Calls

2 calls:

21.0ms	(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))
7.0ms	x

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))`

Compiler

Compiled 17 to 12 computations (29.4% saved)

regimes40.0ms (0.4%)

Memory

-3.5MiB live, 34.7MiB allocated

Counts

21 → 1

Calls

Call 1

Inputs
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 x #s(literal 2/3 binary64)))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x #s(approx (/ 1 (+ (* 1/18 (* x x)) 2/3)) #s(literal 3/2 binary64))))
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64)))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/18 binary64) x) (*.f64 x #s(literal 2/3 binary64))))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x #s(approx (/ 1 (+ (* 1/18 (* x x)) 2/3)) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 #s(literal 3/2 binary64) x)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 #s(approx (+ (* (+ (* -1/480 (* x x)) -1/8) (* x x)) 3/2) #s(literal 3/2 binary64)) x)))
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/180 binary64) (.f64 x x) #s(literal 1/18 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) x))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (/ -1 (tan ( 1/2 x))) (/.f64 #s(literal -2 binary64) x)) #s(literal -3/4 binary64)))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/18 binary64) (*.f64 x x) #s(literal 2/3 binary64)))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 3/2 binary64)) x)))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (/ -1 (tan ( 1/2 x))) (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -2 binary64) x))) #s(literal -3/4 binary64)))
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/30240 binary64) (.f64 x x) #s(literal 1/180 binary64)) (.f64 x x) #s(literal 1/18 binary64)) (.f64 x x) #s(literal 2/3 binary64)) x))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 #s(literal -1/480 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3/2 binary64)) x)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sin x) (* (- 1 (cos x)) 4/3)) (/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/20160 binary64) (.f64 x x) #s(literal -1/480 binary64)) (.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 3/2 binary64)) x)))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (/ -1 (tan ( 1/2 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/15120 binary64) (.f64 x x) #s(literal 1/360 binary64)) (.f64 x x) #s(literal 1/6 binary64)) x (/.f64 #s(literal -2 binary64) x))) #s(literal -3/4 binary64)))

Outputs
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x #s(approx (/ 1 (+ (* 1/18 (* x x)) 2/3)) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 3/2 binary64)))))

Calls

2 calls:

33.0ms	x
6.0ms	(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))

Results

Accuracy	Segments	Branch
52.3%	1	`x`
52.3%	1	`(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))`

Compiler

Compiled 17 to 12 computations (29.4% saved)

regimes6.0ms (0.1%)

Memory

19.9MiB live, 19.8MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 x #s(literal 2/3 binary64)))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x #s(approx (/ 1 (+ (* 1/18 (* x x)) 2/3)) #s(literal 3/2 binary64))))
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/18 binary64) #s(literal 2/3 binary64)) x))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 #s(approx (tan ( 1/2 x)) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 4/3 binary64)))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/18 binary64) x) (*.f64 x #s(literal 2/3 binary64))))

Outputs
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x #s(approx (/ 1 (+ (* 1/18 (* x x)) 2/3)) #s(literal 3/2 binary64))))

Calls

2 calls:

3.0ms	(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))
2.0ms	x

Results

Accuracy	Segments	Branch
51.3%	1	`x`
51.3%	1	`(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))`

Compiler

Compiled 17 to 12 computations (29.4% saved)

regimes38.0ms (0.4%)

Memory

-29.7MiB live, 9.7MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 x #s(literal 2/3 binary64)))

Outputs
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 x #s(literal 2/3 binary64)))

Calls

2 calls:

36.0ms	x
1.0ms	(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))

Results

Accuracy	Segments	Branch
51.0%	1	`x`
51.0%	1	`(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))`

Compiler

Compiled 17 to 12 computations (29.4% saved)

simplify274.0ms (2.8%)

Memory

-43.2MiB live, 80.0MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`-commutative-binary64-.f64`
2×	`1-exp-binary32-exp.f32`
2×	`1-exp-binary64-exp.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	103
1	51	103

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (tan.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 3/4 binary64))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x #s(approx (/ 1 (+ (* 1/18 (* x x)) 2/3)) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 3/2 binary64)))))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x #s(approx (/ 1 (+ (* 1/18 (* x x)) 2/3)) #s(literal 3/2 binary64))))
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 x #s(literal 2/3 binary64)))

Outputs
(/.f64 (tan.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal 3/4 binary64))
(/.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 3/4 binary64))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 4/3 binary64)))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (.f64 #s(literal 4/3 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64)))))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x #s(approx (/ 1 (+ (* 1/18 (* x x)) 2/3)) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 3/2 binary64)))))
#s(approx (/ (/ 1 (/ 2 (* (- 1 (cos x)) 8/3))) (sin x)) (/.f64 x #s(approx (/ 1 (+ (* 1/18 (* x x)) 2/3)) #s(literal 3/2 binary64))))
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 x #s(literal 2/3 binary64)))
#s(approx (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x)) (*.f64 #s(literal 2/3 binary64) x))

soundness1.5s (15.2%)

Memory

37.7MiB live, 740.5MiB allocated

Rules

18 506×	`lower-fma.f64`
18 506×	`lower-fma.f32`
15 756×	`lower-fma.f64`
15 756×	`lower-fma.f32`
12 558×	`lower-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	414
1	252	414
2	600	408
3	1793	408
4	3345	408
5	4708	408
6	5020	408
7	5315	408
8	5937	408
9	7802	408
0	8069	384
0	38	188
0	58	172
1	180	157
2	1056	155
0	8796	152
0	276	2108
1	740	2108
2	1815	2102
3	3189	2102
4	5298	2102
5	7155	2102
0	8178	1965
0	166	2182
1	466	2182
2	1330	2166
3	3518	2160
4	7019	2160
0	8152	2013
0	11	34
0	19	34
1	34	28
2	115	28
3	628	24
0	4915	24
0	42	212
0	67	202
1	204	186
2	1139	180
0	8644	179

Stop Event

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

Compiler

Compiled 178 to 131 computations (26.4% saved)

preprocess104.0ms (1.1%)

Memory: 20.9MiB live, 208.8MiB allocated
Remove: (negabs x)
Compiler: Compiled 176 to 136 computations (22.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze171.0ms (1.7%)

sample1.7s (17.6%)

explain130.0ms (1.3%)

preprocess56.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0%)

localize38.0ms (0.4%)

series6.0ms (0.1%)

simplify200.0ms (2%)

rewrite137.0ms (1.4%)

eval51.0ms (0.5%)

prune32.0ms (0.3%)

simplify338.0ms (3.4%)

localize519.0ms (5.3%)

series28.0ms (0.3%)

simplify207.0ms (2.1%)

rewrite238.0ms (2.4%)

eval340.0ms (3.5%)

prune76.0ms (0.8%)

simplify440.0ms (4.5%)

localize343.0ms (3.5%)

series29.0ms (0.3%)

simplify226.0ms (2.3%)

rewrite256.0ms (2.6%)

eval858.0ms (8.7%)

prune272.0ms (2.8%)

simplify154.0ms (1.6%)

localize251.0ms (2.6%)

series65.0ms (0.7%)

simplify218.0ms (2.2%)

rewrite148.0ms (1.5%)

eval147.0ms (1.5%)

prune50.0ms (0.5%)

regimes71.0ms (0.7%)

regimes29.0ms (0.3%)

regimes40.0ms (0.4%)

regimes6.0ms (0.1%)

regimes38.0ms (0.4%)

simplify274.0ms (2.8%)

soundness1.5s (15.2%)

preprocess104.0ms (1.1%)

end0.0ms (0%)

Profiling