Metrics for tanhf (example 3.4)

analyze116.0ms (1.7%)

Memory

-10.5MiB live, 137.5MiB 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 9 to 8 computations (11.1% saved)

sample1.8s (26.2%)

Memory

68.3MiB live, 1 704.9MiB allocated

Samples

685.0ms	2 231×	2	valid
487.0ms	4 233×	0	valid
182.0ms	526×	3	valid
126.0ms	1 259×	1	valid
8.0ms	7×	4	valid

Precisions

Click to see histograms. Total time spent on operations: 1.3s

ival-cos: 774.0ms (59.9% of total)

ival-sin: 177.0ms (13.7% of total)

ival-sub: 125.0ms (9.7% of total)

ival-div: 102.0ms (7.9% of total)

adjust: 101.0ms (7.8% of total)

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

exact: 5.0ms (0.4% of total)

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

Bogosity

preprocess52.0ms (0.8%)

Memory

-29.8MiB live, 53.1MiB allocated

Algorithm

1×	egg-herbie

Rules

204×	`lower-fma.f64`
204×	`lower-fma.f32`
140×	`lower-*.f64`
140×	`lower-*.f32`
98×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	4

Stop Event

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

Calls

Call 1

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

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

Symmetry

(negabs x)

explain173.0ms (2.6%)

Memory

-7.8MiB live, 120.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
72	-	0	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
52	-	2	(4.0900593254732873e-156)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(cos.f64 x)`
0	-	0	-	`(sin.f64 x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	72	6
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`	u/n	50	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	50

Confusion

	Predicted +	Predicted -
+	122	1
-	0	133

Precision

1.0

Recall

0.991869918699187

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	122	1	0
-	0	5	128

Precision?

0.9609375

Recall?

1.0

Freqs

test

number	freq
0	134
1	122

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

75.0ms	112×	2	valid
30.0ms	286×	0	valid
10.0ms	30×	3	valid
9.0ms	84×	1	valid

Compiler

Compiled 54 to 28 computations (48.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 108.0ms

ival-cos: 47.0ms (43.7% of total)

ival-sub: 38.0ms (35.3% of total)

ival-sin: 11.0ms (10.2% of total)

adjust: 6.0ms (5.6% of total)

ival-div: 5.0ms (4.6% of total)

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	57.1%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify25.0ms (0.4%)

Memory

26.7MiB live, 26.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sin.f64 x)
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	cost-diff	6848	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Rules

204×	`lower-fma.f64`
204×	`lower-fma.f32`
140×	`lower-*.f64`
140×	`lower-*.f32`
82×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize73.0ms (1.1%)

Memory

-28.4MiB live, 46.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	81.4%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
✓	accuracy	76.0%	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Samples

30.0ms	143×	0	valid
16.0ms	56×	2	valid
5.0ms	15×	3	valid
5.0ms	42×	1	valid

Compiler

Compiled 19 to 8 computations (57.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-cos: 18.0ms (56.6% of total)

ival-sin: 5.0ms (15.7% of total)

ival-div: 3.0ms (9.4% of total)

adjust: 3.0ms (9.4% of total)

ival-sub: 2.0ms (6.3% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0%)

Memory

3.7MiB live, 3.7MiB allocated

Counts

4 → 48

Calls

Call 1

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

Outputs
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>

Calls

12 calls:

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

simplify456.0ms (6.8%)

Memory

43.6MiB live, 548.5MiB allocated

Algorithm

1×	egg-herbie

Rules

19 148×	`lower-fma.f64`
19 148×	`lower-fma.f32`
3 796×	`lower-*.f64`
3 796×	`lower-*.f32`
3 232×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	286
1	224	286
2	555	280
3	1656	280
4	3000	280
5	4243	280
6	4592	280
7	5323	280
8	6815	280
0	8390	256

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 47

Calls

Call 1

Inputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)

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

rewrite294.0ms (4.4%)

Memory

-16.0MiB live, 501.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 606×	`lower-*.f64`
4 606×	`lower-*.f32`
3 722×	`lower-/.f32`
3 720×	`lower-/.f64`
2 028×	`lower--.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	10	12
1	39	12
2	245	12
3	2355	11
0	8885	11

Stop Event

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

Counts

4 → 615

Calls

Call 1

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

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

eval170.0ms (2.5%)

Memory: -12.2MiB live, 160.1MiB allocated
Compiler: Compiled 14 403 to 1 633 computations (88.7% saved)

prune94.0ms (1.4%)

Memory

10.6MiB live, 169.6MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	656	6	662
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	657	6	663

Accuracy

100.0%

Counts

663 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
	7.5%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
▶	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
▶	46.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
▶	46.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
▶	46.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
▶	46.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 110 to 74 computations (32.7% saved)

simplify85.0ms (1.3%)

Memory

18.6MiB live, 95.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
✓	cost-diff	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
✓	cost-diff	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	cost-diff	(*.f64 x #s(literal 1/24 binary64))
✓	cost-diff	(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
✓	cost-diff	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	cost-diff	(*.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
✓	cost-diff	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))

Rules

1 918×	`lower-fma.f32`
1 906×	`lower-fma.f64`
746×	`distribute-lft-in`
552×	`lower-+.f64`
552×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	210
0	52	198
1	122	198
2	276	198
3	538	198
4	761	198
5	848	198
6	885	198
7	959	198
8	1081	198
9	1289	198
10	1331	198
11	1334	198
12	1342	198
13	1348	198
14	1352	198
15	1359	198
16	1534	198
17	1790	198
18	1796	198
0	1796	198

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
x
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
x
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x x)
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(*.f64 x #s(literal 1/240 binary64))
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
x
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x x)
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))
(*.f64 x #s(literal 17/40320 binary64))
#s(literal 17/40320 binary64)
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)

Outputs
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
x
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
x
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x x)
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(*.f64 x #s(literal 1/240 binary64))
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
x
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x x)
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64))
(fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))
(*.f64 x #s(literal 17/40320 binary64))
#s(literal 17/40320 binary64)
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)

localize198.0ms (2.9%)

Memory

-19.5MiB live, 216.1MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
✓	accuracy	99.9%	(fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))
✓	accuracy	99.5%	(*.f64 x #s(literal 17/40320 binary64))
✓	accuracy	46.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	accuracy	99.9%	(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
✓	accuracy	99.8%	(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
✓	accuracy	99.8%	(*.f64 x #s(literal 1/240 binary64))
✓	accuracy	46.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	accuracy	99.9%	(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	99.9%	(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
✓	accuracy	99.4%	(*.f64 x #s(literal 1/24 binary64))
✓	accuracy	46.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	accuracy	46.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))

Samples

46.0ms	143×	0	valid
43.0ms	56×	2	valid
21.0ms	42×	1	valid
12.0ms	15×	3	valid

Compiler

Compiled 182 to 34 computations (81.3% saved)

Precisions

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

ival-mult: 27.0ms (27.4% of total)

ival-cos: 18.0ms (18.2% of total)

const: 16.0ms (16.2% of total)

adjust: 11.0ms (11.1% of total)

ival-add: 9.0ms (9.1% of total)

ival-tan: 6.0ms (6.1% of total)

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

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

ival-sub: 2.0ms (2% of total)

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

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

exact: 0.0ms (0% of total)

series13.0ms (0.2%)

Memory

12.0MiB live, 12.0MiB allocated

Counts

20 → 240

Calls

Call 1

Inputs
#<alt (tan.f64 (*.f64 x #s(literal 1/2 binary64)))>
#<alt (*.f64 x #s(literal 1/2 binary64))>
#<alt #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))>
#<alt (*.f64 #s(literal 1/2 binary64) x)>
#<alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))>
#<alt (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))>
#<alt (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))>
#<alt (*.f64 x #s(literal 1/24 binary64))>
#<alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))>
#<alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))>
#<alt (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))>
#<alt (*.f64 x x)>
#<alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))>
#<alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))>
#<alt (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))>
#<alt (*.f64 x #s(literal 1/240 binary64))>
#<alt (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))>
#<alt (*.f64 x #s(literal 17/40320 binary64))>
#<alt (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))>
#<alt (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))>

Outputs
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/24 (pow x 2)))>
#<alt (+ 1/2 (* 1/24 (pow x 2)))>
#<alt (+ 1/2 (* 1/24 (pow x 2)))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* 1/240 (pow x 5))>
#<alt (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* 1/240 (pow x 5))>
#<alt (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))>
#<alt (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))>
#<alt (* 1/240 (pow x 4))>
#<alt (* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* 1/240 (pow x 4))>
#<alt (* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (* 17/40320 (pow x 7))>
#<alt (* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))>
#<alt (* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))>
#<alt (* 17/40320 (pow x 7))>
#<alt (* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))>
#<alt (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))>
#<alt (* 17/40320 (pow x 6))>
#<alt (* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))>
#<alt (* 17/40320 (pow x 6))>
#<alt (* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt 1/24>
#<alt (+ 1/24 (* 1/240 (pow x 2)))>
#<alt (+ 1/24 (* 1/240 (pow x 2)))>
#<alt (+ 1/24 (* 1/240 (pow x 2)))>
#<alt (* 1/240 (pow x 2))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* 1/240 (pow x 2))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* 17/40320 x)>
#<alt (* 17/40320 x)>
#<alt (* 17/40320 x)>
#<alt (* 17/40320 x)>
#<alt (* 17/40320 x)>
#<alt (* 17/40320 x)>
#<alt (* 17/40320 x)>
#<alt (* 17/40320 x)>
#<alt (* 17/40320 x)>
#<alt (* 17/40320 x)>
#<alt (* 17/40320 x)>
#<alt (* 17/40320 x)>
#<alt 1/240>
#<alt (+ 1/240 (* 17/40320 (pow x 2)))>
#<alt (+ 1/240 (* 17/40320 (pow x 2)))>
#<alt (+ 1/240 (* 17/40320 (pow x 2)))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* 17/40320 (pow x 2))>
#<alt (* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt 1/24>
#<alt (+ 1/24 (* 1/240 (pow x 2)))>
#<alt (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))>
#<alt (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))>
#<alt (* 17/40320 (pow x 4))>
#<alt (* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))>
#<alt (* 17/40320 (pow x 4))>
#<alt (* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))>

Calls

60 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(+ (* (* x x) (+ (* x (* x 1/240)) 1/24)) 1/2)
1.0ms	x	@	inf	(* x 1/2)
1.0ms	x	@	inf	(tan (* x 1/2))
1.0ms	x	@	inf	(* x (+ (* x (* x 1/24)) 1/2))
0.0ms	x	@	inf	(* x (+ (* (* x x) (+ (* x (* x 1/240)) 1/24)) 1/2))

simplify366.0ms (5.4%)

Memory

-25.0MiB live, 423.4MiB allocated

Algorithm

1×	egg-herbie

Rules

14 366×	`lower-fma.f64`
14 366×	`lower-fma.f32`
4 532×	`lower-*.f64`
4 532×	`lower-*.f32`
2 914×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	100	1662
1	325	1662
2	843	1657
3	2171	1654
4	4749	1654
0	8097	1525

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

Inputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* 1/24 (pow x 2)))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* 1/240 (pow x 5))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 5))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(* 1/240 (pow x 4))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 4))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 17/40320 (pow x 7))
(* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(* 17/40320 (pow x 7))
(* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
(* 17/40320 (pow x 6))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(* 17/40320 (pow x 6))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
1/24
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/24 (* 1/240 (pow x 2)))
(* 1/240 (pow x 2))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* 1/240 (pow x 2))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* 17/40320 x)
(* 17/40320 x)
(* 17/40320 x)
(* 17/40320 x)
(* 17/40320 x)
(* 17/40320 x)
(* 17/40320 x)
(* 17/40320 x)
(* 17/40320 x)
(* 17/40320 x)
(* 17/40320 x)
(* 17/40320 x)
1/240
(+ 1/240 (* 17/40320 (pow x 2)))
(+ 1/240 (* 17/40320 (pow x 2)))
(+ 1/240 (* 17/40320 (pow x 2)))
(* 17/40320 (pow x 2))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* 17/40320 (pow x 2))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
1/24
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
(* 17/40320 (pow x 4))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* 17/40320 (pow x 4))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))

Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* 1/24 (pow x 3))
(.f64 x (.f64 #s(literal 1/24 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* 1/24 (pow x 3))
(.f64 x (.f64 #s(literal 1/24 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* 1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* 1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* 1/240 (pow x 5))
(.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1/240 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1/240 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))))
(* 1/240 (pow x 5))
(.f64 (.f64 (.f64 x x) #s(literal 1/240 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1/240 binary64) (/.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (*.f64 x x))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1/240 binary64) (/.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (*.f64 x x))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* 1/240 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/240 binary64)))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* 1/240 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/240 binary64)))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* 17/40320 (pow x 7))
(*.f64 #s(literal 17/40320 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 17/40320 binary64) (/.f64 #s(literal 1/240 binary64) (.f64 x x))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (/.f64 #s(literal 1/240 binary64) (.f64 x x)) (+.f64 #s(literal 17/40320 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 17/40320 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1/240 binary64) (.f64 x x)) (/.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))))))
(* 17/40320 (pow x 7))
(*.f64 #s(literal 17/40320 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 17/40320 binary64) (/.f64 #s(literal 1/240 binary64) (.f64 x x))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))
(.f64 (pow.f64 x #s(literal 7 binary64)) (-.f64 #s(literal 17/40320 binary64) (/.f64 (+.f64 #s(literal -1/240 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x x))) (*.f64 x x))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (fma.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (/.f64 (+.f64 #s(literal -1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (.f64 x x)) #s(literal -1/240 binary64)) #s(literal 17/40320 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* 17/40320 (pow x 6))
(.f64 x (.f64 x (.f64 #s(literal 17/40320 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* 17/40320 (pow x 6))
(.f64 x (.f64 x (.f64 #s(literal 17/40320 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))
(* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
1/24
#s(literal 1/24 binary64)
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* 1/240 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/240 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* 1/240 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/240 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* 17/40320 x)
(*.f64 x #s(literal 17/40320 binary64))
(* 17/40320 x)
(*.f64 x #s(literal 17/40320 binary64))
(* 17/40320 x)
(*.f64 x #s(literal 17/40320 binary64))
(* 17/40320 x)
(*.f64 x #s(literal 17/40320 binary64))
(* 17/40320 x)
(*.f64 x #s(literal 17/40320 binary64))
(* 17/40320 x)
(*.f64 x #s(literal 17/40320 binary64))
(* 17/40320 x)
(*.f64 x #s(literal 17/40320 binary64))
(* 17/40320 x)
(*.f64 x #s(literal 17/40320 binary64))
(* 17/40320 x)
(*.f64 x #s(literal 17/40320 binary64))
(* 17/40320 x)
(*.f64 x #s(literal 17/40320 binary64))
(* 17/40320 x)
(*.f64 x #s(literal 17/40320 binary64))
(* 17/40320 x)
(*.f64 x #s(literal 17/40320 binary64))
1/240
#s(literal 1/240 binary64)
(+ 1/240 (* 17/40320 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))
(+ 1/240 (* 17/40320 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))
(+ 1/240 (* 17/40320 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))
(* 17/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal 17/40320 binary64))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))
(* 17/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal 17/40320 binary64))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))
(* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))
1/24
#s(literal 1/24 binary64)
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* 17/40320 (pow x 4))
(.f64 #s(literal 17/40320 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* 17/40320 (pow x 4))
(.f64 #s(literal 17/40320 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))

rewrite373.0ms (5.5%)

Memory

27.4MiB live, 469.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 984×	`lower-*.f32`
4 966×	`lower-*.f64`
4 560×	`lower-/.f64`
4 560×	`lower-/.f32`
3 720×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	191
0	52	179
1	217	179
2	1560	179
0	8169	179

Stop Event

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

Counts

20 → 566

Calls

Call 1

Inputs
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x #s(literal 1/24 binary64))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x x)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x #s(literal 1/240 binary64))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(*.f64 x #s(literal 17/40320 binary64))
(fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64))))) #s(literal -1 binary64)))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (sin.f64 x)) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (sin.f64 x)))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x)) (/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x))) (tan.f64 (/.f64 (neg.f64 x) #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(-.f64 (/.f64 (.f64 #s(literal 1 binary64) (sin.f64 x)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (/.f64 (.f64 (sin.f64 x) (cos.f64 x)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
(-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sin.f64 x) (tan.f64 x)))))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sin.f64 x) (tan.f64 x)))))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) (/.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 x))) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(neg.f64 (tan.f64 (/.f64 (neg.f64 x) #s(literal 2 binary64))))
(neg.f64 (/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (.f64 (sin.f64 x) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 (sin.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 (.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 (sin.f64 x) (cos.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (sin.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) (.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sin.f64 x) (tan.f64 x))))) (-.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (sin.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (sin.f64 x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (*.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x))))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (sin.f64 x)) (.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (sin.f64 x)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (*.f64 (sin.f64 x) #s(literal 1 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (neg.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (neg.f64 (sin.f64 x))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))))) (sin.f64 x)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))))) (*.f64 (sin.f64 x) #s(literal 1 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)))
(/.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 (sin.f64 x) #s(literal 1 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64)) (*.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x))))
(/.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (sin.f64 x)))
(/.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (.f64 (sin.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (neg.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)))) (neg.f64 (neg.f64 (sin.f64 x))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (*.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (neg.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(/.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sin.f64 x) (tan.f64 x))))))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (sin.f64 x))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (sin.f64 x))) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (sin.f64 x))) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (-.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 x))) (neg.f64 (sin.f64 x)))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (tan.f64 x)) (.f64 (sin.f64 x) #s(literal 1 binary64))) (*.f64 (sin.f64 x) (tan.f64 x)))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 x))) (.f64 (sin.f64 x) (neg.f64 (cos.f64 x)))) (*.f64 (sin.f64 x) (neg.f64 (sin.f64 x))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (tan.f64 x)) (.f64 (.f64 (sin.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64)) (tan.f64 x)))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (sin.f64 x)) (.f64 (.f64 (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x))) (.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64)) (sin.f64 x)))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 x))) (.f64 (.f64 (sin.f64 x) #s(literal 1 binary64)) (neg.f64 (cos.f64 x)))) (.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64)) (neg.f64 (sin.f64 x))))
(/.f64 (-.f64 (.f64 #s(literal -1 binary64) (tan.f64 x)) (.f64 (neg.f64 (sin.f64 x)) #s(literal 1 binary64))) (*.f64 (neg.f64 (sin.f64 x)) (tan.f64 x)))
(/.f64 (-.f64 (neg.f64 (sin.f64 x)) (.f64 (neg.f64 (sin.f64 x)) (cos.f64 x))) (.f64 (neg.f64 (sin.f64 x)) (sin.f64 x)))
(/.f64 (-.f64 (.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 x))) (.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 x)))) (*.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 x))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) (.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (sin.f64 x))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))))) (neg.f64 (sin.f64 x))))
(/.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal -1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (neg.f64 (sin.f64 x))))
(/.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal -1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (neg.f64 (sin.f64 x))))
(/.f64 (.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)) (.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (sin.f64 x))))
(/.f64 (.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)) (.f64 (neg.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (sin.f64 x)))
(/.f64 (.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)) (.f64 (neg.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (*.f64 (sin.f64 x) #s(literal 1 binary64))))
(/.f64 (.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)) (.f64 (neg.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (neg.f64 (sin.f64 x))))
(/.f64 (.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (neg.f64 (sin.f64 x))))
(/.f64 (.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal 1 binary64)) (*.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x)))
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(.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64)))
(.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))))) #s(literal 1/13824 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))) #s(literal 1/576 binary64)) (.f64 x (.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64))))))
(.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))))) #s(literal 1/13824 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/576 binary64) (-.f64 (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64)))))))
(.f64 (fma.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))) #s(literal -1/576 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal -1/24 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))))) #s(literal 1/13824 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))) #s(literal 1/576 binary64)) (.f64 x (.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal 1/24 binary64)))))))
(.f64 (neg.f64 (fma.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))) #s(literal -1/576 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) #s(literal -1/24 binary64)))))
(.f64 (-.f64 #s(literal 1/576 binary64) (.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)))))))

eval118.0ms (1.8%)

Memory: 4.6MiB live, 233.6MiB allocated
Compiler: Compiled 24 229 to 1 994 computations (91.8% saved)

prune94.0ms (1.4%)

Memory

0.9MiB live, 233.4MiB allocated

Pruning

9 alts after pruning (4 fresh and 5 done)

	Pruned	Kept	Total
New	839	3	842
Fresh	0	1	1
Picked	0	5	5
Done	0	0	0
Total	839	9	848

Accuracy

100.0%

Counts

848 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.5%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
✓	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
▶	46.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
▶	46.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
▶	46.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
✓	46.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	46.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	46.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	46.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 88 to 59 computations (33% saved)

simplify44.0ms (0.7%)

Memory

12.6MiB live, 50.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	6464	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
✓	cost-diff	0	(*.f64 x #s(literal 1/240 binary64))
✓	cost-diff	0	(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
✓	cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
✓	cost-diff	320	(fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 x (.f64 x x))
✓	cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
✓	cost-diff	320	(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) x)
✓	cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
✓	cost-diff	1088	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))

Rules

580×	`lower-fma.f32`
574×	`lower-fma.f64`
284×	`lower-*.f32`
276×	`lower-*.f64`
228×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	133
0	37	106
1	64	106
2	98	106
3	176	106
4	294	106
5	329	106
6	362	106
7	436	106
8	559	106
9	766	106
10	808	106
11	811	106
12	819	106
13	824	106
14	828	106
15	835	106
16	915	106
17	999	106
18	1003	106
0	1003	106

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
#s(literal 1 binary64)
(/.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))
(.f64 x (.f64 x x))
x
(*.f64 x x)
#s(literal 1/24 binary64)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
(fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
x
(*.f64 x #s(literal 1/240 binary64))
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
(.f64 x (.f64 x x))
(*.f64 x x)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
#s(literal 1 binary64)
#s(literal -1/2 binary64)

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1 binary64)
(/.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(.f64 x (.f64 x x))
x
(*.f64 x x)
#s(literal 1/24 binary64)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))
x
(*.f64 x #s(literal 1/240 binary64))
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
(.f64 x (.f64 x x))
(*.f64 x x)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
#s(literal 1 binary64)
#s(literal 1 binary64)
#s(literal -1/2 binary64)

localize174.0ms (2.6%)

Memory

-31.1MiB live, 213.0MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
✓	accuracy	99.8%	(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
✓	accuracy	99.8%	(.f64 x (.f64 x x))
✓	accuracy	99.8%	(*.f64 x #s(literal 1/240 binary64))
✓	accuracy	46.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	99.8%	(.f64 x (.f64 x x))
✓	accuracy	99.6%	(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))
✓	accuracy	46.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(/.f64 #s(literal 2 binary64) x)
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
✓	accuracy	46.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))

Samples

52.0ms	143×	0	valid
32.0ms	56×	2	valid
13.0ms	42×	1	valid
11.0ms	15×	3	valid

Compiler

Compiled 106 to 26 computations (75.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 87.0ms

ival-sin: 25.0ms (28.6% of total)

ival-cos: 19.0ms (21.8% of total)

ival-mult: 10.0ms (11.4% of total)

adjust: 8.0ms (9.2% of total)

const: 8.0ms (9.2% of total)

ival-add: 7.0ms (8% of total)

ival-div: 6.0ms (6.9% of total)

ival-sub: 2.0ms (2.3% of total)

ival-pow: 2.0ms (2.3% of total)

exact: 1.0ms (1.1% of total)

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

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

series5.0ms (0.1%)

Memory

7.2MiB live, 7.2MiB allocated

Counts

13 → 144

Calls

Call 1

Inputs
#<alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))>
#<alt #s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))>
#<alt (/.f64 #s(literal 2 binary64) x)>
#<alt (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))>
#<alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))>
#<alt (.f64 x (.f64 x x))>
#<alt (*.f64 x x)>
#<alt (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))>
#<alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))>
#<alt (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))>
#<alt (*.f64 x #s(literal 1/240 binary64))>
#<alt (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))>
#<alt (*.f64 x #s(literal 1/2 binary64))>

Outputs
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* 1/240 (pow x 5))>
#<alt (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* 1/240 (pow x 5))>
#<alt (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt 1/24>
#<alt (+ 1/24 (* 1/240 (pow x 2)))>
#<alt (+ 1/24 (* 1/240 (pow x 2)))>
#<alt (+ 1/24 (* 1/240 (pow x 2)))>
#<alt (* 1/240 (pow x 2))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* 1/240 (pow x 2))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>

Calls

36 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(+ (* (* x (* x x)) 1/24) (* x 1/2))
0.0ms	x	@	-inf	(* x (* x x))
0.0ms	x	@	0	(/ 2 x)
0.0ms	x	@	-inf	(+ (* (+ (* x (* x 1/240)) 1/24) (* x (* x x))) (* x 1/2))
0.0ms	x	@	0	(+ (* (* x (* x x)) 1/24) (* x 1/2))

simplify511.0ms (7.6%)

Memory

-5.5MiB live, 524.9MiB allocated

Algorithm

1×	egg-herbie

Rules

16 178×	`lower-fma.f64`
16 178×	`lower-fma.f32`
3 944×	`lower-*.f64`
3 944×	`lower-*.f32`
2 528×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	758
1	165	758
2	417	758
3	1000	758
4	1962	758
5	4681	758
0	8285	707

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

Inputs
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* 1/240 (pow x 5))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 5))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
1/24
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/24 (* 1/240 (pow x 2)))
(* 1/240 (pow x 2))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* 1/240 (pow x 2))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)

Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
(* 1/24 (pow x 3))
(.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
(* 1/24 (pow x 3))
(.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* 1/240 (pow x 5))
(.f64 x (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 1/240 binary64)))))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* 1/240 (pow x 5))
(.f64 x (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 1/240 binary64)))))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
1/24
#s(literal 1/24 binary64)
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* 1/240 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/240 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* 1/240 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/240 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)

rewrite348.0ms (5.2%)

Memory

-1.7MiB live, 428.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

8 438×	`lower-fma.f32`
8 432×	`lower-fma.f64`
4 474×	`lower-*.f32`
4 466×	`lower-*.f64`
3 760×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	110
0	37	85
1	141	85
2	943	85
0	8375	85

Stop Event

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

Counts

13 → 311

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
(/.f64 #s(literal 2 binary64) x)
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
(.f64 x (.f64 x x))
(*.f64 x x)
(fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(*.f64 x #s(literal 1/240 binary64))
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
(*.f64 x #s(literal 1/2 binary64))

Outputs
(exp.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(-.f64 #s(literal 0 binary64) (*.f64 x #s(literal -1/2 binary64)))
(neg.f64 (*.f64 x #s(literal -1/2 binary64)))
(neg.f64 (/.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 x #s(literal 2 binary64))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) x))
(/.f64 (neg.f64 x) #s(literal -2 binary64))
(/.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1/2 binary64) (neg.f64 x))
(*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (.f64 x #s(literal -1/2 binary64)))
(*.f64 (neg.f64 x) #s(literal -1/2 binary64))
(.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))
(exp.f64 (neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -2 binary64) x))
(neg.f64 (/.f64 #s(literal -2 binary64) x))
(/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(/.f64 #s(literal 2 binary64) x)
(/.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(/.f64 (/.f64 #s(literal -2 binary64) x) #s(literal -1 binary64))
(/.f64 #s(literal -2 binary64) (neg.f64 x))
(pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64))
(pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) x))
(*.f64 (/.f64 #s(literal -2 binary64) x) #s(literal -1 binary64))
(*.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(.f64 (pow.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64))))
(+.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64))) (.f64 x #s(literal 1/2 binary64)))
(+.f64 (/.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(-.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64))) (.f64 x #s(literal -1/2 binary64)))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))) (/.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64))))
(fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal 1/24 binary64))))
(fma.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/24 binary64)) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (.f64 x (.f64 (*.f64 x x) #s(literal 1/24 binary64))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64))))
(fma.f64 #s(literal -1/2 binary64) (neg.f64 x) (.f64 x (.f64 (*.f64 x x) #s(literal 1/24 binary64))))
(fma.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (.f64 x (.f64 (*.f64 x x) #s(literal 1/24 binary64))))
(fma.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64))) #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1 binary64) (.f64 x #s(literal -1/2 binary64)) (.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64))))
(fma.f64 (neg.f64 x) #s(literal -1/2 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal 1/24 binary64))))
(fma.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) x (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (.f64 x (.f64 (*.f64 x x) #s(literal 1/24 binary64))))
(fma.f64 (.f64 #s(literal 1/24 binary64) x) (.f64 x x) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (/.f64 x x) (/.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) (.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64)))) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 x x) x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 x (.f64 x x)) x) (/.f64 (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64)))) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 #s(literal 1/24 binary64) x) (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64)))) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64))) x) (/.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64))) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 #s(literal 1/576 binary64) x) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) x) (/.f64 #s(literal 1/576 binary64) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64))) x) x) (/.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64))) (.f64 x (.f64 x x))) x) (/.f64 #s(literal 1/24 binary64) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(fma.f64 (/.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64))) #s(literal 1/24 binary64)) x) (/.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(neg.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/24 binary64)))))))
(neg.f64 (/.f64 (.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/4 binary64))) (neg.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(neg.f64 (/.f64 (neg.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/8 binary64)))) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/24 binary64))))))
(neg.f64 (/.f64 (neg.f64 (.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/4 binary64)))) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))) (.f64 (.f64 x (.f64 x x)) (fma.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x))) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))) (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (*.f64 x x)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))))
(/.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/8 binary64))) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/24 binary64)))))
(/.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/8 binary64))) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))))
(/.f64 (.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/4 binary64))) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/4 binary64)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/24 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64))) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/4 binary64)))) (neg.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) (.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))))
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(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/57600 binary64))) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/57600 binary64))) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/57600 binary64))) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (fma.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/57600 binary64))) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/57600 binary64))) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/57600 binary64))) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64)))) (.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))))) (+.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/57600 binary64))) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal 1/13824 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/57600 binary64)) #s(literal 1/576 binary64)) (.f64 (*.f64 x x) #s(literal -1/5760 binary64)))))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal 1/13824 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/57600 binary64)) #s(literal 1/5760 binary64))))))
(.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/57600 binary64)) #s(literal -1/576 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal 1/13824 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/57600 binary64)) #s(literal 1/576 binary64)) (.f64 (*.f64 x x) #s(literal -1/5760 binary64))))))
(.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/57600 binary64)) #s(literal -1/576 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/24 binary64))))
(.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/57600 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64))))))
(*.f64 x #s(literal 1/240 binary64))
(*.f64 #s(literal 1/240 binary64) x)
#s(literal 1 binary64)
(exp.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(-.f64 #s(literal 0 binary64) (*.f64 x #s(literal -1/2 binary64)))
(neg.f64 (*.f64 x #s(literal -1/2 binary64)))
(neg.f64 (/.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 x #s(literal 2 binary64))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) x))
(/.f64 (neg.f64 x) #s(literal -2 binary64))
(/.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1/2 binary64) (neg.f64 x))
(*.f64 #s(literal -1/2 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (.f64 x #s(literal -1/2 binary64)))
(*.f64 (neg.f64 x) #s(literal -1/2 binary64))
(.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))

eval75.0ms (1.1%)

Memory: -11.2MiB live, 119.2MiB allocated
Compiler: Compiled 12 604 to 893 computations (92.9% saved)

prune48.0ms (0.7%)

Memory

11.4MiB live, 89.7MiB allocated

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	530	1	531
Fresh	0	0	0
Picked	2	2	4
Done	0	5	5
Total	532	8	540

Accuracy

100.0%

Counts

540 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	46.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
✓	46.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
✓	46.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	46.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	46.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	46.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
▶	7.5%	#s(literal 1 binary64)

Compiler

Compiled 80 to 52 computations (35% saved)

simplify3.0ms (0.1%)

Memory

3.9MiB live, 3.9MiB allocated

Algorithm

1×	egg-herbie

Rules

2× 1-exp

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
0	1	1
1	3	1
0	3	1

Stop Event

1×	saturated
1×	saturated
1×	saturated

Calls

Call 1

Inputs
#s(literal 1 binary64)

Outputs
#s(literal 1 binary64)

localize6.0ms (0.1%)

Memory

7.6MiB live, 7.6MiB allocated

Samples

3.0ms

256×

valid

Compiler

Compiled 3 to 4 computations (-33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

exact: 0.0ms (0% of total)

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

series0.0ms (0%)

Memory

0.0MiB live, 0.0MiB allocated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

simplify2.0ms (0%)

Memory

2.4MiB live, 2.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

rewrite7.0ms (0.1%)

Memory

2.5MiB live, 2.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune5.0ms (0.1%)

Memory

4.5MiB live, 4.5MiB allocated

Pruning

8 alts after pruning (0 fresh and 8 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	7	7
Total	8	8

Accuracy

100.0%

Counts

8 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	46.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
✓	46.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
✓	46.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	46.6%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	46.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	46.5%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
✓	7.5%	#s(literal 1 binary64)

Compiler

Compiled 168 to 86 computations (48.8% saved)

regimes20.0ms (0.3%)

Memory

-32.9MiB live, 6.1MiB allocated

Counts

11 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

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

Calls

2 calls:

15.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
4.0ms	x

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes7.0ms (0.1%)

Memory

5.0MiB live, 5.0MiB allocated

Counts

9 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))

Outputs

#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))

#s(literal 1 binary64)

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
50.5%	2	`x`
50.1%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes3.0ms (0.1%)

Memory

2.5MiB live, 2.5MiB allocated

Counts

7 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
#s(literal 1 binary64)

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
50.4%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Memory

2.8MiB live, 2.8MiB allocated

Counts

6 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(literal 1 binary64)

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
50.4%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0.1%)

Memory

4.1MiB live, 4.1MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
49.8%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
50.1%	2	`x`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes2.0ms (0%)

Memory

2.1MiB live, 2.1MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

#s(literal 1 binary64)

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

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
50.1%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0.1%)

Memory

3.4MiB live, 3.4MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
49.5%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
49.8%	2	`x`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes3.0ms (0%)

Memory

3.2MiB live, 3.2MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)

Outputs
#s(literal 1 binary64)

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
7.5%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
7.5%	1	`x`

Compiler

Compiled 10 to 7 computations (30% saved)

bsearch0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.1347184195583039	7.948511662481683

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.1347184195583039	7.948511662481683

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.1347184195583039	7.948511662481683

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.1347184195583039	7.948511662481683

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.1347184195583039	7.948511662481683

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.1347184195583039	7.948511662481683

Compiler

Compiled 11 to 10 computations (9.1% saved)

simplify7.0ms (0.1%)

Memory

4.9MiB live, 4.9MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	150
1	54	150

Stop Event

1×

saturated

Calls

Call 1

Inputs
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 3602879701896397/18014398509481984 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/18014398509481984 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/18014398509481984 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/18014398509481984 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/18014398509481984 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/18014398509481984 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))
#s(literal 1 binary64)

Outputs
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 3602879701896397/18014398509481984 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/18014398509481984 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/18014398509481984 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/18014398509481984 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/18014398509481984 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/18014398509481984 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/18014398509481984 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness906.0ms (13.4%)

Memory

-9.8MiB live, 547.6MiB allocated

Rules

19 148×	`lower-fma.f64`
19 148×	`lower-fma.f32`
8 438×	`lower-fma.f32`
8 432×	`lower-fma.f64`
4 984×	`lower-*.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	286
1	224	286
2	555	280
3	1656	280
4	3000	280
5	4243	280
6	4592	280
7	5323	280
8	6815	280
0	8390	256
0	30	191
0	52	179
1	217	179
2	1560	179
0	8169	179
0	6	15
0	10	12
1	39	12
2	245	12
3	2355	11
0	8885	11
0	24	110
0	37	85
1	141	85
2	943	85
0	8375	85

Stop Event

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

Compiler

Compiled 242 to 128 computations (47.1% saved)

preprocess83.0ms (1.2%)

Memory: -7.3MiB live, 146.4MiB allocated
Remove: (negabs x)
Compiler: Compiled 242 to 92 computations (62% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	4

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	4

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14

analyze116.0ms (1.7%)

sample1.8s (26.2%)

preprocess52.0ms (0.8%)

explain173.0ms (2.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify25.0ms (0.4%)

localize73.0ms (1.1%)

series3.0ms (0%)

simplify456.0ms (6.8%)

rewrite294.0ms (4.4%)

eval170.0ms (2.5%)

prune94.0ms (1.4%)

simplify85.0ms (1.3%)

localize198.0ms (2.9%)

series13.0ms (0.2%)

simplify366.0ms (5.4%)

rewrite373.0ms (5.5%)

eval118.0ms (1.8%)

prune94.0ms (1.4%)

simplify44.0ms (0.7%)

localize174.0ms (2.6%)

series5.0ms (0.1%)

simplify511.0ms (7.6%)

rewrite348.0ms (5.2%)

eval75.0ms (1.1%)

prune48.0ms (0.7%)

simplify3.0ms (0.1%)

localize6.0ms (0.1%)

series0.0ms (0%)

simplify2.0ms (0%)

rewrite7.0ms (0.1%)

eval0.0ms (0%)

prune5.0ms (0.1%)

regimes20.0ms (0.3%)

regimes7.0ms (0.1%)

regimes3.0ms (0.1%)

regimes3.0ms (0%)

regimes5.0ms (0.1%)

regimes2.0ms (0%)

regimes3.0ms (0.1%)

regimes3.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

soundness906.0ms (13.4%)

preprocess83.0ms (1.2%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	4

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14