Metrics for tanhf (example 3.4)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze112.0ms (2%)

Memory

17.5MiB live, 134.3MiB 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)

sample2.3s (41.2%)

Memory

35.1MiB live, 1 676.2MiB allocated

Samples

928.0ms	2 240×	2	valid
522.0ms	4 188×	0	valid
206.0ms	563×	3	valid
201.0ms	1 262×	1	valid
3.0ms	3×	4	valid

Precisions

Click to see histograms. Total time spent on operations: 1.6s

ival-cos: 1.1s (65.1% of total)

ival-sin: 217.0ms (13.3% of total)

adjust: 121.0ms (7.4% of total)

ival-div: 120.0ms (7.3% of total)

ival-sub: 99.0ms (6% of total)

ival-true: 6.0ms (0.4% of total)

exact: 5.0ms (0.3% of total)

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

Bogosity

explain173.0ms (3.1%)

Memory

16.8MiB live, 130.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
68	2	(-5.36013753895037e-162)	0	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
63	0	-	4	(-5.36013753895037e-162)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(cos.f64 x)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	70	1
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`	u/n	59	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	59

Confusion

	Predicted +	Predicted -
+	128	0
-	1	127

Precision

0.9922480620155039

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	128	0	0
-	1	1	126

Precision?

0.9846153846153847

Recall?

1.0

Freqs

test

number	freq
0	127
1	129

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

36.0ms	126×	2	valid
28.0ms	268×	0	valid
16.0ms	46×	3	valid
8.0ms	72×	1	valid

Compiler

Compiled 45 to 22 computations (51.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 72.0ms

ival-cos: 42.0ms (58.6% of total)

ival-sin: 11.0ms (15.4% of total)

adjust: 6.0ms (8.4% of total)

ival-div: 6.0ms (8.4% of total)

ival-sub: 5.0ms (7% of total)

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

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

exact: 0.0ms (0% of total)

preprocess81.0ms (1.5%)

Memory

-27.4MiB live, 19.1MiB 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))
(tan.f64 (/.f64 x #s(literal 2 binary64)))

Symmetry

(negabs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.3%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify23.0ms (0.4%)

Memory

23.4MiB live, 23.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
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	6592	(/.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))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(sin.f64 x)

localize58.0ms (1%)

Memory

-2.1MiB live, 70.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(sin.f64 x)
accuracy	0	(cos.f64 x)
accuracy	14.372342651986031	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
accuracy	14.610274428609635	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Samples

22.0ms	63×	2	valid
19.0ms	134×	0	valid
8.0ms	23×	3	valid
4.0ms	36×	1	valid

Compiler

Compiled 19 to 8 computations (57.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-cos: 23.0ms (59.8% of total)

ival-sin: 7.0ms (18.2% of total)

adjust: 3.0ms (7.8% of total)

ival-div: 3.0ms (7.8% of total)

ival-sub: 2.0ms (5.2% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

1.6MiB live, 1.6MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

3 calls:

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

simplify203.0ms (3.7%)

Memory

-11.7MiB live, 140.5MiB 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	1661	280
4	3000	280
5	4254	280
6	4606	280
7	5336	280
8	6824	280
0	8376	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))))))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(sin x)
(sin x)
(sin 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))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(sin x)
(sin x)
(sin x)
(sin x)

Outputs
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) (.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) x)
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #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))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 x #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))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)

rewrite207.0ms (3.7%)

Memory

8.1MiB live, 206.7MiB allocated

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
(*.f64 (pow.f64 (/.f64 (neg.f64 (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal -2 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal -2 binary64)))
(.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (cos.f64 (/.f64 x #s(literal -2 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sin.f64 x)))
(*.f64 (pow.f64 (/.f64 (neg.f64 (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal -2 binary64))) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (cos.f64 (/.f64 x #s(literal -2 binary64))) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x)) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) #s(literal 1 binary64)) (pow.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (pow.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)) (pow.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (sin.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x)) #s(literal 2 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (sin.f64 x)) (+.f64 (pow.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x)) #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x)) (-.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 1 binary64) (-.f64 (cos.f64 x) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (sin.f64 x) (sin.f64 x)) #s(literal -1 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) #s(literal -1 binary64)) (pow.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64)) (pow.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) #s(literal -1 binary64)))
(.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (sin.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))
(.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (sin.f64 x)) (+.f64 (pow.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x)) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x)) (-.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(*.f64 (/.f64 (neg.f64 (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 (cos.f64 x) #s(literal 1 binary64)))
(*.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))))
(*.f64 (pow.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (-.f64 (pow.f64 (sin.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 x) #s(literal -3 binary64))) #s(literal -1 binary64)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 x) #s(literal -2 binary64))))
(.f64 (pow.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (sin.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 x) (cos.f64 x))) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (cos.f64 (/.f64 x #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64)) (cos.f64 (/.f64 x #s(literal -2 binary64))))
(*.f64 (pow.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 (cos.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (sin.f64 x)))
(*.f64 (pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (sin.f64 x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)) (.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x)))
(*.f64 (/.f64 (sin.f64 x) (sin.f64 x)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (pow.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 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 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)))
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(*.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (pow.f64 (pow.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))
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eval91.0ms (1.6%)

Memory: -7.2MiB live, 153.5MiB allocated
Compiler: Compiled 13 164 to 1 644 computations (87.5% saved)

prune17.0ms (0.3%)

Memory

-7.5MiB live, 40.9MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	657	5	662
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	658	5	663

Accuracy

100.0%

Counts

663 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.8%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
▶	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
▶	49.2%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
▶	49.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
▶	49.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))

Compiler

Compiled 68 to 56 computations (17.6% saved)

simplify38.0ms (0.7%)

Memory

19.7MiB live, 56.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

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

Rules

580×	`lower-fma.f32`
574×	`lower-fma.f64`
284×	`lower-*.f32`
274×	`lower-*.f64`
250×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	124
0	36	113
1	61	113
2	94	113
3	158	113
4	257	113
5	287	113
6	323	113
7	397	113
8	520	113
9	727	113
10	769	113
11	772	113
12	780	113
13	785	113
14	789	113
15	796	113
16	876	113
17	956	113
18	960	113
0	960	113

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize132.0ms (2.4%)

Memory

11.9MiB live, 131.2MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
accuracy	0.01953125	(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
accuracy	0.0703125	(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
accuracy	0.4927918769491142	(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
accuracy	32.482937736450644	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
accuracy	0	(*.f64 x x)
accuracy	0.05859375	(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
accuracy	0.5062093707769397	(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
accuracy	32.41859051573066	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
accuracy	0	(*.f64 x #s(literal 1/2 binary64))
accuracy	32.20219962382269	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))

Samples

49.0ms	134×	0	valid
38.0ms	63×	2	valid
18.0ms	23×	3	valid
11.0ms	36×	1	valid

Compiler

Compiled 106 to 25 computations (76.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 97.0ms

ival-cos: 23.0ms (23.7% of total)

ival-sin: 20.0ms (20.6% of total)

ival-mult: 14.0ms (14.4% of total)

adjust: 10.0ms (10.3% of total)

const: 8.0ms (8.3% of total)

ival-add: 8.0ms (8.3% of total)

ival-tan: 6.0ms (6.2% of total)

ival-div: 3.0ms (3.1% of total)

ival-sub: 3.0ms (3.1% of total)

ival-pow: 2.0ms (2.1% of total)

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

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

exact: 0.0ms (0% of total)

series33.0ms (0.6%)

Memory

-23.5MiB live, 13.9MiB allocated

Counts

13 → 144

Calls

Call 1

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

Outputs
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))) (taylor 0 x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))) (taylor 0 x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/24 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/24 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/24 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
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#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor -inf x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor -inf x) (#s(alt (tan.f64 (.f64 #s(literal 1/2 binary64) x)) (patch (tan.f64 (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 3)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 1/24 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (sin x)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/240 (pow x 5)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 1/240 (pow x 4)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/240 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (patch (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

-inf

((tan (* 1/2 x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (* x 1/2) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (pow 1 -1/2))

2.0ms

inf

((tan (* 1/2 x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (* x 1/2) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (pow 1 -1/2))

2.0ms

((tan (* 1/2 x)) (* 1/2 x) (/ (- 1 (cos x)) (sin x)) (* x 1/2) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (pow 1 -1/2))

simplify176.0ms (3.2%)

Memory

-0.0MiB live, 147.7MiB allocated

Algorithm

1×	egg-herbie

Rules

14 916×	`lower-fma.f64`
14 916×	`lower-fma.f32`
3 880×	`lower-*.f64`
3 880×	`lower-*.f32`
2 216×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	962
1	188	962
2	481	962
3	1154	962
4	2335	962
5	5623	962
0	8383	881

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

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))))))))
(* 1/2 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))))))))
(* 1/2 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))))))))
(* 1/2 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))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* 1/24 (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))))))))
(* 1/2 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))))))
1/2
(+ 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)))))
1/24
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/24 (* 1/240 (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)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 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 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (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)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 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 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 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)))))
(/ (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 (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 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (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)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 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)))
(* 1/240 (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 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)))))

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

rewrite229.0ms (4.1%)

Memory

3.1MiB live, 190.2MiB allocated

Rules

6 880×	`lower-fma.f32`
6 874×	`lower-fma.f64`
4 964×	`lower-*.f32`
4 954×	`lower-*.f64`
3 382×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	108
0	36	97
1	128	97
2	768	97
3	7671	97
0	8254	97

Stop Event

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

Counts

13 → 522

Calls

Call 1

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

Outputs
(*.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (cos.f64 x) (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (sin.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))
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(*.f64 (pow.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))
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(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (sin.f64 x)) (pow.f64 (fma.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))
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(*.f64 (/.f64 #s(literal -1 binary64) (sin.f64 x)) (-.f64 (cos.f64 x) #s(literal 1 binary64)))
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(*.f64 #s(literal -1 binary64) (tan.f64 (/.f64 (neg.f64 x) #s(literal 2 binary64))))
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(*.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sin.f64 x)))
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(.f64 (tan.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(.f64 (sin.f64 x) (/.f64 (sin.f64 x) (.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x))))
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 (sin.f64 x) #s(literal -1 binary64)))
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(/.f64 (/.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 x))) (sin.f64 x)) (sin.f64 x))
(/.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (sin.f64 x))
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(/.f64 (-.f64 (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/57600 binary64) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64)))) (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/57600 binary64) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))))) (.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/24 binary64))) (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/24 binary64))))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/57600 binary64) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))) (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/57600 binary64) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/24 binary64))) #s(literal 3 binary64))) (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/57600 binary64) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64)))) (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/57600 binary64) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64)))) (fma.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/24 binary64))) (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/57600 binary64) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64)))) (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (*.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64)))) (neg.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/5760 binary64) #s(literal 1/576 binary64))))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 4 binary64)) #s(literal 1/331776 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64)) (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal -1/24 binary64))))
(/.f64 (.f64 (fma.f64 #s(literal 1/191102976000000 binary64) (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64)) #s(literal -1/191102976 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/33177600 binary64) #s(literal 1/331776 binary64)) (pow.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 4 binary64))) (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal -1/24 binary64))))
(/.f64 (.f64 (fma.f64 #s(literal 1/191102976000000 binary64) (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64)) #s(literal -1/191102976 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/13824 binary64)) (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/5760 binary64) #s(literal 1/576 binary64)))))
(/.f64 (.f64 (fma.f64 #s(literal 1/2641807540224000000000 binary64) (pow.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 3 binary64)) #s(literal 1/2641807540224 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/191102976000000 binary64) (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64)) (-.f64 #s(literal 1/191102976 binary64) (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/191102976000 binary64)))) (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal -1/5760 binary64) #s(literal 1/576 binary64)))))
(/.f64 (.f64 (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64)))
(/.f64 (.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal -1/5760 binary64) #s(literal 1/576 binary64))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))) (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64)) #s(literal 1/576 binary64))) (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64)) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 4 binary64)) #s(literal 1/331776 binary64)) (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64)) (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64))))
(/.f64 (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (*.f64 x x))))
(/.f64 (fma.f64 #s(literal 1/191102976000000 binary64) (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64)) #s(literal -1/191102976 binary64)) (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64)) (+.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/33177600 binary64) #s(literal 1/331776 binary64)) (pow.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 4 binary64)))))
(/.f64 (fma.f64 #s(literal 1/191102976000000 binary64) (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64)) #s(literal -1/191102976 binary64)) (.f64 (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal -1/5760 binary64) #s(literal 1/576 binary64))) (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/13824 binary64))))
(/.f64 (fma.f64 #s(literal 1/2641807540224000000000 binary64) (pow.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 3 binary64)) #s(literal 1/2641807540224 binary64)) (.f64 (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal -1/5760 binary64) #s(literal 1/576 binary64))) (fma.f64 #s(literal 1/191102976000000 binary64) (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64)) (-.f64 #s(literal 1/191102976 binary64) (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/191102976000 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64))) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64))) (neg.f64 (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/5760 binary64) #s(literal 1/576 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(/.f64 (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64)) (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal -1/24 binary64)))
(/.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/5760 binary64) #s(literal 1/576 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (.f64 x x))) (-.f64 #s(literal 1/576 binary64) (*.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64))) (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal -1/24 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64))) (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/5760 binary64) #s(literal 1/576 binary64)))))
(neg.f64 (/.f64 (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64)) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))))
(neg.f64 (/.f64 (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/13824 binary64)) (neg.f64 (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/5760 binary64) #s(literal 1/576 binary64))))))
(fma.f64 (/.f64 (.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/13824000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/13824 binary64))) (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/5760 binary64) (.f64 x x) #s(literal 1/576 binary64))) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 (/.f64 (.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/576 binary64))) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 (.f64 (.f64 #s(literal 1/57600 binary64) (.f64 x x)) x) (/.f64 x (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/240 binary64)) (/.f64 #s(literal 1/240 binary64) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 (.f64 #s(literal 1/57600 binary64) (.f64 x x)) (/.f64 (.f64 x x) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 #s(literal 1/57600 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/57600 binary64) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 (.f64 #s(literal 1/240 binary64) x) (/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/240 binary64)) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 (*.f64 #s(literal 1/240 binary64) x) x #s(literal 1/24 binary64))
(fma.f64 (.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 #s(literal 1/240 binary64) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/240 binary64)) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/57600 binary64) (.f64 x x)) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64))) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))
(fma.f64 x (*.f64 #s(literal 1/240 binary64) x) #s(literal 1/24 binary64))
(-.f64 (/.f64 #s(literal 1/576 binary64) (-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (.f64 x x)))) (/.f64 (.f64 #s(literal 1/57600 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (*.f64 x x)))))
(-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/57600 binary64) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64)))) (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))))
(+.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/57600 binary64) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal -1/24 binary64)))) (neg.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(+.f64 (.f64 #s(literal 1/240 binary64) (.f64 x x)) #s(literal 1/24 binary64))
(+.f64 #s(literal 1/24 binary64) (.f64 #s(literal 1/240 binary64) (.f64 x x)))
#s(literal 1 binary64)

eval132.0ms (2.4%)

Memory: 6.7MiB live, 159.2MiB allocated
Compiler: Compiled 14 507 to 1 967 computations (86.4% saved)

prune26.0ms (0.5%)

Memory

-6.4MiB live, 64.3MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	700	2	702
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	701	6	707

Accuracy

100.0%

Counts

707 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
▶	49.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 x #s(literal 1/2 binary64))))
✓	49.2%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
✓	49.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	49.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))
▶	7.8%	#s(literal 1 binary64)

Compiler

Compiled 43 to 34 computations (20.9% saved)

simplify33.0ms (0.6%)

Memory

-4.5MiB live, 45.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

266×	`lower-fma.f32`
264×	`lower-fma.f64`
178×	`lower-*.f32`
172×	`lower-*.f64`
120×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	41
0	18	38
1	36	36
2	58	36
3	73	36
4	94	36
5	118	36
6	151	36
7	225	36
8	349	36
9	555	36
10	597	36
11	600	36
12	608	36
13	614	36
14	618	36
15	625	36
16	658	36
17	676	36
18	678	36
0	678	34

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize78.0ms (1.4%)

Memory

13.8MiB live, 121.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x #s(literal 1/2 binary64))
accuracy	0.08203125	(fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 x #s(literal 1/2 binary64)))
accuracy	0.38671875	(*.f64 #s(literal 1/24 binary64) x)
accuracy	32.41859051573066	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 x #s(literal 1/2 binary64))))

Samples

26.0ms	134×	0	valid
26.0ms	63×	2	valid
11.0ms	23×	3	valid
6.0ms	36×	1	valid

Compiler

Compiled 33 to 15 computations (54.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-cos: 23.0ms (41.6% of total)

ival-mult: 11.0ms (19.9% of total)

adjust: 6.0ms (10.8% of total)

ival-sin: 5.0ms (9% of total)

ival-div: 3.0ms (5.4% of total)

ival-sub: 3.0ms (5.4% of total)

const: 3.0ms (5.4% of total)

ival-add: 1.0ms (1.8% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

12.5MiB live, 12.5MiB allocated

Counts

5 → 60

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

inf

((+ (* (* x x) (* 1/24 x)) (* x 1/2)) (/ (- 1 (cos x)) (sin x)) (* x x) (* 1/24 x) (* x 1/2))

1.0ms

-inf

((+ (* (* x x) (* 1/24 x)) (* x 1/2)) (/ (- 1 (cos x)) (sin x)) (* x x) (* 1/24 x) (* x 1/2))

1.0ms

((+ (* (* x x) (* 1/24 x)) (* x 1/2)) (/ (- 1 (cos x)) (sin x)) (* x x) (* 1/24 x) (* x 1/2))

simplify187.0ms (3.4%)

Memory

10.8MiB live, 131.7MiB allocated

Algorithm

1×	egg-herbie

Rules

6 696×	`lower-fma.f64`
6 696×	`lower-fma.f32`
5 198×	`lower-*.f64`
5 198×	`lower-*.f32`
2 104×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	282
1	106	282
2	260	282
3	593	282
4	978	282
5	1680	282
6	3001	282
7	4194	282
8	5162	282
9	5857	282
10	6736	282
11	7161	282
12	7944	282
0	8070	267

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

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

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

rewrite257.0ms (4.6%)

Memory

-25.5MiB live, 254.1MiB allocated

Rules

6 274×	`lower-fma.f32`
6 272×	`lower-fma.f64`
4 796×	`lower-*.f32`
4 790×	`lower-*.f64`
2 458×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	37
0	18	34
1	68	32
2	474	32
3	4836	31
0	8786	29

Stop Event

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

Counts

5 → 135

Calls

Call 1

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

Outputs
(.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 x x) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64) (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))))) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (fma.f64 #s(literal 1/4 binary64) x (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))))
(.f64 (/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))) (-.f64 (pow.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 2 binary64)) (pow.f64 (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)))))))
(.f64 (/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))) (fma.f64 #s(literal 1/191102976 binary64) (pow.f64 x #s(literal 18 binary64)) (pow.f64 (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))) #s(literal 3 binary64)))) (fma.f64 (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))) (-.f64 (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 2 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 x x) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 #s(literal -1/4 binary64) (.f64 x x) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))))) (.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x))
(.f64 (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) x) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))
(.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x)
(.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal 1/2 binary64) x))) (fma.f64 #s(literal -1/4 binary64) (.f64 x x) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))))
(.f64 (pow.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) #s(literal -1 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))))
(.f64 (neg.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 x x) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))))) (pow.f64 (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64)))
(.f64 (neg.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)))) (pow.f64 (neg.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))))) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 x x) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal 1/2 binary64) x))))
(.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64)))))))
(.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) (pow.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) #s(literal -1 binary64))))
(.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))) (pow.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x))
(.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x) (.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x)))
(.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 1/2 binary64) x)))))
(.f64 x (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)))) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 x x) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))) x) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal 1/2 binary64) x)))) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 x x))))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/191102976 binary64) (pow.f64 x #s(literal 18 binary64))) (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal 1/2 binary64) x)))) (+.f64 (fma.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 4 binary64))) (pow.f64 (*.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 2 binary64))))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/191102976 binary64) (pow.f64 x #s(literal 18 binary64))) (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) #s(literal -1 binary64))) (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/13824 binary64) (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (.f64 (fma.f64 (pow.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 3 binary64)) #s(literal 1/2641807540224 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 9 binary64))) (pow.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))) #s(literal -1 binary64))) (fma.f64 #s(literal 1/191102976 binary64) (pow.f64 x #s(literal 18 binary64)) (-.f64 (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/13824 binary64)) #s(literal 1/8 binary64)))))
(/.f64 (.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))) #s(literal 1 binary64)) (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))))
(/.f64 (-.f64 (pow.f64 (.f64 x (/.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) #s(literal 2 binary64)) (pow.f64 (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) #s(literal 2 binary64))) (fma.f64 x (/.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))) (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(/.f64 (-.f64 (pow.f64 (.f64 x (/.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 x (/.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) #s(literal 2 binary64)) (.f64 (.f64 x (/.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 x x) (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)))))) (neg.f64 (fma.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 1/2 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/13824 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64)) (.f64 x (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/48 binary64))))))))
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(fma.f64 x (.f64 (.f64 #s(literal 1/24 binary64) x) x) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))) (/.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 3 binary64))))))
(-.f64 (.f64 x (/.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))))
(+.f64 (.f64 x (/.f64 (.f64 #s(literal 1/576 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)))) (neg.f64 (.f64 x (/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))))))
(+.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)) (.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x) #s(literal -1 binary64))) #s(literal -1 binary64)))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal 1/2 binary64)) x))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 x #s(literal 1/24 binary64))
(*.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) x)
(*.f64 (neg.f64 x) #s(literal -1/2 binary64))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x (exp.f64 (log.f64 #s(literal 1/2 binary64))))
(*.f64 x #s(literal 1/2 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(/.f64 (exp.f64 (log.f64 (neg.f64 x))) (exp.f64 (log.f64 #s(literal -2 binary64))))
(/.f64 (neg.f64 (neg.f64 x)) #s(literal 2 binary64))
(/.f64 (neg.f64 x) #s(literal -2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) x)))
(/.f64 #s(literal 1 binary64) (exp.f64 (log.f64 (/.f64 #s(literal 2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(/.f64 x (exp.f64 (log.f64 #s(literal 2 binary64))))
(/.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 #s(literal -1/2 binary64) x))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) x)))

eval22.0ms (0.4%)

Memory: 25.8MiB live, 25.8MiB allocated
Compiler: Compiled 3 848 to 543 computations (85.9% saved)

prune26.0ms (0.5%)

Memory

-21.2MiB live, 16.9MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	195	6	201

Accuracy

100.0%

Counts

201 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
✓	49.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 x #s(literal 1/2 binary64))))
✓	49.2%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
✓	49.3%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	49.7%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))
✓	7.8%	#s(literal 1 binary64)

Compiler

Compiled 96 to 60 computations (37.5% saved)

regimes9.0ms (0.2%)

Memory

19.8MiB live, 19.8MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	x
4.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 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 8 to 7 computations (12.5% saved)

regimes18.0ms (0.3%)

Memory

-6.0MiB live, 31.3MiB allocated

Counts

6 → 2

Calls

Call 1

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

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

Calls

2 calls:

9.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
8.0ms	x

Results

Accuracy	Segments	Branch
53.4%	2	`x`
53.2%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes7.0ms (0.1%)

Memory

14.3MiB live, 14.3MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
53.4%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes12.0ms (0.2%)

Memory

-31.5MiB live, 10.8MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

#s(literal 1 binary64)

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

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

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

Calls

1 calls:

11.0ms

Results

Accuracy	Segments	Branch
53.4%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes6.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
53.2%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes5.0ms (0.1%)

Memory

11.2MiB live, 11.2MiB 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:

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

Results

Accuracy	Segments	Branch
7.8%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
7.8%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

bsearch20.0ms (0.4%)

Memory

-11.6MiB live, 25.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	0.0004687394080849533	14.308298960345043

Samples

11.0ms

128×

valid

Compiler

Compiled 130 to 114 computations (12.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-cos: 4.0ms (45.3% of total)

ival-sin: 4.0ms (45.3% of total)

ival-sub: 1.0ms (11.3% of total)

ival-div: 1.0ms (11.3% of total)

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.0004687394080849533	14.308298960345043

Compiler

Compiled 106 to 106 computations (0% saved)

bsearch1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.0004687394080849533	14.308298960345043

Compiler

Compiled 90 to 98 computations (-8.9% saved)

bsearch1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.0004687394080849533	14.308298960345043

Compiler

Compiled 50 to 74 computations (-48% saved)

simplify23.0ms (0.4%)

Memory

-0.0MiB live, 38.7MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	91
1	37	91

Stop Event

1×

saturated

Calls

Call 1

Inputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
#s(literal 1 binary64)

Outputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 6980579422424269/2251799813685248 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness739.0ms (13.3%)

Memory

-14.3MiB live, 354.2MiB allocated

Rules

19 148×	`lower-fma.f64`
19 148×	`lower-fma.f32`
6 880×	`lower-fma.f32`
6 874×	`lower-fma.f64`
4 964×	`lower-*.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	108
0	36	97
1	128	97
2	768	97
3	7671	97
0	8254	97
0	6	15
0	10	12
1	39	12
2	245	12
3	2355	11
0	8885	11
0	79	286
1	224	286
2	555	280
3	1661	280
4	3000	280
5	4254	280
6	4606	280
7	5336	280
8	6824	280
0	8376	256

Stop Event

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

Compiler

Compiled 135 to 84 computations (37.8% saved)

preprocess89.0ms (1.6%)

Memory: 10.0MiB live, 164.8MiB allocated
Remove: (negabs x)
Compiler: Compiled 164 to 86 computations (47.6% 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	23	124
0	36	113
1	61	113
2	94	113
3	158	113
4	257	113
5	287	113
6	323	113
7	397	113
8	520	113
9	727	113
10	769	113
11	772	113
12	780	113
13	785	113
14	789	113
15	796	113
16	876	113
17	956	113
18	960	113
0	960	113

Iter	Nodes	Cost
0	13	41
0	18	38
1	36	36
2	58	36
3	73	36
4	94	36
5	118	36
6	151	36
7	225	36
8	349	36
9	555	36
10	597	36
11	600	36
12	608	36
13	614	36
14	618	36
15	625	36
16	658	36
17	676	36
18	678	36
0	678	34

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	23	124
0	36	113
1	61	113
2	94	113
3	158	113
4	257	113
5	287	113
6	323	113
7	397	113
8	520	113
9	727	113
10	769	113
11	772	113
12	780	113
13	785	113
14	789	113
15	796	113
16	876	113
17	956	113
18	960	113
0	960	113

Iter	Nodes	Cost
0	13	41
0	18	38
1	36	36
2	58	36
3	73	36
4	94	36
5	118	36
6	151	36
7	225	36
8	349	36
9	555	36
10	597	36
11	600	36
12	608	36
13	614	36
14	618	36
15	625	36
16	658	36
17	676	36
18	678	36
0	678	34

start0.0ms (0%)

analyze112.0ms (2%)

sample2.3s (41.2%)

explain173.0ms (3.1%)

preprocess81.0ms (1.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify23.0ms (0.4%)

localize58.0ms (1%)

series3.0ms (0.1%)

simplify203.0ms (3.7%)

rewrite207.0ms (3.7%)

eval91.0ms (1.6%)

prune17.0ms (0.3%)

simplify38.0ms (0.7%)

localize132.0ms (2.4%)

series33.0ms (0.6%)

simplify176.0ms (3.2%)

rewrite229.0ms (4.1%)

eval132.0ms (2.4%)

prune26.0ms (0.5%)

simplify33.0ms (0.6%)

localize78.0ms (1.4%)

series6.0ms (0.1%)

simplify187.0ms (3.4%)

rewrite257.0ms (4.6%)

eval22.0ms (0.4%)

prune26.0ms (0.5%)

regimes9.0ms (0.2%)

regimes18.0ms (0.3%)

regimes7.0ms (0.1%)

regimes12.0ms (0.2%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

bsearch20.0ms (0.4%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

simplify23.0ms (0.4%)

soundness739.0ms (13.3%)

preprocess89.0ms (1.6%)

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

Iter	Nodes	Cost
0	23	124
0	36	113
1	61	113
2	94	113
3	158	113
4	257	113
5	287	113
6	323	113
7	397	113
8	520	113
9	727	113
10	769	113
11	772	113
12	780	113
13	785	113
14	789	113
15	796	113
16	876	113
17	956	113
18	960	113
0	960	113

Iter	Nodes	Cost
0	13	41
0	18	38
1	36	36
2	58	36
3	73	36
4	94	36
5	118	36
6	151	36
7	225	36
8	349	36
9	555	36
10	597	36
11	600	36
12	608	36
13	614	36
14	618	36
15	625	36
16	658	36
17	676	36
18	678	36
0	678	34