Metrics for tanhf (example 3.4)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze113.0ms (2.1%)

Memory

-12.9MiB live, 140.6MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample1.8s (33.8%)

Memory

75.3MiB live, 1 672.6MiB allocated

Samples

652.0ms	2 182×	2	valid
470.0ms	4 257×	0	valid
235.0ms	602×	3	valid
158.0ms	1 213×	1	valid
2.0ms	2×	4	valid

Precisions

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

ival-cos: 768.0ms (60.3% of total)

ival-sin: 187.0ms (14.7% of total)

adjust: 109.0ms (8.6% of total)

ival-div: 105.0ms (8.2% of total)

ival-sub: 89.0ms (7% of total)

ival-true: 7.0ms (0.5% of total)

exact: 6.0ms (0.5% of total)

ival-assert: 4.0ms (0.3% of total)

Bogosity

explain265.0ms (5%)

Memory

-5.8MiB live, 153.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
72	152	(-1.0948402402852244e+145)	0	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
72	0	-	72	(-1.9189812812229288e-268)	`(/.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	224	1

Confusion

	Predicted +	Predicted -
+	145	0
-	79	32

Precision

0.6473214285714286

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	145	0	0
-	79	1	31

Precision?

0.6444444444444445

Recall?

1.0

Freqs

test

number	freq
0	32
1	224

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

85.0ms	154×	2	valid
35.0ms	46×	3	valid
28.0ms	252×	0	valid
7.0ms	60×	1	valid

Compiler

Compiled 96 to 46 computations (52.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 94.0ms

ival-cos: 62.0ms (65.6% of total)

ival-sin: 11.0ms (11.6% of total)

adjust: 8.0ms (8.5% of total)

ival-div: 7.0ms (7.4% of total)

ival-sub: 6.0ms (6.4% of total)

ival-true: 1.0ms (1.1% of total)

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

exact: 0.0ms (0% of total)

preprocess44.0ms (0.8%)

Memory

-2.3MiB live, 35.6MiB allocated

Algorithm

1×	egg-herbie

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

prune1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.5%	(/.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

10.9MiB live, 10.9MiB 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))

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)

localize108.0ms (2%)

Memory

-13.8MiB live, 61.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(sin.f64 x)
accuracy	0	(cos.f64 x)
accuracy	14.702661555645198	(-.f64 #s(literal 1 binary64) (cos.f64 x))
accuracy	16.867090233349177	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Samples

58.0ms	126×	0	valid
24.0ms	77×	2	valid
8.0ms	23×	3	valid
3.0ms	30×	1	valid

Compiler

Compiled 36 to 14 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 85.0ms

ival-sin: 51.0ms (60.2% of total)

ival-cos: 22.0ms (26% of total)

adjust: 4.0ms (4.7% of total)

ival-div: 3.0ms (3.5% of total)

ival-sub: 3.0ms (3.5% 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

4.4MiB live, 4.4MiB 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))

simplify227.0ms (4.3%)

Memory

-4.4MiB live, 155.9MiB allocated

Algorithm

1×	egg-herbie

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)

rewrite148.0ms (2.8%)

Memory

16.9MiB live, 208.6MiB allocated

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
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval235.0ms (4.4%)

Memory: 10.3MiB live, 129.2MiB allocated
Compiler: Compiled 13 164 to 1 644 computations (87.5% saved)

prune14.0ms (0.3%)

Memory

0.5MiB live, 36.8MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	658	4	662
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	659	4	663

Accuracy

100.0%

Counts

663 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.9%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
▶	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
▶	53.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
▶	53.2%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))

Compiler

Compiled 20 to 19 computations (5% saved)

simplify27.0ms (0.5%)

Memory

-26.2MiB live, 12.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Score
cost-diff	6464	(pow.f64 #s(literal 1 binary64) #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))
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)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	66
0	26	58
1	42	58
2	57	58
3	74	58
4	98	58
5	122	58
6	155	58
7	229	58
8	352	58
9	562	58
10	604	58
11	607	58
12	615	58
13	620	58
14	624	58
15	631	58
16	664	58
17	688	58
18	690	58
0	690	58

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#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)
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
#s(literal 1 binary64)
#s(literal -1/2 binary64)

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

localize101.0ms (1.9%)

Memory

-8.7MiB live, 115.6MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 #s(literal 1 binary64) #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))
accuracy	0	(*.f64 x x)
accuracy	0.04296875	(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
accuracy	0.09375	(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
accuracy	30.050614278630103	#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	29.940780754014934	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))

Samples

34.0ms	77×	2	valid
31.0ms	126×	0	valid
12.0ms	23×	3	valid
7.0ms	30×	1	valid

Compiler

Compiled 109 to 33 computations (69.7% saved)

Precisions

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

ival-cos: 24.0ms (35.7% of total)

adjust: 8.0ms (11.9% of total)

ival-mult: 7.0ms (10.4% of total)

ival-tan: 6.0ms (8.9% of total)

ival-sin: 5.0ms (7.4% of total)

const: 4.0ms (5.9% of total)

ival-add: 4.0ms (5.9% of total)

ival-div: 3.0ms (4.5% of total)

ival-sub: 3.0ms (4.5% of total)

ival-pow: 2.0ms (3% of total)

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

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

exact: 0.0ms (0% of total)

series7.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB allocated

Counts

9 → 96

Calls

Call 1

Inputs
#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 (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 (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 #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 (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 (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 (/ (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 (/ (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 (/ (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 (/ (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>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((/ (- 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) (tan (* 1/2 x)) (* 1/2 x) (pow 1 -1/2))
2.0ms	x	@	-inf	((/ (- 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) (tan (* 1/2 x)) (* 1/2 x) (pow 1 -1/2))
1.0ms	x	@	0	((/ (- 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) (tan (* 1/2 x)) (* 1/2 x) (pow 1 -1/2))

Time

Variable

Point

Expression

2.0ms

inf

((/ (- 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) (tan (* 1/2 x)) (* 1/2 x) (pow 1 -1/2))

2.0ms

-inf

((/ (- 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) (tan (* 1/2 x)) (* 1/2 x) (pow 1 -1/2))

1.0ms

((/ (- 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) (tan (* 1/2 x)) (* 1/2 x) (pow 1 -1/2))

simplify176.0ms (3.3%)

Memory

31.4MiB live, 106.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	556
1	114	556
2	285	556
3	660	556
4	1236	556
5	2808	556
6	3651	556
7	4498	556
8	4915	556
9	5453	556
10	6084	556
11	6835	556
12	7410	556
0	8145	520

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

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)
(* 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)
(* 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)
(/ (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)
(/ (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)

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

rewrite345.0ms (6.5%)

Memory

-13.2MiB live, 147.0MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	18	57
0	26	52
1	85	52
2	454	52
3	3931	40
0	11557	40

Stop Event

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

Counts

9 → 178

Calls

Call 1

Inputs
#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)
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval64.0ms (1.2%)

Memory: -1.4MiB live, 50.2MiB allocated
Compiler: Compiled 4 181 to 743 computations (82.2% saved)

prune15.0ms (0.3%)

Memory

-9.5MiB live, 26.4MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	272	2	274
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	273	5	278

Accuracy

100.0%

Counts

278 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
▶	53.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
✓	53.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	53.2%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))
▶	6.9%	#s(literal 1 binary64)

Compiler

Compiled 29 to 25 computations (13.8% saved)

simplify26.0ms (0.5%)

Memory

14.6MiB live, 14.6MiB 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 #s(literal 1/2 binary64) x)))
cost-diff	320	(fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))

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	348	36
9	554	36
10	596	36
11	599	36
12	607	36
13	613	36
14	617	36
15	624	36
16	657	36
17	680	36
18	682	36
0	682	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 #s(literal 1/2 binary64) x)))
(fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 x x)
x
(*.f64 #s(literal 1/24 binary64) x)
#s(literal 1/24 binary64)
(*.f64 #s(literal 1/2 binary64) x)
#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 #s(literal 1/2 binary64) x)))
#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 #s(literal 1/2 binary64) x))
(.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 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)

localize90.0ms (1.7%)

Memory

-19.8MiB live, 99.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.05078125	(fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))
accuracy	0.359375	(*.f64 #s(literal 1/24 binary64) x)
accuracy	30.050614278630103	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))

Samples

33.0ms	77×	2	valid
31.0ms	126×	0	valid
10.0ms	22×	3	valid
5.0ms	30×	1	valid
1.0ms	1×	5	exit

Compiler

Compiled 67 to 24 computations (64.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 61.0ms

ival-cos: 28.0ms (45.6% of total)

ival-mult: 11.0ms (17.9% of total)

adjust: 6.0ms (9.8% of total)

ival-sin: 5.0ms (8.2% of total)

const: 4.0ms (6.5% of total)

ival-div: 3.0ms (4.9% of total)

ival-sub: 3.0ms (4.9% of total)

ival-add: 1.0ms (1.6% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

9.3MiB live, 9.3MiB allocated

Counts

5 → 60

Calls

Call 1

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

-inf

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

1.0ms

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

simplify191.0ms (3.6%)

Memory

24.6MiB live, 132.2MiB allocated

Algorithm

1×	egg-herbie

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))

rewrite200.0ms (3.8%)

Memory

-36.5MiB live, 222.8MiB allocated

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 #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 #s(literal 1/2 binary64) x)))
(*.f64 x x)
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval33.0ms (0.6%)

Memory: 21.1MiB live, 87.0MiB allocated
Compiler: Compiled 3 848 to 543 computations (85.9% saved)

prune18.0ms (0.3%)

Memory

-25.5MiB live, 26.2MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	195	5	200

Accuracy

100.0%

Counts

200 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
✓	53.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
✓	53.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	53.2%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))
✓	6.9%	#s(literal 1 binary64)

Compiler

Compiled 68 to 46 computations (32.4% saved)

regimes6.0ms (0.1%)

Memory

16.6MiB live, 16.6MiB allocated

Counts

7 → 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 #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:

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

Results

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes6.0ms (0.1%)

Memory

-25.0MiB live, 14.3MiB allocated

Counts

5 → 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 #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)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
#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
56.2%	2	`x`
56.0%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes2.0ms (0%)

Memory

8.7MiB live, 8.7MiB 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:

2.0ms

Results

Accuracy	Segments	Branch
56.2%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes4.0ms (0.1%)

Memory

10.1MiB live, 10.1MiB 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

2 calls:

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

Results

Accuracy	Segments	Branch
55.8%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
55.9%	2	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0.1%)

Memory

7.2MiB live, 7.2MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)

Outputs
#s(literal 1 binary64)

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
6.9%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
6.9%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

bsearch154.0ms (2.9%)

Memory

9.3MiB live, 48.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
153.0ms	2.170259495541874e-5	50.44192046136823

Samples

147.0ms

144×

valid

Compiler

Compiled 118 to 118 computations (0% saved)

Precisions

Click to see histograms. Total time spent on operations: 144.0ms

ival-sin: 138.0ms (95.9% of total)

ival-cos: 4.0ms (2.8% of total)

ival-sub: 1.0ms (0.7% of total)

ival-div: 1.0ms (0.7% of total)

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

exact: 0.0ms (0% of total)

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

bsearch10.0ms (0.2%)

Memory

-34.5MiB live, 5.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	2.170259495541874e-5	50.44192046136823

Compiler

Compiled 100 to 109 computations (-9% saved)

bsearch10.0ms (0.2%)

Memory

34.7MiB live, 34.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
9.0ms	2.170259495541874e-5	50.44192046136823

Samples

6.0ms

64×

valid

Compiler

Compiled 55 to 82 computations (-49.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-cos: 2.0ms (42.6% of total)

ival-sin: 2.0ms (42.6% of total)

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

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

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

exact: 0.0ms (0% of total)

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

simplify25.0ms (0.5%)

Memory

-30.5MiB live, 48.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	65
1	32	65

Stop Event

1×

saturated

Calls

Call 1

Inputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 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 6530219459687219/4503599627370496 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 3602879701896397/1125899906842624 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 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 3602879701896397/1125899906842624 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 6530219459687219/4503599627370496 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness714.0ms (13.5%)

Memory

2.5MiB live, 341.4MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	18	57
0	26	52
1	85	52
2	454	52
3	3931	40
0	11557	40
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
0	6	15
0	10	12
1	39	12
2	245	12
3	2355	11
0	8885	11

Stop Event

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

Compiler

Compiled 127 to 88 computations (30.7% saved)

preprocess88.0ms (1.7%)

Memory: -13.2MiB live, 102.8MiB allocated
Remove: (negabs x)
Compiler: Compiled 126 to 78 computations (38.1% 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	18	66
0	26	58
1	42	58
2	57	58
3	74	58
4	98	58
5	122	58
6	155	58
7	229	58
8	352	58
9	562	58
10	604	58
11	607	58
12	615	58
13	620	58
14	624	58
15	631	58
16	664	58
17	688	58
18	690	58
0	690	58

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	348	36
9	554	36
10	596	36
11	599	36
12	607	36
13	613	36
14	617	36
15	624	36
16	657	36
17	680	36
18	682	36
0	682	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	18	66
0	26	58
1	42	58
2	57	58
3	74	58
4	98	58
5	122	58
6	155	58
7	229	58
8	352	58
9	562	58
10	604	58
11	607	58
12	615	58
13	620	58
14	624	58
15	631	58
16	664	58
17	688	58
18	690	58
0	690	58

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	348	36
9	554	36
10	596	36
11	599	36
12	607	36
13	613	36
14	617	36
15	624	36
16	657	36
17	680	36
18	682	36
0	682	34

start0.0ms (0%)

analyze113.0ms (2.1%)

sample1.8s (33.8%)

explain265.0ms (5%)

preprocess44.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify23.0ms (0.4%)

localize108.0ms (2%)

series3.0ms (0.1%)

simplify227.0ms (4.3%)

rewrite148.0ms (2.8%)

eval235.0ms (4.4%)

prune14.0ms (0.3%)

simplify27.0ms (0.5%)

localize101.0ms (1.9%)

series7.0ms (0.1%)

simplify176.0ms (3.3%)

rewrite345.0ms (6.5%)

eval64.0ms (1.2%)

prune15.0ms (0.3%)

simplify26.0ms (0.5%)

localize90.0ms (1.7%)

series5.0ms (0.1%)

simplify191.0ms (3.6%)

rewrite200.0ms (3.8%)

eval33.0ms (0.6%)

prune18.0ms (0.3%)

regimes6.0ms (0.1%)

regimes6.0ms (0.1%)

regimes2.0ms (0%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch154.0ms (2.9%)

bsearch10.0ms (0.2%)

bsearch10.0ms (0.2%)

simplify25.0ms (0.5%)

soundness714.0ms (13.5%)

preprocess88.0ms (1.7%)

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	18	66
0	26	58
1	42	58
2	57	58
3	74	58
4	98	58
5	122	58
6	155	58
7	229	58
8	352	58
9	562	58
10	604	58
11	607	58
12	615	58
13	620	58
14	624	58
15	631	58
16	664	58
17	688	58
18	690	58
0	690	58

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	348	36
9	554	36
10	596	36
11	599	36
12	607	36
13	613	36
14	617	36
15	624	36
16	657	36
17	680	36
18	682	36
0	682	34