Metrics for cos2 (problem 3.4.1)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze2.0ms (0%)

Memory

1.9MiB live, 1.9MiB 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
50%	50%	50%	0%	0%	0%	0%	2
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 10 to 8 computations (20% saved)

sample2.0s (23.1%)

Memory

64.9MiB live, 2 019.7MiB allocated

Samples

768.0ms	2 255×	2	valid
446.0ms	4 179×	0	valid
318.0ms	601×	3	valid
123.0ms	1 221×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 1.4s

ival-cos: 1.0s (71.4% of total)

ival-div: 144.0ms (10.2% of total)

adjust: 94.0ms (6.7% of total)

ival-sub: 94.0ms (6.7% of total)

ival-mult: 55.0ms (3.9% of total)

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

exact: 5.0ms (0.4% of total)

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

Bogosity

explain134.0ms (1.6%)

Memory

4.6MiB live, 160.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
69	-	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
68	-	-	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(cos.f64 x)`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	69	7
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`	u/u	63	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	63
↳	`(*.f64 x x)`	underflow	63
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`	n/o	5	0
↳	`(*.f64 x x)`	overflow	75

Confusion

	Predicted +	Predicted -
+	135	0
-	2	119

Precision

0.9854014598540146

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	135	0	0
-	2	6	113

Precision?

0.9440559440559441

Recall?

1.0

Freqs

test

number	freq
0	119
1	137

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

40.0ms	138×	2	valid
23.0ms	256×	0	valid
15.0ms	40×	3	valid
10.0ms	78×	1	valid

Compiler

Compiled 50 to 22 computations (56% saved)

Precisions

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

ival-cos: 46.0ms (67.5% of total)

ival-div: 6.0ms (8.8% of total)

adjust: 6.0ms (8.8% of total)

ival-sub: 5.0ms (7.3% of total)

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

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

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

exact: 0.0ms (0% of total)

preprocess54.0ms (0.6%)

Memory

-22.6MiB live, 52.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	32	17
2	102	16
3	299	16
4	757	16
5	1185	16
6	1294	16
7	1310	16
0	6	8
0	10	8
1	19	8
2	30	8
3	46	8
4	82	8
5	131	8
6	188	8
7	323	8
8	621	8
9	1027	8
10	1138	8
0	1138	8

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)) (*.f64 x x))

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

Symmetry

(abs x)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.7%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify22.0ms (0.3%)

Memory

27.6MiB live, 27.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	-384	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(cos.f64 x)
cost-diff	0	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
0	10	19
1	19	19
2	30	19
3	46	19
4	82	19
5	131	19
6	188	19
7	323	19
8	621	19
9	1027	19
10	1138	19
0	1138	19

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize57.0ms (0.7%)

Memory

-8.7MiB live, 69.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0	(cos.f64 x)
accuracy	15.67212506232622	(-.f64 #s(literal 1 binary64) (cos.f64 x))
accuracy	15.805048619395071	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Samples

25.0ms	69×	2	valid
10.0ms	128×	0	valid
10.0ms	20×	3	valid
4.0ms	39×	1	valid

Compiler

Compiled 21 to 8 computations (61.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-cos: 26.0ms (63.5% of total)

ival-div: 7.0ms (17.1% of total)

adjust: 3.0ms (7.3% of total)

ival-sub: 3.0ms (7.3% of total)

ival-mult: 2.0ms (4.9% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0%)

Memory

4.0MiB live, 4.0MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

3 calls:

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

simplify301.0ms (3.5%)

Memory

-37.2MiB live, 168.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	284
1	105	284
2	258	284
3	609	284
4	1290	284
5	1996	284
6	2309	284
7	3163	284
8	4640	284
9	6288	284
10	7165	284
11	7380	284
12	7398	284
13	7400	284
14	7806	284
0	8015	266

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1
(+ 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)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))

Outputs
(* 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 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/720 binary64) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 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
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(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))
(- 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)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)

rewrite155.0ms (1.8%)

Memory

25.7MiB live, 174.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
0	10	17
1	40	17
2	268	17
3	2810	17
0	9656	17

Stop Event

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

Counts

4 → 629

Calls

Call 1

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

Outputs
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eval77.0ms (0.9%)

Memory: -2.0MiB live, 151.4MiB allocated
Compiler: Compiled 13 903 to 1 656 computations (88.1% saved)

prune21.0ms (0.3%)

Memory

23.1MiB live, 61.8MiB allocated

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	663	14	677
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	663	15	678

Accuracy

100.0%

Counts

678 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	21.1%	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (*.f64 x x))
	51.3%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	51.2%	(/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 (/.f64 (cos.f64 x) x))) (neg.f64 x))
	13.9%	(/.f64 (-.f64 (neg.f64 x) (.f64 (.f64 (neg.f64 x) x) (/.f64 (cos.f64 x) x))) (.f64 (.f64 (neg.f64 x) x) x))
✓	49.7%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
	30.4%	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
	50.5%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
	50.5%	(*.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
▶	51.3%	(*.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
▶	75.1%	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
	11.8%	(.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (pow.f64 x #s(literal -4 binary64)))
	51.1%	#s(approx (/ (- 1 (cos x)) (* x x)) (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)))
▶	51.4%	#s(approx (/ (- 1 (cos x)) (* x x)) (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)))
	51.0%	#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
▶	52.1%	#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))

Compiler

Compiled 320 to 210 computations (34.4% saved)

simplify125.0ms (1.5%)

Memory

15.2MiB live, 128.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (*.f64 x x))
cost-diff	320	(-.f64 (.f64 x x) (.f64 (*.f64 x x) (cos.f64 x)))
cost-diff	1664	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x))
cost-diff	0	(cos.f64 x)
cost-diff	0	(-.f64 (cos.f64 x) #s(literal 1 binary64))
cost-diff	0	(/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x)
cost-diff	704	(*.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
cost-diff	0	(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))
cost-diff	0	#s(approx (/ (- 1 (cos x)) (* x x)) (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)))
cost-diff	0	#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
cost-diff	0	(tan.f64 (/.f64 x #s(literal 2 binary64)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(sin.f64 x)
cost-diff	384	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	168
0	49	160
1	98	150
2	203	146
3	525	144
4	1501	144
5	3053	144
6	4759	144
7	6154	144
8	7489	144
0	8024	144

Stop Event

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

Calls

Call 1

Inputs
(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (sin.f64 x) (*.f64 x x))
(sin.f64 x)
x
(*.f64 x x)
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (* x x)) (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)))
(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))
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
#s(literal 1/720 binary64)
(*.f64 x x)
x
#s(literal -1/24 binary64)
#s(literal 1/2 binary64)
(*.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
(/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x)
(-.f64 (cos.f64 x) #s(literal 1 binary64))
(cos.f64 x)
x
#s(literal 1 binary64)
(/.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (*.f64 x x))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x))
(-.f64 (.f64 x x) (.f64 (*.f64 x x) (cos.f64 x)))
(*.f64 x x)
x
(.f64 (.f64 x x) (cos.f64 x))
(cos.f64 x)

Outputs
(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)) (sin.f64 x))
(/.f64 (sin.f64 x) (*.f64 x x))
(/.f64 (/.f64 (sin.f64 x) x) x)
(sin.f64 x)
x
(*.f64 x x)
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (* x x)) (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)))
(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))
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
#s(literal 1/720 binary64)
(*.f64 x x)
x
#s(literal -1/24 binary64)
#s(literal 1/2 binary64)
(*.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x)
(-.f64 (cos.f64 x) #s(literal 1 binary64))
(cos.f64 x)
x
#s(literal 1 binary64)
(/.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (*.f64 x x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(-.f64 (.f64 x x) (.f64 (*.f64 x x) (cos.f64 x)))
(*.f64 (fma.f64 (neg.f64 x) (cos.f64 x) x) x)
(*.f64 x x)
x
(.f64 (.f64 x x) (cos.f64 x))
(.f64 (.f64 (cos.f64 x) x) x)
(cos.f64 x)

localize196.0ms (2.3%)

Memory

-28.7MiB live, 217.5MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.08203125	(.f64 (.f64 x x) (cos.f64 x))
accuracy	13.159484969488481	(-.f64 (.f64 x x) (.f64 (*.f64 x x) (cos.f64 x)))
accuracy	15.805048619395071	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (*.f64 x x))
accuracy	42.466580939076216	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x))
accuracy	0	(cos.f64 x)
accuracy	0.1328125	(*.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
accuracy	14.789601394454218	(/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x)
accuracy	15.67212506232622	(-.f64 (cos.f64 x) #s(literal 1 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(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))
accuracy	0.2696108853401222	(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
accuracy	31.10316867931706	#s(approx (/ (- 1 (cos x)) (* x x)) (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)))
accuracy	30.642651714954976	#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
accuracy	0	(sin.f64 x)
accuracy	0.00390625	(tan.f64 (/.f64 x #s(literal 2 binary64)))
accuracy	0.125	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
accuracy	15.283111842477963	(/.f64 (sin.f64 x) (*.f64 x x))

Samples

101.0ms	72×	2	valid
39.0ms	128×	0	valid
16.0ms	40×	1	valid
13.0ms	16×	3	valid

Compiler

Compiled 159 to 30 computations (81.1% saved)

Precisions

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

adjust: 27.0ms (18.7% of total)

ival-sub: 26.0ms (18% of total)

ival-cos: 23.0ms (15.9% of total)

ival-sin: 21.0ms (14.5% of total)

ival-div: 17.0ms (11.8% of total)

ival-mult: 14.0ms (9.7% of total)

const: 8.0ms (5.5% of total)

ival-tan: 5.0ms (3.5% of total)

ival-add: 3.0ms (2.1% of total)

exact: 1.0ms (0.7% of total)

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

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

series17.0ms (0.2%)

Memory

25.4MiB live, 25.4MiB allocated

Counts

17 → 204

Calls

Call 1

Inputs
#s(alt (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (patch (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (tan.f64 (/.f64 x #s(literal 2 binary64))) (patch (tan.f64 (/.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64)) (patch #s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- 1 (cos x)) (* x x)) (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))) (patch #s(approx (/ (- 1 (cos x)) (* x x)) (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))) #<representation binary64>) () ())
#s(alt (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)) (patch (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)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (patch (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x)) (patch (.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (patch (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt (-.f64 (cos.f64 x) #s(literal 1 binary64)) (patch (-.f64 (cos.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (patch (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (patch (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (.f64 x x)) (patch (/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (.f64 x x)) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 x) (.f64 x x)) (patch (/.f64 (sin.f64 x) (.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 x x) (cos.f64 x)) (patch (.f64 (.f64 x x) (cos.f64 x)) #<representation binary64>) () ())

Outputs
#s(alt 1/2 (taylor 0 x) (#s(alt (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (patch (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/24 (pow x 2))) (taylor 0 x) (#s(alt (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (patch (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))) (taylor 0 x) (#s(alt (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (patch (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))) (taylor 0 x) (#s(alt (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (patch (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/6 (pow x 2)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (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 x #s(literal 2 binary64))) (patch (tan.f64 (/.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/24 (pow x 2)))) (taylor 0 x) (#s(alt (tan.f64 (/.f64 x #s(literal 2 binary64))) (patch (tan.f64 (/.f64 x #s(literal 2 binary64))) #<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 x #s(literal 2 binary64))) (patch (tan.f64 (/.f64 x #s(literal 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 (tan.f64 (/.f64 x #s(literal 2 binary64))) (patch (tan.f64 (/.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64)) (patch #s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/24 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64)) (patch #s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64)) (patch #s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64)) (patch #s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (* x x)) (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))) (patch #s(approx (/ (- 1 (cos x)) (* x x)) (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))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/24 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (* x x)) (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))) (patch #s(approx (/ (- 1 (cos x)) (* x x)) (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))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (* x x)) (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))) (patch #s(approx (/ (- 1 (cos x)) (* x x)) (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))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))) (taylor 0 x) (#s(alt #s(approx (/ (- 1 (cos x)) (* x x)) (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))) (patch #s(approx (/ (- 1 (cos x)) (* x x)) (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))) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor 0 x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/24 (pow x 2))) (taylor 0 x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))) (taylor 0 x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))) (taylor 0 x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt -1/24 (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (patch (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/720 (pow x 2)) 1/24) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (patch (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/720 (pow x 2)) 1/24) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (patch (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/720 (pow x 2)) 1/24) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (patch (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor 0 x) (#s(alt (.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x)) (patch (.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/24 (pow x 2))) (taylor 0 x) (#s(alt (.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x)) (patch (.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))) (taylor 0 x) (#s(alt (.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x)) (patch (.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))) (taylor 0 x) (#s(alt (.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x)) (patch (.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor 0 x) (#s(alt (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (patch (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/24 (pow x 2)) 1/2)) (taylor 0 x) (#s(alt (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (patch (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) (taylor 0 x) (#s(alt (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (patch (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2)) (taylor 0 x) (#s(alt (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (patch (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (pow x 2)) (taylor 0 x) (#s(alt (-.f64 (cos.f64 x) #s(literal 1 binary64)) (patch (-.f64 (cos.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (- 1 (cos x))) (taylor inf x) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (patch (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) #<representation binary64>) () ())) ())
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#s(alt (/ (sin x) (pow x 2)) (taylor inf x) (#s(alt (/.f64 (sin.f64 x) (.f64 x x)) (patch (/.f64 (sin.f64 x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (pow x 2)) (taylor inf x) (#s(alt (/.f64 (sin.f64 x) (.f64 x x)) (patch (/.f64 (sin.f64 x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (pow x 2)) (taylor inf x) (#s(alt (/.f64 (sin.f64 x) (.f64 x x)) (patch (/.f64 (sin.f64 x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (pow x 2)) (taylor inf x) (#s(alt (/.f64 (sin.f64 x) (.f64 x x)) (patch (/.f64 (sin.f64 x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (cos x)) (taylor inf x) (#s(alt (.f64 (.f64 x x) (cos.f64 x)) (patch (.f64 (.f64 x x) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (cos x)) (taylor inf x) (#s(alt (.f64 (.f64 x x) (cos.f64 x)) (patch (.f64 (.f64 x x) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (cos x)) (taylor inf x) (#s(alt (.f64 (.f64 x x) (cos.f64 x)) (patch (.f64 (.f64 x x) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (cos x)) (taylor inf x) (#s(alt (.f64 (.f64 x x) (cos.f64 x)) (patch (.f64 (.f64 x x) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (patch (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (patch (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (patch (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x)))) (taylor -inf x) (#s(alt (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (patch (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (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 x #s(literal 2 binary64))) (patch (tan.f64 (/.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor -inf x) (#s(alt (tan.f64 (/.f64 x #s(literal 2 binary64))) (patch (tan.f64 (/.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor -inf x) (#s(alt (tan.f64 (/.f64 x #s(literal 2 binary64))) (patch (tan.f64 (/.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (sin (* 1/2 x)) (cos (* 1/2 x))) (taylor -inf x) (#s(alt (tan.f64 (/.f64 x #s(literal 2 binary64))) (patch (tan.f64 (/.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64)) (patch #s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64)) (patch #s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64)) (patch #s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64)) (patch #s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (* x x)) (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))) (patch #s(approx (/ (- 1 (cos x)) (* x x)) (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))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (* x x)) (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))) (patch #s(approx (/ (- 1 (cos x)) (* x x)) (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))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (* x x)) (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))) (patch #s(approx (/ (- 1 (cos x)) (* x x)) (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))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ (- 1 (cos x)) (* x x)) (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))) (patch #s(approx (/ (- 1 (cos x)) (* x x)) (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))) #<representation binary64>) () ())) ())
#s(alt (* 1/720 (pow x 4)) (taylor -inf x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (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)) (patch (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)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (/ (- (cos x) 1) (pow x 2))) (taylor -inf x) (#s(alt (.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x)) (patch (.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (cos x) 1) (pow x 2))) (taylor -inf x) (#s(alt (.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x)) (patch (.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (cos x) 1) x) (taylor -inf x) (#s(alt (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (patch (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (/ (- (cos x) 1) x) (taylor -inf x) (#s(alt (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (patch (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (/ (- (cos x) 1) x) (taylor -inf x) (#s(alt (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (patch (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
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#s(alt (- (cos x) 1) (taylor -inf x) (#s(alt (-.f64 (cos.f64 x) #s(literal 1 binary64)) (patch (-.f64 (cos.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
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#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
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#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (patch (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (patch (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (cos x))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (patch (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (cos x))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (patch (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (cos x))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (patch (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (cos x))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (patch (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (.f64 x x)) (patch (/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (.f64 x x)) (patch (/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (.f64 x x)) (patch (/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (cos x)) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (.f64 x x)) (patch (/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (sin.f64 x) (.f64 x x)) (patch (/.f64 (sin.f64 x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (sin.f64 x) (.f64 x x)) (patch (/.f64 (sin.f64 x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (sin.f64 x) (.f64 x x)) (patch (/.f64 (sin.f64 x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (sin x) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (sin.f64 x) (.f64 x x)) (patch (/.f64 (sin.f64 x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (cos x)) (taylor -inf x) (#s(alt (.f64 (.f64 x x) (cos.f64 x)) (patch (.f64 (.f64 x x) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (cos x)) (taylor -inf x) (#s(alt (.f64 (.f64 x x) (cos.f64 x)) (patch (.f64 (.f64 x x) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (cos x)) (taylor -inf x) (#s(alt (.f64 (.f64 x x) (cos.f64 x)) (patch (.f64 (.f64 x x) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (cos x)) (taylor -inf x) (#s(alt (.f64 (.f64 x x) (cos.f64 x)) (patch (.f64 (.f64 x x) (cos.f64 x)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	((* (/ (sin x) (* x x)) (tan (/ x 2))) (sin x) (* x x) (tan (/ x 2)) (/ (- 1 (cos x)) (* x x)) (/ (- 1 (cos x)) (* x x)) (+ (* (+ (* 1/720 (* x x)) -1/24) (* x x)) 1/2) (+ (* 1/720 (* x x)) -1/24) (* (/ (- (cos x) 1) x) (/ -1 x)) (/ (- (cos x) 1) x) (- (cos x) 1) (cos x) (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (- (* x x) (* (* x x) (cos x))) (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (/ (sin x) (* x x)) (* (* x x) (cos x)))
4.0ms	x	@	inf	((* (/ (sin x) (* x x)) (tan (/ x 2))) (sin x) (* x x) (tan (/ x 2)) (/ (- 1 (cos x)) (* x x)) (/ (- 1 (cos x)) (* x x)) (+ (* (+ (* 1/720 (* x x)) -1/24) (* x x)) 1/2) (+ (* 1/720 (* x x)) -1/24) (* (/ (- (cos x) 1) x) (/ -1 x)) (/ (- (cos x) 1) x) (- (cos x) 1) (cos x) (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (- (* x x) (* (* x x) (cos x))) (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (/ (sin x) (* x x)) (* (* x x) (cos x)))
2.0ms	x	@	0	((* (/ (sin x) (* x x)) (tan (/ x 2))) (sin x) (* x x) (tan (/ x 2)) (/ (- 1 (cos x)) (* x x)) (/ (- 1 (cos x)) (* x x)) (+ (* (+ (* 1/720 (* x x)) -1/24) (* x x)) 1/2) (+ (* 1/720 (* x x)) -1/24) (* (/ (- (cos x) 1) x) (/ -1 x)) (/ (- (cos x) 1) x) (- (cos x) 1) (cos x) (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (- (* x x) (* (* x x) (cos x))) (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (/ (sin x) (* x x)) (* (* x x) (cos x)))

Time

Variable

Point

Expression

5.0ms

-inf

((* (/ (sin x) (* x x)) (tan (/ x 2))) (sin x) (* x x) (tan (/ x 2)) (/ (- 1 (cos x)) (* x x)) (/ (- 1 (cos x)) (* x x)) (+ (* (+ (* 1/720 (* x x)) -1/24) (* x x)) 1/2) (+ (* 1/720 (* x x)) -1/24) (* (/ (- (cos x) 1) x) (/ -1 x)) (/ (- (cos x) 1) x) (- (cos x) 1) (cos x) (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (- (* x x) (* (* x x) (cos x))) (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (/ (sin x) (* x x)) (* (* x x) (cos x)))

4.0ms

inf

((* (/ (sin x) (* x x)) (tan (/ x 2))) (sin x) (* x x) (tan (/ x 2)) (/ (- 1 (cos x)) (* x x)) (/ (- 1 (cos x)) (* x x)) (+ (* (+ (* 1/720 (* x x)) -1/24) (* x x)) 1/2) (+ (* 1/720 (* x x)) -1/24) (* (/ (- (cos x) 1) x) (/ -1 x)) (/ (- (cos x) 1) x) (- (cos x) 1) (cos x) (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (- (* x x) (* (* x x) (cos x))) (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (/ (sin x) (* x x)) (* (* x x) (cos x)))

2.0ms

((* (/ (sin x) (* x x)) (tan (/ x 2))) (sin x) (* x x) (tan (/ x 2)) (/ (- 1 (cos x)) (* x x)) (/ (- 1 (cos x)) (* x x)) (+ (* (+ (* 1/720 (* x x)) -1/24) (* x x)) 1/2) (+ (* 1/720 (* x x)) -1/24) (* (/ (- (cos x) 1) x) (/ -1 x)) (/ (- (cos x) 1) x) (- (cos x) 1) (cos x) (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (- (* x x) (* (* x x) (cos x))) (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (/ (sin x) (* x x)) (* (* x x) (cos x)))

simplify164.0ms (1.9%)

Memory

-17.3MiB live, 136.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	128	1640
1	357	1640
2	903	1628
3	3019	1628
4	4442	1628
5	6771	1628
0	8525	1520

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 203

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
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))))
(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
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
-1/24
(- (* 1/720 (pow x 2)) 1/24)
(- (* 1/720 (pow x 2)) 1/24)
(- (* 1/720 (pow x 2)) 1/24)
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(* -1/2 x)
(* x (- (* 1/24 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
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)))
(* 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))))
(* 1/2 (pow x 4))
(* (pow x 4) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 4) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 4) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ 1 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))) x)
(pow x 2)
(* (pow x 2) (+ 1 (* -1/2 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(sin x)
(sin x)
(sin x)
(sin x)
(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 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(* 1/720 (pow x 4))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* 1/720 (pow x 2))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(cos x)
(cos x)
(cos x)
(cos x)
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(* (pow x 2) (- 1 (cos x)))
(* (pow x 2) (- 1 (cos x)))
(* (pow x 2) (- 1 (cos x)))
(* (pow x 2) (- 1 (cos x)))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(* (pow x 2) (cos x))
(* (pow x 2) (cos x))
(* (pow x 2) (cos x))
(* (pow x 2) (cos x))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(sin x)
(sin x)
(sin x)
(sin x)
(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 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(* 1/720 (pow x 4))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* 1/720 (pow x 2))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(cos x)
(cos x)
(cos x)
(cos x)
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(* (pow x 2) (- 1 (cos x)))
(* (pow x 2) (- 1 (cos x)))
(* (pow x 2) (- 1 (cos x)))
(* (pow x 2) (- 1 (cos x)))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(* (pow x 2) (cos x))
(* (pow x 2) (cos x))
(* (pow x 2) (cos x))
(* (pow x 2) (cos x))

Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(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))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(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 (* -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)
(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 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(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))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(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))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(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))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(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))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(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))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(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))
-1/24
#s(literal -1/24 binary64)
(- (* 1/720 (pow x 2)) 1/24)
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
(- (* 1/720 (pow x 2)) 1/24)
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
(- (* 1/720 (pow x 2)) 1/24)
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(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))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(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))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* x (- (* 1/24 (pow x 2)) 1/2))
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)
(* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(.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) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(.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)
(* -1/2 (pow x 2))
(.f64 (.f64 #s(literal -1/2 binary64) x) x)
(* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))
(.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) x) x)
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(.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) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(.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 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.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 #s(literal 1 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #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)
(* 1/2 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(* (pow x 4) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* (pow x 4) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (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)))
(* (pow x 4) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (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)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(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))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(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))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* -1/6 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))) x)
(/.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) x)
(/.f64 (fma.f64 (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)) (*.f64 x x) #s(literal 1 binary64)) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1/2 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/2 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (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)
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 x x)) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 x x)) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 x x)) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 x x)) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 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)
(/ (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 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(* 1/720 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/720 binary64))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64)) x) x)
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(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))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(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))
(* 1/720 (pow x 2))
(.f64 #s(literal 1/720 binary64) (.f64 x x))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- (cos x) 1) x)
(/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x)
(/ (- (cos x) 1) x)
(/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x)
(/ (- (cos x) 1) x)
(/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x)
(/ (- (cos x) 1) x)
(/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x)
(- (cos x) 1)
(-.f64 (cos.f64 x) #s(literal 1 binary64))
(- (cos x) 1)
(-.f64 (cos.f64 x) #s(literal 1 binary64))
(- (cos x) 1)
(-.f64 (cos.f64 x) #s(literal 1 binary64))
(- (cos x) 1)
(-.f64 (cos.f64 x) #s(literal 1 binary64))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(* (pow x 2) (- 1 (cos x)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(* (pow x 2) (- 1 (cos x)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(* (pow x 2) (- 1 (cos x)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(* (pow x 2) (- 1 (cos x)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (sin x) (pow x 2))
(/.f64 (/.f64 (sin.f64 x) x) x)
(/ (sin x) (pow x 2))
(/.f64 (/.f64 (sin.f64 x) x) x)
(/ (sin x) (pow x 2))
(/.f64 (/.f64 (sin.f64 x) x) x)
(/ (sin x) (pow x 2))
(/.f64 (/.f64 (sin.f64 x) x) x)
(* (pow x 2) (cos x))
(.f64 (.f64 (cos.f64 x) x) x)
(* (pow x 2) (cos x))
(.f64 (.f64 (cos.f64 x) x) x)
(* (pow x 2) (cos x))
(.f64 (.f64 (cos.f64 x) x) x)
(* (pow x 2) (cos x))
(.f64 (.f64 (cos.f64 x) x) x)
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 x x)) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 x x)) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 x x)) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 x x)) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 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)
(/ (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 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(* 1/720 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/720 binary64))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64)) x) x)
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(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))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(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))
(* 1/720 (pow x 2))
(.f64 #s(literal 1/720 binary64) (.f64 x x))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- (cos x) 1) x)
(/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x)
(/ (- (cos x) 1) x)
(/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x)
(/ (- (cos x) 1) x)
(/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x)
(/ (- (cos x) 1) x)
(/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x)
(- (cos x) 1)
(-.f64 (cos.f64 x) #s(literal 1 binary64))
(- (cos x) 1)
(-.f64 (cos.f64 x) #s(literal 1 binary64))
(- (cos x) 1)
(-.f64 (cos.f64 x) #s(literal 1 binary64))
(- (cos x) 1)
(-.f64 (cos.f64 x) #s(literal 1 binary64))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(* (pow x 2) (- 1 (cos x)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(* (pow x 2) (- 1 (cos x)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(* (pow x 2) (- 1 (cos x)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(* (pow x 2) (- 1 (cos x)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (sin x) (pow x 2))
(/.f64 (/.f64 (sin.f64 x) x) x)
(/ (sin x) (pow x 2))
(/.f64 (/.f64 (sin.f64 x) x) x)
(/ (sin x) (pow x 2))
(/.f64 (/.f64 (sin.f64 x) x) x)
(/ (sin x) (pow x 2))
(/.f64 (/.f64 (sin.f64 x) x) x)
(* (pow x 2) (cos x))
(.f64 (.f64 (cos.f64 x) x) x)
(* (pow x 2) (cos x))
(.f64 (.f64 (cos.f64 x) x) x)
(* (pow x 2) (cos x))
(.f64 (.f64 (cos.f64 x) x) x)
(* (pow x 2) (cos x))
(.f64 (.f64 (cos.f64 x) x) x)

rewrite159.0ms (1.9%)

Memory

24.3MiB live, 176.0MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	143
0	49	135
1	202	119
2	1474	119
0	8470	119

Stop Event

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

Counts

17 → 1 054

Calls

Call 1

Inputs
(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(sin.f64 x)
(*.f64 x x)
(tan.f64 (/.f64 x #s(literal 2 binary64)))
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (* x x)) (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)))
(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))
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
(*.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
(/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x)
(-.f64 (cos.f64 x) #s(literal 1 binary64))
(cos.f64 x)
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x))
(-.f64 (.f64 x x) (.f64 (*.f64 x x) (cos.f64 x)))
(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (*.f64 x x))
(/.f64 (sin.f64 x) (*.f64 x x))
(.f64 (.f64 x x) (cos.f64 x))

Outputs
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eval668.0ms (7.9%)

Memory: 16.5MiB live, 399.4MiB allocated
Compiler: Compiled 29 954 to 3 365 computations (88.8% saved)

prune47.0ms (0.6%)

Memory

3.6MiB live, 119.3MiB allocated

Pruning

22 alts after pruning (17 fresh and 5 done)

	Pruned	Kept	Total
New	1 472	12	1 484
Fresh	4	5	9
Picked	1	4	5
Done	0	1	1
Total	1 477	22	1 499

Accuracy

100.0%

Counts

1 499 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.2%	(/.f64 (fma.f64 (neg.f64 x) (/.f64 (cos.f64 x) x) #s(literal 1 binary64)) (*.f64 x x))
▶	21.1%	(/.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (cos.f64 x)) x) x (.f64 x x)) (.f64 x x)) (.f64 x x))
	21.2%	(/.f64 (/.f64 (fma.f64 x x (.f64 (.f64 (cos.f64 x) x) (neg.f64 x))) (.f64 x x)) (.f64 x x))
✓	21.1%	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (*.f64 x x))
	51.3%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	51.2%	(/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 (/.f64 (cos.f64 x) x))) (neg.f64 x))
✓	49.7%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
	30.4%	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
	11.8%	(/.f64 (.f64 x (-.f64 x (.f64 (cos.f64 x) x))) (.f64 (.f64 (neg.f64 x) x) (*.f64 (neg.f64 x) x)))
▶	49.7%	(/.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 (cos.f64 x) x)) x)) (*.f64 x x))
	50.5%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
	21.1%	(.f64 (/.f64 (fma.f64 (/.f64 (.f64 x x) #s(literal -1 binary64)) (/.f64 (neg.f64 (cos.f64 x)) (*.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
	22.3%	(.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (.f64 (*.f64 (cos.f64 x) x) x) (neg.f64 x)) #s(literal -1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
✓	51.3%	(*.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
▶	75.1%	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
▶	27.7%	(.f64 (/.f64 #s(approx (- (cos x) 1) (.f64 (*.f64 #s(literal -1/2 binary64) x) x)) x) (/.f64 #s(literal -1 binary64) x))
	11.8%	(.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (pow.f64 x #s(literal -4 binary64)))
	52.0%	(.f64 #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x))
	51.1%	#s(approx (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (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)))
▶	51.0%	#s(approx (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
✓	51.4%	#s(approx (/ (- 1 (cos x)) (* x x)) (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)))
✓	52.1%	#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))

Compiler

Compiled 504 to 314 computations (37.7% saved)

simplify116.0ms (1.4%)

Memory

-25.5MiB live, 132.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(neg.f64 (cos.f64 x))
cost-diff	0	(*.f64 (neg.f64 (cos.f64 x)) x)
cost-diff	320	(fma.f64 (.f64 (neg.f64 (cos.f64 x)) x) x (.f64 x x))
cost-diff	1664	(/.f64 (fma.f64 (.f64 (neg.f64 (cos.f64 x)) x) x (.f64 x x)) (*.f64 x x))
cost-diff	0	(*.f64 (cos.f64 x) x)
cost-diff	0	(-.f64 x (*.f64 (cos.f64 x) x))
cost-diff	320	(.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 (cos.f64 x) x)) x))
cost-diff	1024	(/.f64 (-.f64 x (*.f64 (cos.f64 x) x)) x)
cost-diff	0	(.f64 (.f64 #s(literal -1/2 binary64) x) x)
cost-diff	0	#s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))
cost-diff	0	(/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)) x)
cost-diff	192	(.f64 (/.f64 #s(approx (- (cos x) 1) (.f64 (*.f64 #s(literal -1/2 binary64) x) x)) x) (/.f64 #s(literal -1 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	#s(approx (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
cost-diff	0	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(sin.f64 x)
cost-diff	384	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	38	225
0	66	208
1	135	189
2	288	176
3	654	176
4	1718	176
5	4140	176
6	7556	176
0	8106	176

Stop Event

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

Calls

Call 1

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

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

localize268.0ms (3.2%)

Memory

13.2MiB live, 266.8MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.1328125	(*.f64 (neg.f64 (cos.f64 x)) x)
accuracy	15.248279690284422	(fma.f64 (.f64 (neg.f64 (cos.f64 x)) x) x (.f64 x x))
accuracy	15.805048619395071	(/.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (cos.f64 x)) x) x (.f64 x x)) (.f64 x x)) (.f64 x x))
accuracy	42.466580939076216	(/.f64 (fma.f64 (.f64 (neg.f64 (cos.f64 x)) x) x (.f64 x x)) (*.f64 x x))
accuracy	0.1328125	(*.f64 (cos.f64 x) x)
accuracy	4.837506558682372	(/.f64 (-.f64 x (*.f64 (cos.f64 x) x)) x)
accuracy	10.715440381003816	(-.f64 x (*.f64 (cos.f64 x) x))
accuracy	15.805048619395071	(/.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 (cos.f64 x) x)) x)) (*.f64 x x))
accuracy	0	(*.f64 #s(literal -1/2 binary64) x)
accuracy	0.1328125	(.f64 (/.f64 #s(approx (- (cos x) 1) (.f64 (*.f64 #s(literal -1/2 binary64) x) x)) x) (/.f64 #s(literal -1 binary64) x))
accuracy	14.789601394454218	(/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)) x)
accuracy	30.64272543819078	#s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))
accuracy	0	(*.f64 x x)
accuracy	0.2917668307025324	(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
accuracy	31.35408059835413	#s(approx (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
accuracy	0	(sin.f64 x)
accuracy	0.00390625	(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
accuracy	0.125	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
accuracy	15.283111842477963	(/.f64 (sin.f64 x) (*.f64 x x))

Samples

118.0ms	72×	2	valid
44.0ms	128×	0	valid
37.0ms	40×	1	valid
34.0ms	16×	3	valid

Compiler

Compiled 206 to 38 computations (81.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 159.0ms

ival-mult: 66.0ms (41.4% of total)

ival-div: 23.0ms (14.4% of total)

ival-cos: 22.0ms (13.8% of total)

ival-sin: 15.0ms (9.4% of total)

adjust: 11.0ms (6.9% of total)

ival-sub: 7.0ms (4.4% of total)

ival-tan: 5.0ms (3.1% of total)

const: 4.0ms (2.5% of total)

ival-add: 4.0ms (2.5% of total)

ival-neg: 2.0ms (1.3% of total)

exact: 1.0ms (0.6% of total)

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

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

series43.0ms (0.5%)

Memory

-17.3MiB live, 20.0MiB allocated

Counts

22 → 264

Calls

Call 1

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

Outputs
#s(alt 1/2 (taylor 0 x) (#s(alt (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) (patch (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/24 (pow x 2))) (taylor 0 x) (#s(alt (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) (patch (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))) (taylor 0 x) (#s(alt (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) (patch (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))) (taylor 0 x) (#s(alt (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (.f64 #s(literal 1/2 binary64) x))) (patch (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (.f64 #s(literal 1/2 binary64) 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 (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 (taylor 0 x) (#s(alt #s(approx (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))) (patch #s(approx (/ (/ (- ( x x) (* (* x x) (cos x))) (* x x)) (* x x)) (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 #s(approx (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))) (patch #s(approx (/ (/ (- ( x x) (* (* x x) (cos x))) (* x x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
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#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 (* -1 (cos x))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 (cos.f64 x) x)) x)) (.f64 x x)) (patch (/.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 (cos.f64 x) x)) x)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1 (cos x))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 (cos.f64 x) x)) x)) (.f64 x x)) (patch (/.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 (cos.f64 x) x)) x)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1 (cos x))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 (cos.f64 x) x)) x)) (.f64 x x)) (patch (/.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 (cos.f64 x) x)) x)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1 (cos x))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 (cos.f64 x) x)) x)) (.f64 x x)) (patch (/.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 (cos.f64 x) x)) x)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1 (cos x))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (cos.f64 x)) x) x (.f64 x x)) (.f64 x x)) (.f64 x x)) (patch (/.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (cos.f64 x)) x) x (.f64 x x)) (.f64 x x)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1 (cos x))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (cos.f64 x)) x) x (.f64 x x)) (.f64 x x)) (.f64 x x)) (patch (/.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (cos.f64 x)) x) x (.f64 x x)) (.f64 x x)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1 (cos x))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (cos.f64 x)) x) x (.f64 x x)) (.f64 x x)) (.f64 x x)) (patch (/.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (cos.f64 x)) x) x (.f64 x x)) (.f64 x x)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1 (cos x))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (cos.f64 x)) x) x (.f64 x x)) (.f64 x x)) (.f64 x x)) (patch (/.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (cos.f64 x)) x) x (.f64 x x)) (.f64 x x)) (.f64 x x)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

29.0ms

inf

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

5.0ms

-inf

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

2.0ms

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

simplify221.0ms (2.6%)

Memory

13.8MiB live, 293.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	141	1969
1	403	1954
2	987	1951
3	3147	1951
4	4335	1951
5	5364	1951
0	8181	1837

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 262

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
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))))
(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
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* -1/24 (pow x 2)))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(* -1/2 x)
(* x (- (* 1/24 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 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))))
(* 1/2 (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))))
(* 1/2 (pow x 3))
(* (pow x 3) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 3) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 3) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
x
(* x (+ 1 (* -1/2 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* 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))))
(* 1/2 (pow x 4))
(* (pow x 4) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 4) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 4) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* -1 x)
(* x (- (* 1/2 (pow x 2)) 1))
(* x (- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1))
(* x (- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1))
-1
(- (* 1/2 (pow x 2)) 1)
(- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1)
(- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1)
(/ 1 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))) x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(sin x)
(sin x)
(sin x)
(sin x)
(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 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(* x (- 1 (cos x)))
(* x (- 1 (cos x)))
(* x (- 1 (cos x)))
(* x (- 1 (cos x)))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(* (pow x 2) (+ 1 (* -1 (cos x))))
(* (pow x 2) (+ 1 (* -1 (cos x))))
(* (pow x 2) (+ 1 (* -1 (cos x))))
(* (pow x 2) (+ 1 (* -1 (cos x))))
(* -1 (* x (cos x)))
(* -1 (* x (cos x)))
(* -1 (* x (cos x)))
(* -1 (* x (cos x)))
(* -1 (cos x))
(* -1 (cos x))
(* -1 (cos x))
(* -1 (cos x))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(sin x)
(sin x)
(sin x)
(sin x)
(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 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(* x (+ 1 (* -1 (cos x))))
(* x (+ 1 (* -1 (cos x))))
(* x (+ 1 (* -1 (cos x))))
(* x (+ 1 (* -1 (cos x))))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(* (pow x 2) (+ 1 (* -1 (cos x))))
(* (pow x 2) (+ 1 (* -1 (cos x))))
(* (pow x 2) (+ 1 (* -1 (cos x))))
(* (pow x 2) (+ 1 (* -1 (cos x))))
(* -1 (* x (cos x)))
(* -1 (* x (cos x)))
(* -1 (* x (cos x)))
(* -1 (* x (cos x)))
(* -1 (cos x))
(* -1 (cos x))
(* -1 (cos x))
(* -1 (cos x))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))

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

rewrite235.0ms (2.8%)

Memory

-46.8MiB live, 293.3MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	195
0	66	178
1	251	146
2	1670	146
0	8565	146

Stop Event

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

Counts

22 → 1 292

Calls

Call 1

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

Outputs
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eval262.0ms (3.1%)

Memory: 15.8MiB live, 317.8MiB allocated
Compiler: Compiled 36 945 to 3 225 computations (91.3% saved)

prune86.0ms (1%)

Memory

5.8MiB live, 132.8MiB allocated

Pruning

29 alts after pruning (21 fresh and 8 done)

	Pruned	Kept	Total
New	1 694	10	1 704
Fresh	1	11	12
Picked	2	3	5
Done	0	5	5
Total	1 697	29	1 726

Accuracy

100.0%

Counts

1 726 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.2%	(/.f64 (fma.f64 (neg.f64 x) (/.f64 (cos.f64 x) x) #s(literal 1 binary64)) (*.f64 x x))
	21.2%	(/.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (cos.f64 x)) x) x (/.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) x))) (.f64 x x)) (*.f64 x x))
✓	21.1%	(/.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (cos.f64 x)) x) x (.f64 x x)) (.f64 x x)) (.f64 x x))
	2.2%	(/.f64 (/.f64 (fma.f64 #s(approx (* (neg (cos x)) x) (neg.f64 x)) x (.f64 x x)) (.f64 x x)) (*.f64 x x))
	21.2%	(/.f64 (/.f64 (fma.f64 x x (.f64 (.f64 (cos.f64 x) x) (neg.f64 x))) (.f64 x x)) (.f64 x x))
✓	21.1%	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (*.f64 x x))
	49.7%	(/.f64 (/.f64 (-.f64 x (.f64 (cos.f64 x) x)) x) (.f64 x x))
	51.3%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	27.7%	(/.f64 (/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)) (neg.f64 x)) x)
	51.2%	(/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 (/.f64 (cos.f64 x) x))) (neg.f64 x))
▶	41.6%	(/.f64 (-.f64 x (.f64 (cos.f64 x) x)) (neg.f64 (.f64 (*.f64 x x) (neg.f64 x))))
✓	49.7%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
▶	30.4%	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
	27.7%	(/.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 #s(approx (- (cos x) 1) (.f64 (*.f64 #s(literal -1/2 binary64) x) x)))) (neg.f64 x))
▶	49.7%	(/.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (/.f64 x (/.f64 #s(literal 1 binary64) (cos.f64 x)))) x)) (.f64 x x))
	50.5%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
▶	27.7%	(/.f64 #s(literal -1 binary64) (/.f64 x (/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)) x)))
	27.7%	(/.f64 #s(literal -1 binary64) (.f64 (/.f64 x #s(approx (- (cos x) 1) (.f64 (*.f64 #s(literal -1/2 binary64) x) x))) x))
	21.1%	(.f64 (/.f64 (fma.f64 (/.f64 (.f64 x x) #s(literal -1 binary64)) (/.f64 (neg.f64 (cos.f64 x)) (*.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
	22.3%	(.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (.f64 (*.f64 (cos.f64 x) x) x) (neg.f64 x)) #s(literal -1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
✓	51.3%	(*.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
✓	75.1%	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
	11.8%	(.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (pow.f64 x #s(literal -4 binary64)))
	26.2%	(.f64 (neg.f64 #s(approx (- (cos x) 1) (.f64 (*.f64 #s(literal -1/2 binary64) x) x))) (pow.f64 x #s(literal -2 binary64)))
▶	52.0%	(.f64 #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x))
	51.1%	#s(approx (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (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)))
✓	51.0%	#s(approx (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
✓	51.4%	#s(approx (/ (- 1 (cos x)) (* x x)) (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)))
✓	52.1%	#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))

Compiler

Compiled 658 to 420 computations (36.2% saved)

simplify229.0ms (2.7%)

Memory

6.6MiB live, 80.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 x (/.f64 x (/.f64 #s(literal 1 binary64) (cos.f64 x))))
cost-diff	320	(*.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (/.f64 x (/.f64 #s(literal 1 binary64) (cos.f64 x)))) x))
cost-diff	1024	(/.f64 (-.f64 x (/.f64 x (/.f64 #s(literal 1 binary64) (cos.f64 x)))) x)
cost-diff	1088	(/.f64 x (/.f64 #s(literal 1 binary64) (cos.f64 x)))
cost-diff	0	(*.f64 (cos.f64 x) x)
cost-diff	0	(-.f64 x (*.f64 (cos.f64 x) x))
cost-diff	256	(neg.f64 (.f64 (.f64 x x) (neg.f64 x)))
cost-diff	6080	(/.f64 (-.f64 x (.f64 (cos.f64 x) x)) (neg.f64 (.f64 (*.f64 x x) (neg.f64 x))))
cost-diff	0	#s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))
cost-diff	0	(/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)) x)
cost-diff	384	(/.f64 x (/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)) x))
cost-diff	576	(/.f64 #s(literal -1 binary64) (/.f64 x (/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)) x)))
cost-diff	-384	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (cos x) #s(literal 1 binary64))
cost-diff	0	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
cost-diff	0	(/.f64 #s(literal -1 binary64) x)
cost-diff	0	(*.f64 #s(literal -1/2 binary64) x)
cost-diff	0	#s(approx (/ (- (cos x) 1) x) (*.f64 #s(literal -1/2 binary64) x))
cost-diff	192	(.f64 #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	229
0	57	221
1	120	211
2	294	197
3	1259	189
4	3148	189
5	4666	189
6	5477	189
7	5741	189
8	5879	189
9	5961	189
10	6754	189
11	7148	189
12	7312	189
13	7746	189
0	8710	189

Stop Event

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

Calls

Call 1

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

Outputs
(.f64 #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(approx (/ (- (cos x) 1) x) (*.f64 #s(literal -1/2 binary64) x)) (neg.f64 x))
#s(approx (/ (- (cos x) 1) x) (*.f64 #s(literal -1/2 binary64) x))
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(/.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) x) x)
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (cos x) #s(literal 1 binary64))
(*.f64 x x)
x
(/.f64 #s(literal -1 binary64) (/.f64 x (/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)) x)))
(/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64))) (*.f64 (neg.f64 x) x))
#s(literal -1 binary64)
(/.f64 x (/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)) x))
(/.f64 (.f64 x x) #s(approx (- (cos x) 1) (.f64 (*.f64 x x) #s(literal -1/2 binary64))))
x
(/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)) x)
(/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64))) x)
#s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))
#s(approx (- (cos x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal -1/2 binary64) x) x)
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
(/.f64 (-.f64 x (.f64 (cos.f64 x) x)) (neg.f64 (.f64 (*.f64 x x) (neg.f64 x))))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(-.f64 x (*.f64 (cos.f64 x) x))
x
(*.f64 (cos.f64 x) x)
(cos.f64 x)
(neg.f64 (.f64 (.f64 x x) (neg.f64 x)))
(pow.f64 x #s(literal 3 binary64))
(.f64 (.f64 x x) (neg.f64 x))
(pow.f64 (neg.f64 x) #s(literal 3 binary64))
(*.f64 x x)
(neg.f64 x)
(/.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (/.f64 x (/.f64 #s(literal 1 binary64) (cos.f64 x)))) x)) (.f64 x x))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(*.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (/.f64 x (/.f64 #s(literal 1 binary64) (cos.f64 x)))) x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(/.f64 (-.f64 x (/.f64 x (/.f64 #s(literal 1 binary64) (cos.f64 x)))) x)
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(-.f64 x (/.f64 x (/.f64 #s(literal 1 binary64) (cos.f64 x))))
(-.f64 x (*.f64 (cos.f64 x) x))
x
(/.f64 x (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (cos.f64 x) x)
(/.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
(*.f64 x x)

localize371.0ms (4.4%)

Memory

-9.0MiB live, 162.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.16796875	(/.f64 x (/.f64 #s(literal 1 binary64) (cos.f64 x)))
accuracy	4.837506558682372	(/.f64 (-.f64 x (/.f64 x (/.f64 #s(literal 1 binary64) (cos.f64 x)))) x)
accuracy	10.715440381003816	(-.f64 x (/.f64 x (/.f64 #s(literal 1 binary64) (cos.f64 x))))
accuracy	15.805048619395071	(/.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (/.f64 x (/.f64 #s(literal 1 binary64) (cos.f64 x)))) x)) (.f64 x x))
accuracy	0.0703125	(.f64 (.f64 x x) (neg.f64 x))
accuracy	0.1328125	(*.f64 (cos.f64 x) x)
accuracy	10.715440381003816	(-.f64 x (*.f64 (cos.f64 x) x))
accuracy	25.745310483120118	(/.f64 (-.f64 x (.f64 (cos.f64 x) x)) (neg.f64 (.f64 (*.f64 x x) (neg.f64 x))))
accuracy	0.03125	(/.f64 x (/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)) x))
accuracy	0.5467164244019732	(/.f64 #s(literal -1 binary64) (/.f64 x (/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)) x)))
accuracy	14.789601394454218	(/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)) x)
accuracy	30.64272543819078	#s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x))
accuracy	0	(*.f64 x x)
accuracy	15.67212506232622	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
accuracy	15.805048619395071	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
accuracy	28.441708084553355	#s(approx (cos x) #s(literal 1 binary64))
accuracy	0	(/.f64 #s(literal -1 binary64) x)
accuracy	0	(*.f64 #s(literal -1/2 binary64) x)
accuracy	0.1328125	(.f64 #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x))
accuracy	30.80564745877686	#s(approx (/ (- (cos x) 1) x) (*.f64 #s(literal -1/2 binary64) x))

Samples

85.0ms	20×	3	valid
74.0ms	70×	2	valid
59.0ms	38×	1	valid
29.0ms	128×	0	valid

Compiler

Compiled 193 to 30 computations (84.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 175.0ms

ival-cos: 91.0ms (52.1% of total)

ival-div: 32.0ms (18.3% of total)

ival-sub: 28.0ms (16% of total)

ival-mult: 14.0ms (8% of total)

adjust: 7.0ms (4% of total)

ival-neg: 2.0ms (1.1% of total)

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

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

exact: 0.0ms (0% of total)

series41.0ms (0.5%)

Memory

-8.6MiB live, 27.8MiB allocated

Counts

22 → 264

Calls

Call 1

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

Outputs
#s(alt 1/2 (taylor 0 x) (#s(alt (.f64 #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x)) (patch (.f64 #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/24 (pow x 2))) (taylor 0 x) (#s(alt (.f64 #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x)) (patch (.f64 #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))) (taylor 0 x) (#s(alt (.f64 #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x)) (patch (.f64 #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))) (taylor 0 x) (#s(alt (.f64 #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x)) (patch (.f64 #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor 0 x) (#s(alt #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/24 (pow x 2)) 1/2)) (taylor 0 x) (#s(alt #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)) (taylor 0 x) (#s(alt #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2)) (taylor 0 x) (#s(alt #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (/ (- (cos x) 1) x) (.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 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) x) (patch (/.f64 #s(literal -1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) x) (patch (/.f64 #s(literal -1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) x) (patch (/.f64 #s(literal -1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) x) (patch (/.f64 #s(literal -1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (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) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (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) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<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 #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 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 (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (.f64 x x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/24 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (.f64 x x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (.f64 x x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
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Calls

3 calls:

Time

Variable

Point

Expression

6.0ms

-inf

((* (/ (- (cos x) 1) x) (/ -1 x)) (/ (- (cos x) 1) x) (* -1/2 x) (/ -1 x) (- 1 (cos x)) (cos x) (* x x) (/ (- 1 (cos x)) (* x x)) (/ -1 (/ x (/ (- (cos x) 1) x))) (/ x (/ (- (cos x) 1) x)) (/ (- (cos x) 1) x) (- (cos x) 1) (/ (- x (* (cos x) x)) (neg (* (* x x) (neg x)))) (neg (* (* x x) (neg x))) (- x (* (cos x) x)) (* (cos x) x) (/ x (/ 1 (cos x))) (/ (- x (/ x (/ 1 (cos x)))) x) (* 1 (/ (- x (/ x (/ 1 (cos x)))) x)) (- x (/ x (/ 1 (cos x)))) (* (* x x) (neg x)) (/ (* 1 (/ (- x (/ x (/ 1 (cos x)))) x)) (* x x)))

3.0ms

inf

((* (/ (- (cos x) 1) x) (/ -1 x)) (/ (- (cos x) 1) x) (* -1/2 x) (/ -1 x) (- 1 (cos x)) (cos x) (* x x) (/ (- 1 (cos x)) (* x x)) (/ -1 (/ x (/ (- (cos x) 1) x))) (/ x (/ (- (cos x) 1) x)) (/ (- (cos x) 1) x) (- (cos x) 1) (/ (- x (* (cos x) x)) (neg (* (* x x) (neg x)))) (neg (* (* x x) (neg x))) (- x (* (cos x) x)) (* (cos x) x) (/ x (/ 1 (cos x))) (/ (- x (/ x (/ 1 (cos x)))) x) (* 1 (/ (- x (/ x (/ 1 (cos x)))) x)) (- x (/ x (/ 1 (cos x)))) (* (* x x) (neg x)) (/ (* 1 (/ (- x (/ x (/ 1 (cos x)))) x)) (* x x)))

2.0ms

((* (/ (- (cos x) 1) x) (/ -1 x)) (/ (- (cos x) 1) x) (* -1/2 x) (/ -1 x) (- 1 (cos x)) (cos x) (* x x) (/ (- 1 (cos x)) (* x x)) (/ -1 (/ x (/ (- (cos x) 1) x))) (/ x (/ (- (cos x) 1) x)) (/ (- (cos x) 1) x) (- (cos x) 1) (/ (- x (* (cos x) x)) (neg (* (* x x) (neg x)))) (neg (* (* x x) (neg x))) (- x (* (cos x) x)) (* (cos x) x) (/ x (/ 1 (cos x))) (/ (- x (/ x (/ 1 (cos x)))) x) (* 1 (/ (- x (/ x (/ 1 (cos x)))) x)) (- x (/ x (/ 1 (cos x)))) (* (* x x) (neg x)) (/ (* 1 (/ (- x (/ x (/ 1 (cos x)))) x)) (* x x)))

simplify210.0ms (2.5%)

Memory

6.8MiB live, 246.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	95	1820
1	249	1768
2	601	1768
3	1848	1768
4	3837	1768
5	4425	1768
6	6307	1768
0	8169	1666

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 262

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(* -1/2 x)
(* x (- (* 1/24 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
-2
(- (* -1/6 (pow x 2)) 2)
(- (* (pow x 2) (- (* -1/120 (pow x 2)) 1/6)) 2)
(- (* (pow x 2) (- (* (pow x 2) (- (* -1/3024 (pow x 2)) 1/120)) 1/6)) 2)
(* -1/2 x)
(* x (- (* 1/24 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 1/2 (pow x 3))
(* (pow x 3) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 3) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 3) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
x
(* x (+ 1 (* -1/2 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
x
(* x (+ 1 (* -1/2 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* 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))))
(* 1/2 (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))))
(* 1/2 (pow x 3))
(* (pow x 3) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 3) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 3) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* -1 (pow x 3))
(* -1 (pow x 3))
(* -1 (pow x 3))
(* -1 (pow x 3))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/ (pow x 2) (- (cos x) 1))
(/ (pow x 2) (- (cos x) 1))
(/ (pow x 2) (- (cos x) 1))
(/ (pow x 2) (- (cos x) 1))
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* x (- 1 (cos x)))
(* x (- 1 (cos x)))
(* x (- 1 (cos x)))
(* x (- 1 (cos x)))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(* x (- 1 (cos x)))
(* x (- 1 (cos x)))
(* x (- 1 (cos x)))
(* x (- 1 (cos x)))
(* -1 (pow x 3))
(* -1 (pow x 3))
(* -1 (pow x 3))
(* -1 (pow x 3))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(* -1 (/ (- (cos x) 1) (pow x 2)))
(/ (pow x 2) (- (cos x) 1))
(/ (pow x 2) (- (cos x) 1))
(/ (pow x 2) (- (cos x) 1))
(/ (pow x 2) (- (cos x) 1))
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* x (+ 1 (* -1 (cos x))))
(* x (+ 1 (* -1 (cos x))))
(* x (+ 1 (* -1 (cos x))))
(* x (+ 1 (* -1 (cos x))))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(* x (+ 1 (* -1 (cos x))))
(* x (+ 1 (* -1 (cos x))))
(* x (+ 1 (* -1 (cos x))))
(* x (+ 1 (* -1 (cos x))))
(* -1 (pow x 3))
(* -1 (pow x 3))
(* -1 (pow x 3))
(* -1 (pow x 3))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))

Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(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))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(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))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* x (- (* 1/24 (pow x 2)) 1/2))
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)
(* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(.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) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(.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)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 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 (*.f64 x x) #s(literal -1/24 binary64) #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 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.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 #s(literal 1 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
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(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))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(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))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(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))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(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))
-2
#s(literal -2 binary64)
(- (* -1/6 (pow x 2)) 2)
(fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -2 binary64))
(- (* (pow x 2) (- (* -1/120 (pow x 2)) 1/6)) 2)
(fma.f64 (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal -2 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -1/3024 (pow x 2)) 1/120)) 1/6)) 2)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/3024 binary64) (.f64 x x) #s(literal -1/120 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal -2 binary64))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* x (- (* 1/24 (pow x 2)) 1/2))
(.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)
(* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(.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) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(.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)
(* -1/2 (pow x 2))
(.f64 (.f64 #s(literal -1/2 binary64) x) x)
(* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))
(.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) x) x)
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(.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) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(.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)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(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))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(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))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(* 1/2 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64))
(* (pow x 3) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
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rewrite199.0ms (2.3%)

Memory

13.5MiB live, 326.3MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	194
0	57	186
1	228	166
2	1658	162
0	8566	162

Stop Event

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

Counts

22 → 1 022

Calls

Call 1

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

Outputs
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eval200.0ms (2.4%)

Memory: 10.8MiB live, 388.5MiB allocated
Compiler: Compiled 26 145 to 2 779 computations (89.4% saved)

prune51.0ms (0.6%)

Memory

18.6MiB live, 146.0MiB allocated

Pruning

24 alts after pruning (13 fresh and 11 done)

	Pruned	Kept	Total
New	1 368	3	1 371
Fresh	6	10	16
Picked	2	3	5
Done	0	8	8
Total	1 376	24	1 400

Accuracy

100.0%

Counts

1 400 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	41.6%	(/.f64 (fma.f64 (neg.f64 (cos.f64 x)) x x) (neg.f64 (.f64 (.f64 x x) (neg.f64 x))))
	50.2%	(/.f64 (fma.f64 (neg.f64 x) (/.f64 (cos.f64 x) x) #s(literal 1 binary64)) (*.f64 x x))
	21.2%	(/.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (cos.f64 x)) x) x (/.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) x))) (.f64 x x)) (*.f64 x x))
✓	21.1%	(/.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (cos.f64 x)) x) x (.f64 x x)) (.f64 x x)) (.f64 x x))
	21.2%	(/.f64 (/.f64 (fma.f64 x x (.f64 (.f64 (cos.f64 x) x) (neg.f64 x))) (.f64 x x)) (.f64 x x))
✓	21.1%	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (*.f64 x x))
	49.7%	(/.f64 (/.f64 (-.f64 x (.f64 (cos.f64 x) x)) x) (.f64 x x))
	51.3%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	41.6%	(/.f64 (-.f64 x (.f64 (cos.f64 x) x)) (.f64 (*.f64 x x) x))
✓	49.7%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
✓	30.4%	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
✓	49.7%	(/.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (/.f64 x (/.f64 #s(literal 1 binary64) (cos.f64 x)))) x)) (.f64 x x))
	50.5%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
	82.1%	(/.f64 #s(literal -1 binary64) #s(approx (/ x (/ (- (cos x) 1) x)) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -2 binary64))))
	21.1%	(.f64 (/.f64 (fma.f64 (/.f64 (.f64 x x) #s(literal -1 binary64)) (/.f64 (neg.f64 (cos.f64 x)) (*.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
	22.3%	(.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (.f64 (*.f64 (cos.f64 x) x) x) (neg.f64 x)) #s(literal -1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
✓	51.3%	(*.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
✓	75.1%	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
	11.8%	(.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (pow.f64 x #s(literal -4 binary64)))
✓	52.0%	(.f64 #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x))
	51.1%	#s(approx (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (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)))
✓	51.0%	#s(approx (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
✓	51.4%	#s(approx (/ (- 1 (cos x)) (* x x)) (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)))
✓	52.1%	#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))

Compiler

Compiled 818 to 329 computations (59.8% saved)

regimes31.0ms (0.4%)

Memory

-43.9MiB live, 59.1MiB allocated

Counts

40 → 2

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
(.f64 #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x))
#s(approx (/ (- 1 (cos x)) (* x x)) (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 #s(literal -1 binary64) #s(approx (/ x (/ (- (cos x) 1) x)) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -2 binary64))))
#s(approx (/ (- 1 (cos x)) (* x x)) (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)))
#s(approx (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (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)))
(/.f64 (/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)) (neg.f64 x)) x)
(.f64 (/.f64 #s(approx (- (cos x) 1) (.f64 (*.f64 #s(literal -1/2 binary64) x) x)) x) (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal -1 binary64) (.f64 (/.f64 x #s(approx (- (cos x) 1) (.f64 (*.f64 #s(literal -1/2 binary64) x) x))) x))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 #s(approx (- (cos x) 1) (.f64 (*.f64 #s(literal -1/2 binary64) x) x)))) (neg.f64 x))
(/.f64 #s(literal -1 binary64) (/.f64 x (/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)) x)))
(/.f64 (/.f64 (fma.f64 #s(approx (* (neg (cos x)) x) (neg.f64 x)) x (.f64 x x)) (.f64 x x)) (*.f64 x x))
(.f64 (neg.f64 #s(approx (- (cos x) 1) (.f64 (*.f64 #s(literal -1/2 binary64) x) x))) (pow.f64 x #s(literal -2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/.f64 (-.f64 x (.f64 (cos.f64 x) x)) (.f64 (*.f64 x x) x))
(*.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
(/.f64 (-.f64 x (.f64 (cos.f64 x) x)) (neg.f64 (.f64 (*.f64 x x) (neg.f64 x))))
(/.f64 (fma.f64 (neg.f64 (cos.f64 x)) x x) (neg.f64 (.f64 (.f64 x x) (neg.f64 x))))
(/.f64 (/.f64 (-.f64 x (.f64 (cos.f64 x) x)) x) (.f64 x x))
(/.f64 (fma.f64 (neg.f64 x) (/.f64 (cos.f64 x) x) #s(literal 1 binary64)) (*.f64 x x))
(/.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 (cos.f64 x) x)) x)) (*.f64 x x))
(/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 (/.f64 (cos.f64 x) x))) (neg.f64 x))
(/.f64 (.f64 x (-.f64 x (.f64 (cos.f64 x) x))) (.f64 (.f64 (neg.f64 x) x) (*.f64 (neg.f64 x) x)))
(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (*.f64 x x))
(/.f64 (/.f64 (fma.f64 x x (.f64 (.f64 (cos.f64 x) x) (neg.f64 x))) (.f64 x x)) (.f64 x x))
(/.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (cos.f64 x)) x) x (.f64 x x)) (.f64 x x)) (.f64 x x))
(/.f64 (-.f64 (neg.f64 x) (.f64 (.f64 (neg.f64 x) x) (/.f64 (cos.f64 x) x))) (.f64 (.f64 (neg.f64 x) x) x))
(/.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (/.f64 x (/.f64 #s(literal 1 binary64) (cos.f64 x)))) x)) (.f64 x x))
(.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (.f64 (*.f64 (cos.f64 x) x) x) (neg.f64 x)) #s(literal -1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
(.f64 (/.f64 (fma.f64 (/.f64 (.f64 x x) #s(literal -1 binary64)) (/.f64 (neg.f64 (cos.f64 x)) (*.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
(/.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (cos.f64 x)) x) x (/.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) x))) (.f64 x x)) (*.f64 x x))
(*.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (pow.f64 x #s(literal -4 binary64)))
(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))

Outputs

#s(approx (/ (- 1 (cos x)) (* x x)) (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)))

(*.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))

Calls

2 calls:

16.0ms	x
12.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Results

Accuracy	Segments	Branch
99.8%	2	`x`
99.0%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes12.0ms (0.1%)

Memory

20.7MiB live, 20.7MiB allocated

Counts

36 → 2

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
(.f64 #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x))
#s(approx (/ (- 1 (cos x)) (* x x)) (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 #s(literal -1 binary64) #s(approx (/ x (/ (- (cos x) 1) x)) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -2 binary64))))
#s(approx (/ (- 1 (cos x)) (* x x)) (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)))
#s(approx (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (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)))
(/.f64 (/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)) (neg.f64 x)) x)
(.f64 (/.f64 #s(approx (- (cos x) 1) (.f64 (*.f64 #s(literal -1/2 binary64) x) x)) x) (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal -1 binary64) (.f64 (/.f64 x #s(approx (- (cos x) 1) (.f64 (*.f64 #s(literal -1/2 binary64) x) x))) x))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 #s(approx (- (cos x) 1) (.f64 (*.f64 #s(literal -1/2 binary64) x) x)))) (neg.f64 x))
(/.f64 #s(literal -1 binary64) (/.f64 x (/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)) x)))
(/.f64 (/.f64 (fma.f64 #s(approx (* (neg (cos x)) x) (neg.f64 x)) x (.f64 x x)) (.f64 x x)) (*.f64 x x))
(.f64 (neg.f64 #s(approx (- (cos x) 1) (.f64 (*.f64 #s(literal -1/2 binary64) x) x))) (pow.f64 x #s(literal -2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/.f64 (-.f64 x (.f64 (cos.f64 x) x)) (.f64 (*.f64 x x) x))
(*.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
(/.f64 (-.f64 x (.f64 (cos.f64 x) x)) (neg.f64 (.f64 (*.f64 x x) (neg.f64 x))))
(/.f64 (fma.f64 (neg.f64 (cos.f64 x)) x x) (neg.f64 (.f64 (.f64 x x) (neg.f64 x))))
(/.f64 (/.f64 (-.f64 x (.f64 (cos.f64 x) x)) x) (.f64 x x))
(/.f64 (fma.f64 (neg.f64 x) (/.f64 (cos.f64 x) x) #s(literal 1 binary64)) (*.f64 x x))
(/.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 (cos.f64 x) x)) x)) (*.f64 x x))
(/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 (/.f64 (cos.f64 x) x))) (neg.f64 x))
(/.f64 (.f64 x (-.f64 x (.f64 (cos.f64 x) x))) (.f64 (.f64 (neg.f64 x) x) (*.f64 (neg.f64 x) x)))
(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (cos.f64 x))) (.f64 x x)) (*.f64 x x))
(/.f64 (/.f64 (fma.f64 x x (.f64 (.f64 (cos.f64 x) x) (neg.f64 x))) (.f64 x x)) (.f64 x x))
(/.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (cos.f64 x)) x) x (.f64 x x)) (.f64 x x)) (.f64 x x))
(/.f64 (-.f64 (neg.f64 x) (.f64 (.f64 (neg.f64 x) x) (/.f64 (cos.f64 x) x))) (.f64 (.f64 (neg.f64 x) x) x))
(/.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (/.f64 x (/.f64 #s(literal 1 binary64) (cos.f64 x)))) x)) (.f64 x x))
(.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (.f64 (*.f64 (cos.f64 x) x) x) (neg.f64 x)) #s(literal -1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
(.f64 (/.f64 (fma.f64 (/.f64 (.f64 x x) #s(literal -1 binary64)) (/.f64 (neg.f64 (cos.f64 x)) (*.f64 x x)) #s(literal -1 binary64)) x) (/.f64 #s(literal -1 binary64) x))
(/.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (cos.f64 x)) x) x (/.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) x))) (.f64 x x)) (*.f64 x x))

Outputs

#s(approx (/ (- 1 (cos x)) (* x x)) (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)))

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

Calls

1 calls:

10.0ms

Results

Accuracy	Segments	Branch
99.8%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes10.0ms (0.1%)

Memory

-25.1MiB live, 13.5MiB allocated

Counts

17 → 2

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
(.f64 #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x))
#s(approx (/ (- 1 (cos x)) (* x x)) (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 #s(literal -1 binary64) #s(approx (/ x (/ (- (cos x) 1) x)) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -2 binary64))))
#s(approx (/ (- 1 (cos x)) (* x x)) (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)))
#s(approx (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (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)))
(/.f64 (/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)) (neg.f64 x)) x)
(.f64 (/.f64 #s(approx (- (cos x) 1) (.f64 (*.f64 #s(literal -1/2 binary64) x) x)) x) (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal -1 binary64) (.f64 (/.f64 x #s(approx (- (cos x) 1) (.f64 (*.f64 #s(literal -1/2 binary64) x) x))) x))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 #s(approx (- (cos x) 1) (.f64 (*.f64 #s(literal -1/2 binary64) x) x)))) (neg.f64 x))
(/.f64 #s(literal -1 binary64) (/.f64 x (/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)) x)))
(/.f64 (/.f64 (fma.f64 #s(approx (* (neg (cos x)) x) (neg.f64 x)) x (.f64 x x)) (.f64 x x)) (*.f64 x x))
(.f64 (neg.f64 #s(approx (- (cos x) 1) (.f64 (*.f64 #s(literal -1/2 binary64) x) x))) (pow.f64 x #s(literal -2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Outputs

#s(approx (/ (- 1 (cos x)) (* x x)) (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)))

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

Calls

1 calls:

9.0ms

Results

Accuracy	Segments	Branch
99.0%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes10.0ms (0.1%)

Memory

21.5MiB live, 21.5MiB allocated

Counts

16 → 1

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (* x x)) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x))
(.f64 #s(approx (/ (- (cos x) 1) x) (.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x))
#s(approx (/ (- 1 (cos x)) (* x x)) (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 #s(literal -1 binary64) #s(approx (/ x (/ (- (cos x) 1) x)) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -2 binary64))))
#s(approx (/ (- 1 (cos x)) (* x x)) (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)))
#s(approx (/ (/ (- (* x x) (* (* x x) (cos x))) (* x x)) (* x x)) (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)))
(/.f64 (/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)) (neg.f64 x)) x)
(.f64 (/.f64 #s(approx (- (cos x) 1) (.f64 (*.f64 #s(literal -1/2 binary64) x) x)) x) (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal -1 binary64) (.f64 (/.f64 x #s(approx (- (cos x) 1) (.f64 (*.f64 #s(literal -1/2 binary64) x) x))) x))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 #s(approx (- (cos x) 1) (.f64 (*.f64 #s(literal -1/2 binary64) x) x)))) (neg.f64 x))
(/.f64 #s(literal -1 binary64) (/.f64 x (/.f64 #s(approx (- (cos x) 1) (.f64 (.f64 #s(literal -1/2 binary64) x) x)) x)))
(/.f64 (/.f64 (fma.f64 #s(approx (* (neg (cos x)) x) (neg.f64 x)) x (.f64 x x)) (.f64 x x)) (*.f64 x x))
(.f64 (neg.f64 #s(approx (- (cos x) 1) (.f64 (*.f64 #s(literal -1/2 binary64) x) x))) (pow.f64 x #s(literal -2 binary64)))

Outputs
(/.f64 #s(literal -1 binary64) #s(approx (/ x (/ (- (cos x) 1) x)) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -2 binary64))))

Calls

2 calls:

5.0ms	x
4.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Results

Accuracy	Segments	Branch
82.1%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`
82.1%	1	`x`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes5.0ms (0.1%)

Memory

11.2MiB live, 11.2MiB allocated

Counts

6 → 2

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
80.1%	2	`x`
55.5%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes7.0ms (0.1%)

Memory

-29.3MiB live, 9.4MiB allocated

Accuracy

Total -0.8b remaining (-2.5%)

Threshold costs -0.8b (-2.5%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

2 calls:

5.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
2.0ms	x

Results

Accuracy	Segments	Branch
52.1%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`
52.1%	1	`x`

Compiler

Compiled 9 to 7 computations (22.2% saved)

bsearch15.0ms (0.2%)

Memory

31.9MiB live, 31.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	0.04028993806797688	96202.993662193

Samples

8.0ms

144×

valid

Compiler

Compiled 236 to 181 computations (23.3% saved)

Precisions

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

ival-cos: 2.0ms (40.6% of total)

ival-sub: 1.0ms (20.3% of total)

ival-div: 1.0ms (20.3% of total)

ival-mult: 1.0ms (20.3% of total)

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

exact: 0.0ms (0% of total)

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

bsearch2.0ms (0%)

Memory

3.2MiB live, 3.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.04028993806797688	96202.993662193

Compiler

Compiled 236 to 172 computations (27.1% saved)

bsearch5.0ms (0.1%)

Memory

-33.9MiB live, 3.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
5.0ms	0.04028993806797688	96202.993662193

Compiler

Compiled 236 to 172 computations (27.1% saved)

bsearch16.0ms (0.2%)

Memory

29.8MiB live, 29.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	8.754731683211003e+75	5.287620491997895e+80

Samples

9.0ms

128×

valid

Compiler

Compiled 91 to 98 computations (-7.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-cos: 4.0ms (58.9% of total)

ival-sub: 1.0ms (14.7% of total)

ival-div: 1.0ms (14.7% of total)

ival-mult: 1.0ms (14.7% of total)

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

exact: 0.0ms (0% of total)

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

simplify31.0ms (0.4%)

Memory

-29.7MiB live, 53.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	162
1	51	162
2	57	162
3	61	162
4	63	162

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal 7566047373982433/72057594037927936 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (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))) (.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(if (<=.f64 x #s(literal 7566047373982433/72057594037927936 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (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))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x))
(if (<=.f64 x #s(literal 7566047373982433/72057594037927936 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (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))) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 x x)))
(/.f64 #s(literal -1 binary64) #s(approx (/ x (/ (- (cos x) 1) x)) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -2 binary64))))
(if (<=.f64 x #s(literal 59999999999999996395855892718367073181509239082549374496860282078218155982848 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x)))
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))

Outputs
(if (<=.f64 x #s(literal 7566047373982433/72057594037927936 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (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))) (.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(if (<=.f64 x #s(literal 7566047373982433/72057594037927936 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (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))) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 x #s(literal -2 binary64))))
(if (<=.f64 x #s(literal 7566047373982433/72057594037927936 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (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))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x))
(if (<=.f64 x #s(literal 7566047373982433/72057594037927936 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (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))) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 x x)))
(/.f64 #s(literal -1 binary64) #s(approx (/ x (/ (- (cos x) 1) x)) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -2 binary64))))
(if (<=.f64 x #s(literal 59999999999999996395855892718367073181509239082549374496860282078218155982848 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (*.f64 x x)))
#s(approx (/ (- 1 (cos x)) (* x x)) #s(literal 1/2 binary64))

soundness1.6s (18.4%)

Memory

15.6MiB live, 690.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	284
1	105	284
2	258	284
3	609	284
4	1290	284
5	1996	284
6	2309	284
7	3163	284
8	4640	284
9	6288	284
10	7165	284
11	7380	284
12	7398	284
13	7400	284
14	7806	284
0	8015	266
0	95	1820
1	249	1768
2	601	1768
3	1848	1768
4	3837	1768
5	4425	1768
6	6307	1768
0	8169	1666
0	6	17
0	10	17
1	40	17
2	268	17
3	2810	17
0	9656	17
0	128	1640
1	357	1640
2	903	1628
3	3019	1628
4	4442	1628
5	6771	1628
0	8525	1520
0	38	195
0	66	178
1	251	146
2	1670	146
0	8565	146

Stop Event

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

Compiler

Compiled 212 to 98 computations (53.8% saved)

preprocess84.0ms (1%)

Memory: 22.6MiB live, 136.2MiB allocated
Compiler: Compiled 298 to 122 computations (59.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze2.0ms (0%)

sample2.0s (23.1%)

explain134.0ms (1.6%)

preprocess54.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify22.0ms (0.3%)

localize57.0ms (0.7%)

series3.0ms (0%)

simplify301.0ms (3.5%)

rewrite155.0ms (1.8%)

eval77.0ms (0.9%)

prune21.0ms (0.3%)

simplify125.0ms (1.5%)

localize196.0ms (2.3%)

series17.0ms (0.2%)

simplify164.0ms (1.9%)

rewrite159.0ms (1.9%)

eval668.0ms (7.9%)

prune47.0ms (0.6%)

simplify116.0ms (1.4%)

localize268.0ms (3.2%)

series43.0ms (0.5%)

simplify221.0ms (2.6%)

rewrite235.0ms (2.8%)

eval262.0ms (3.1%)

prune86.0ms (1%)

simplify229.0ms (2.7%)

localize371.0ms (4.4%)

series41.0ms (0.5%)

simplify210.0ms (2.5%)

rewrite199.0ms (2.3%)

eval200.0ms (2.4%)

prune51.0ms (0.6%)

regimes31.0ms (0.4%)

regimes12.0ms (0.1%)

regimes10.0ms (0.1%)

regimes10.0ms (0.1%)

regimes5.0ms (0.1%)

regimes7.0ms (0.1%)

bsearch15.0ms (0.2%)

bsearch2.0ms (0%)

bsearch5.0ms (0.1%)

bsearch16.0ms (0.2%)

simplify31.0ms (0.4%)

soundness1.6s (18.4%)

preprocess84.0ms (1%)

end0.0ms (0%)

Profiling