Metrics for ENA, Section 1.4, Mentioned, A

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze3.0ms (0%)

Memory

8.8MiB live, 8.8MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	49.6%	50.4%	0%	0%	0%	0
0%	0%	49.6%	50.4%	0%	0%	0%	1
0%	0%	49.6%	50.4%	0%	0%	0%	2
50%	24.8%	24.8%	50.4%	0%	0%	0%	3
75%	37.2%	12.4%	50.4%	0%	0%	0%	4
87.5%	43.4%	6.2%	50.4%	0%	0%	0%	5
93.8%	46.5%	3.1%	50.4%	0%	0%	0%	6
96.9%	48.1%	1.6%	50.4%	0%	0%	0%	7
98.4%	48.8%	0.8%	50.4%	0%	0%	0%	8
99.2%	49.2%	0.4%	50.4%	0%	0%	0%	9
99.6%	49.4%	0.2%	50.4%	0%	0%	0%	10
99.8%	49.5%	0.1%	50.4%	0%	0%	0%	11
99.9%	49.6%	0%	50.4%	0%	0%	0%	12

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample3.1s (33.3%)

Memory

-85.7MiB live, 3 059.4MiB allocated

Samples

2.2s	5 724×	2	valid
402.0ms	2 447×	1	valid
11.0ms	85×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 2.1s

ival-cos: 1.3s (62.1% of total)

const: 259.0ms (12.5% of total)

adjust: 247.0ms (12% of total)

ival-sub: 158.0ms (7.7% of total)

ival-<=: 97.0ms (4.7% of total)

ival-and: 12.0ms (0.6% of total)

exact: 5.0ms (0.2% of total)

ival-assert: 4.0ms (0.2% of total)

Bogosity

explain167.0ms (1.8%)

Memory

-45.7MiB live, 215.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
131	1	(-1.1181352526505912e-161)	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(cos.f64 x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	132	0

Confusion

	Predicted +	Predicted -
+	131	0
-	1	124

Precision

0.9924242424242424

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	131	0	0
-	1	0	124

Precision?

0.9924242424242424

Recall?

1.0

Freqs

test

number	freq
0	124
1	132

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

89.0ms	348×	2	valid
13.0ms	160×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 71.0ms

ival-cos: 53.0ms (74.5% of total)

adjust: 10.0ms (14.1% of total)

ival-sub: 7.0ms (9.8% of total)

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

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

exact: 0.0ms (0% of total)

preprocess14.0ms (0.1%)

Memory

15.7MiB live, 15.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	16	8
2	35	8
3	55	8
4	87	8
5	101	8
6	107	8
0	4	4
0	6	4
1	10	4
2	14	4
3	19	4
4	25	4
5	33	4
6	43	4
7	54	4
8	57	4
0	57	4

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 4 to 4 computations (0% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.9%	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Compiler

Compiled 4 to 4 computations (0% saved)

simplify4.0ms (0%)

Memory

3.3MiB live, 3.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
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	4	8
0	6	8
1	10	8
2	14	8
3	19	8
4	25	8
5	33	8
6	43	8
7	54	8
8	57	8
0	57	8

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize85.0ms (0.9%)

Memory

7.2MiB live, 79.7MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(cos.f64 x)
accuracy	30.114186590105078	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Samples

72.0ms	174×	2	valid
7.0ms	80×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 18 to 10 computations (44.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 69.0ms

ival-cos: 60.0ms (87.2% of total)

adjust: 5.0ms (7.3% of total)

ival-sub: 4.0ms (5.8% of total)

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

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

exact: 0.0ms (0% of total)

series1.0ms (0%)

Memory

2.5MiB live, 2.5MiB allocated

Counts

2 → 24

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>) () ())

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>) () ())

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 (- 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 (- 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>) () ())) ())

Calls

3 calls:

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

simplify581.0ms (6.2%)

Memory

6.4MiB live, 308.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	144
1	101	144
2	246	144
3	588	144
4	1237	144
5	1916	144
6	2187	144
7	2836	144
8	4071	144
9	5644	144
10	6543	144
11	6823	144
12	6862	144
13	6862	144
14	7274	144
15	7556	144
16	7597	144
17	7599	144
18	7599	144
19	7599	144
20	7599	144
21	7609	144
22	7609	144
23	7609	144
0	8514	132

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 24

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)))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)

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)))
(- 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)
(- 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)

rewrite214.0ms (2.3%)

Memory

-17.2MiB live, 311.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
0	6	6
1	23	6
2	142	6
3	1153	6
0	9240	6

Stop Event

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

Counts

2 → 314

Calls

Call 1

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

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

eval65.0ms (0.7%)

Memory: 11.9MiB live, 90.2MiB allocated
Compiler: Compiled 9 533 to 916 computations (90.4% saved)

prune9.0ms (0.1%)

Memory

5.7MiB live, 41.2MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	333	5	338
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	334	5	339

Accuracy

100.0%

Counts

339 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.9%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
▶	52.1%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
▶	100.0%	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))
▶	100.0%	#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
▶	99.6%	#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))

Compiler

Compiled 74 to 60 computations (18.9% saved)

simplify12.0ms (0.1%)

Memory

-11.4MiB live, 23.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	126
0	38	126
1	61	126
2	89	126
3	126	126
4	153	126
5	176	126
6	198	126
7	221	126
8	226	126
0	226	126

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize185.0ms (2%)

Memory

10.0MiB live, 256.8MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0	#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
accuracy	0.00390625	(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
accuracy	0.0078125	(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
accuracy	0	(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
accuracy	0	(*.f64 x x)
accuracy	0	#s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
accuracy	30.114186590105078	(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(.f64 (.f64 x x) #s(literal 1/2 binary64))
accuracy	0.28173897622938354	#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
accuracy	0.32903163143851444	#s(approx (cos x) #s(literal 1 binary64))
accuracy	30.114186590105078	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
accuracy	0	(/.f64 x #s(literal 2 binary64))
accuracy	0	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))
accuracy	0	(tan.f64 (/.f64 x #s(literal 2 binary64)))
accuracy	0	(sin.f64 x)

Samples

124.0ms	174×	2	valid
41.0ms	80×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 207 to 44 computations (78.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 139.0ms

ival-mult: 53.0ms (38.1% of total)

ival-cos: 46.0ms (33.1% of total)

adjust: 21.0ms (15.1% of total)

ival-sub: 4.0ms (2.9% of total)

ival-tan: 4.0ms (2.9% of total)

const: 4.0ms (2.9% of total)

ival-div: 2.0ms (1.4% of total)

ival-add: 2.0ms (1.4% of total)

ival-sin: 2.0ms (1.4% of total)

exact: 1.0ms (0.7% of total)

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

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

series19.0ms (0.2%)

Memory

15.5MiB live, 46.4MiB allocated

Counts

16 → 192

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
9.0ms	x	@	inf	((* (sin x) (tan (/ x 2))) (sin x) (tan (/ x 2)) (/ x 2) (- 1 (cos x)) (cos x) (- 1 (cos x)) (* (* x x) 1/2) (* x x) (- 1 (cos x)) (cos x) (+ (* -1/2 (* x x)) 1) (- 1 (cos x)) (* (* (+ (* -1/24 (* x x)) 1/2) x) x) (* (+ (* -1/24 (* x x)) 1/2) x) (+ (* -1/24 (* x x)) 1/2))
2.0ms	x	@	-inf	((* (sin x) (tan (/ x 2))) (sin x) (tan (/ x 2)) (/ x 2) (- 1 (cos x)) (cos x) (- 1 (cos x)) (* (* x x) 1/2) (* x x) (- 1 (cos x)) (cos x) (+ (* -1/2 (* x x)) 1) (- 1 (cos x)) (* (* (+ (* -1/24 (* x x)) 1/2) x) x) (* (+ (* -1/24 (* x x)) 1/2) x) (+ (* -1/24 (* x x)) 1/2))
2.0ms	x	@	0	((* (sin x) (tan (/ x 2))) (sin x) (tan (/ x 2)) (/ x 2) (- 1 (cos x)) (cos x) (- 1 (cos x)) (* (* x x) 1/2) (* x x) (- 1 (cos x)) (cos x) (+ (* -1/2 (* x x)) 1) (- 1 (cos x)) (* (* (+ (* -1/24 (* x x)) 1/2) x) x) (* (+ (* -1/24 (* x x)) 1/2) x) (+ (* -1/24 (* x x)) 1/2))

Time

Variable

Point

Expression

9.0ms

inf

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

2.0ms

-inf

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

2.0ms

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

simplify200.0ms (2.1%)

Memory

8.7MiB live, 283.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	102	1286
1	272	1280
2	689	1280
3	2133	1280
4	4257	1280
5	6593	1280
0	8559	1190

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 191

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))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 (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)))
(* 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))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 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
(+ 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
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -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 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* -1/24 (pow x 2))))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* -1/24 (pow x 2)))
(/ (* (sin x) (sin (* 1/2 x))) (cos (* 1/2 x)))
(/ (* (sin x) (sin (* 1/2 x))) (cos (* 1/2 x)))
(/ (* (sin x) (sin (* 1/2 x))) (cos (* 1/2 x)))
(/ (* (sin x) (sin (* 1/2 x))) (cos (* 1/2 x)))
(sin x)
(sin x)
(sin x)
(sin x)
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -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))
(/ (* (sin x) (sin (* 1/2 x))) (cos (* 1/2 x)))
(/ (* (sin x) (sin (* 1/2 x))) (cos (* 1/2 x)))
(/ (* (sin x) (sin (* 1/2 x))) (cos (* 1/2 x)))
(/ (* (sin x) (sin (* 1/2 x))) (cos (* 1/2 x)))
(sin x)
(sin x)
(sin x)
(sin x)
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 3))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (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))

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

rewrite190.0ms (2%)

Memory

9.5MiB live, 229.7MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	109
0	38	109
1	129	109
2	770	109
3	6267	106
0	8414	106

Stop Event

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

Counts

16 → 609

Calls

Call 1

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

Outputs
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eval394.0ms (4.2%)

Memory: -30.4MiB live, 276.0MiB allocated
Compiler: Compiled 15 108 to 2 131 computations (85.9% saved)

prune25.0ms (0.3%)

Memory

-16.6MiB live, 69.5MiB allocated

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	843	3	846
Fresh	0	0	0
Picked	2	3	5
Done	0	0	0
Total	845	6	851

Accuracy

100.0%

Counts

851 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.9%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
✓	52.1%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
▶	4.2%	(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
▶	100.0%	#s(approx (- 1 (cos x)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))))
✓	100.0%	#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
▶	99.6%	#s(approx (- 1 (cos x)) (.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x))

Compiler

Compiled 46 to 38 computations (17.4% saved)

simplify6.0ms (0.1%)

Memory

9.9MiB live, 9.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
cost-diff	0	#s(approx (cos x) #s(literal 1 binary64))
cost-diff	0	(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
cost-diff	0	(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64)))
cost-diff	0	#s(approx (- 1 (cos x)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))))
cost-diff	0	#s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64))
cost-diff	0	(.f64 #s(approx (+ ( -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x)
cost-diff	0	(.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x)
cost-diff	0	#s(approx (- 1 (cos x)) (.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	104
0	29	104
1	46	104
2	55	104
3	60	104
4	67	104
5	75	104
6	85	104
7	96	104
8	99	104
0	99	100

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

Outputs
#s(approx (- 1 (cos x)) (.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x))
(.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x)
(.f64 #s(approx (+ ( -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x)
#s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
#s(approx (- 1 (cos x)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))))
#s(approx (- 1 (cos x)) (fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64)))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(pow.f64 x #s(literal 4 binary64))
#s(literal 4 binary64)
#s(literal -1/24 binary64)
(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (cos x) #s(literal 1 binary64))
#s(literal 1 binary64)

localize183.0ms (1.9%)

Memory

17.6MiB live, 204.3MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	0.32903163143851444	#s(approx (cos x) #s(literal 1 binary64))
accuracy	0	(pow.f64 x #s(literal 4 binary64))
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0	#s(approx (- 1 (cos x)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))))
accuracy	0.1015625	(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
accuracy	0	#s(approx (- 1 (cos x)) (.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x))
accuracy	0.00390625	(.f64 #s(approx (+ ( -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x)
accuracy	0.0078125	(.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x)
accuracy	0.288650052486077	#s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64))

Samples

149.0ms	174×	2	valid
20.0ms	80×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 136 to 36 computations (73.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 149.0ms

adjust: 38.0ms (25.5% of total)

const: 30.0ms (20.2% of total)

ival-sub: 29.0ms (19.5% of total)

ival-cos: 28.0ms (18.8% of total)

ival-mult: 12.0ms (8.1% of total)

ival-add: 8.0ms (5.4% of total)

ival-pow: 3.0ms (2% of total)

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

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

exact: 0.0ms (0% of total)

series8.0ms (0.1%)

Memory

17.7MiB live, 17.7MiB allocated

Counts

11 → 132

Calls

Call 1

Inputs
#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x) (patch (.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (+ ( -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) (patch (.f64 #s(approx (+ ( -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())
#s(alt #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) (patch #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- 1 (cos x)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64)))) (patch #s(approx (- 1 (cos x)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))) (patch (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64)) (patch (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (+.f64 #s(approx (cos x) #s(literal 1 binary64)) #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 (pow.f64 x #s(literal 4 binary64)) (patch (pow.f64 x #s(literal 4 binary64)) #<representation binary64>) () ())

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

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

inf

((- 1 (cos x)) (* (* (+ (* -1/24 (* x x)) 1/2) x) x) (* (+ (* -1/24 (* x x)) 1/2) x) (+ (* -1/24 (* x x)) 1/2) (- 1 (cos x)) (+ (* (* 1/2 x) x) (* (pow x 4) -1/24)) (* 1/2 x) (* (pow x 4) -1/24) (+ (cos x) 1) (cos x) (pow x 4))

2.0ms

-inf

((- 1 (cos x)) (* (* (+ (* -1/24 (* x x)) 1/2) x) x) (* (+ (* -1/24 (* x x)) 1/2) x) (+ (* -1/24 (* x x)) 1/2) (- 1 (cos x)) (+ (* (* 1/2 x) x) (* (pow x 4) -1/24)) (* 1/2 x) (* (pow x 4) -1/24) (+ (cos x) 1) (cos x) (pow x 4))

1.0ms

((- 1 (cos x)) (* (* (+ (* -1/24 (* x x)) 1/2) x) x) (* (+ (* -1/24 (* x x)) 1/2) x) (+ (* -1/24 (* x x)) 1/2) (- 1 (cos x)) (+ (* (* 1/2 x) x) (* (pow x 4) -1/24)) (* 1/2 x) (* (pow x 4) -1/24) (+ (cos x) 1) (cos x) (pow x 4))

simplify172.0ms (1.8%)

Memory

-53.7MiB live, 166.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	832
1	154	832
2	375	832
3	1011	832
4	2546	832
5	5941	832
0	8123	772

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

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

Outputs
(* 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 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (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 2))
(.f64 (.f64 x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* 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 (* -1/24 (pow x 2))))
(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (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 2))
(.f64 (.f64 x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
2
#s(literal 2 binary64)
(+ 2 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64))
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 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* -1/24 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/24 binary64))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(* -1/24 (pow x 2))
(.f64 #s(literal -1/24 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 #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))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(+ 1 (cos x))
(+.f64 (cos.f64 x) #s(literal 1 binary64))
(+ 1 (cos x))
(+.f64 (cos.f64 x) #s(literal 1 binary64))
(+ 1 (cos x))
(+.f64 (cos.f64 x) #s(literal 1 binary64))
(+ 1 (cos x))
(+.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)
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* -1/24 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/24 binary64))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(* -1/24 (pow x 2))
(.f64 #s(literal -1/24 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 #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))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(+ 1 (cos x))
(+.f64 (cos.f64 x) #s(literal 1 binary64))
(+ 1 (cos x))
(+.f64 (cos.f64 x) #s(literal 1 binary64))
(+ 1 (cos x))
(+.f64 (cos.f64 x) #s(literal 1 binary64))
(+ 1 (cos x))
(+.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)
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))

rewrite171.0ms (1.8%)

Memory

37.8MiB live, 223.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	97
0	29	97
1	102	97
2	617	97
3	5535	97
0	8367	93

Stop Event

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

Counts

11 → 189

Calls

Call 1

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

Outputs
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eval36.0ms (0.4%)

Memory: -1.9MiB live, 90.5MiB allocated
Compiler: Compiled 5 441 to 723 computations (86.7% saved)

prune10.0ms (0.1%)

Memory

-5.0MiB live, 31.2MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	319	2	321
Fresh	0	0	0
Picked	2	1	3
Done	0	3	3
Total	321	6	327

Accuracy

100.0%

Counts

327 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.9%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
✓	52.1%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
▶	100.0%	#s(approx (- 1 (cos x)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal -1/24 binary64))))
✓	100.0%	#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
✓	99.6%	#s(approx (- 1 (cos x)) (.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x))
▶	4.2%	#s(approx (+ (cos x) 1) #s(literal 2 binary64))

Compiler

Compiled 48 to 37 computations (22.9% saved)

simplify8.0ms (0.1%)

Memory

-24.3MiB live, 13.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	65
0	21	65
1	37	57
2	61	49
3	96	49
4	107	49
5	118	49
6	128	49
7	142	49
8	146	49
0	146	49

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

Outputs
#s(approx (+ (cos x) 1) #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (- 1 (cos x)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal -1/24 binary64))))
#s(approx (- 1 (cos x)) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal -1/24 binary64)))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 4 binary64))))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
(.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/24 binary64))
(*.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 4 binary64)))
(.f64 (.f64 x x) (*.f64 x x))
(pow.f64 x #s(literal 4 binary64))
(*.f64 x x)
#s(literal -1/24 binary64)

localize135.0ms (1.4%)

Memory

-3.9MiB live, 239.8MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0	#s(approx (- 1 (cos x)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal -1/24 binary64))))
accuracy	0.1015625	(.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/24 binary64))
accuracy	0.11947250976844202	(.f64 (.f64 x x) (*.f64 x x))
accuracy	0.3134083294388077	#s(approx (+ (cos x) 1) #s(literal 2 binary64))

Samples

81.0ms	174×	2	valid
22.0ms	2×	0	valid
15.0ms	80×	1	valid

Compiler

Compiled 108 to 27 computations (75% saved)

Precisions

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

ival-mult: 30.0ms (34.4% of total)

ival-cos: 30.0ms (34.4% of total)

adjust: 11.0ms (12.6% of total)

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

ival-sub: 5.0ms (5.7% of total)

const: 4.0ms (4.6% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

19.3MiB live, 19.3MiB allocated

Counts

6 → 72

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify239.0ms (2.5%)

Memory

7.0MiB live, 156.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	406
1	118	406
2	271	406
3	629	406
4	1377	406
5	2340	406
6	3012	406
7	5788	406
0	8179	385

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

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

Outputs
2
#s(literal 2 binary64)
(+ 2 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64))
(+ 2 (* (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 2 binary64))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (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 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(+ 1 (cos x))
(-.f64 (cos.f64 x) #s(literal -1 binary64))
(+ 1 (cos x))
(-.f64 (cos.f64 x) #s(literal -1 binary64))
(+ 1 (cos x))
(-.f64 (cos.f64 x) #s(literal -1 binary64))
(+ 1 (cos x))
(-.f64 (cos.f64 x) #s(literal -1 binary64))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(+ 1 (cos x))
(-.f64 (cos.f64 x) #s(literal -1 binary64))
(+ 1 (cos x))
(-.f64 (cos.f64 x) #s(literal -1 binary64))
(+ 1 (cos x))
(-.f64 (cos.f64 x) #s(literal -1 binary64))
(+ 1 (cos x))
(-.f64 (cos.f64 x) #s(literal -1 binary64))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))

rewrite203.0ms (2.2%)

Memory

-14.7MiB live, 189.2MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	58
0	21	50
1	72	42
2	478	42
3	5132	42
0	9204	42

Stop Event

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

Counts

6 → 129

Calls

Call 1

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

Outputs
#<batchref>
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#<batchref>

eval42.0ms (0.4%)

Memory: 0.4MiB live, 38.0MiB allocated
Compiler: Compiled 3 955 to 537 computations (86.4% saved)

prune6.0ms (0.1%)

Memory

17.7MiB live, 17.7MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	201	6	207

Accuracy

100.0%

Counts

207 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.9%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
✓	52.1%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
✓	100.0%	#s(approx (- 1 (cos x)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal -1/24 binary64))))
✓	100.0%	#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
✓	99.6%	#s(approx (- 1 (cos x)) (.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x))
✓	4.2%	#s(approx (+ (cos x) 1) #s(literal 2 binary64))

Compiler

Compiled 128 to 77 computations (39.8% saved)

regimes25.0ms (0.3%)

Memory

-28.2MiB live, 19.7MiB allocated

Counts

11 → 1

Calls

Call 1

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

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

Calls

3 calls:

18.0ms	x
3.0ms	(cos.f64 x)
3.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Results

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

Compiler

Compiled 7 to 7 computations (0% saved)

regimes8.0ms (0.1%)

Memory

10.9MiB live, 10.9MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 7 to 7 computations (0% saved)

regimes7.0ms (0.1%)

Memory

10.2MiB live, 10.2MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
99.6%	1	`(cos.f64 x)`

Compiler

Compiled 7 to 7 computations (0% saved)

regimes6.0ms (0.1%)

Memory

9.8MiB live, 9.8MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
99.6%	1	`(cos.f64 x)`

Compiler

Compiled 7 to 7 computations (0% saved)

regimes21.0ms (0.2%)

Memory

-30.2MiB live, 9.5MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs
#s(approx (+ (cos x) 1) #s(literal 2 binary64))
(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))

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

Calls

3 calls:

17.0ms	x
1.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))
1.0ms	(cos.f64 x)

Results

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

Compiler

Compiled 7 to 7 computations (0% saved)

regimes5.0ms (0%)

Memory

7.4MiB live, 7.4MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (+ (cos x) 1) #s(literal 2 binary64))
(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))

Outputs
#s(approx (+ (cos x) 1) #s(literal 2 binary64))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
4.2%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
4.2%	1	`(cos.f64 x)`
4.2%	1	`x`

Compiler

Compiled 7 to 7 computations (0% saved)

simplify41.0ms (0.4%)

Memory

-9.4MiB live, 30.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	74
1	42	74
2	46	74
3	48	74
4	49	74

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness2.7s (28.2%)

Memory

6.8MiB live, 775.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	832
1	154	832
2	375	832
3	1011	832
4	2546	832
5	5941	832
0	8123	772
0	41	144
1	101	144
2	246	144
3	588	144
4	1237	144
5	1916	144
6	2187	144
7	2836	144
8	4071	144
9	5644	144
10	6543	144
11	6823	144
12	6862	144
13	6862	144
14	7274	144
15	7556	144
16	7597	144
17	7599	144
18	7599	144
19	7599	144
20	7599	144
21	7609	144
22	7609	144
23	7609	144
0	8514	132
0	24	109
0	38	109
1	129	109
2	770	109
3	6267	106
0	8414	106
0	21	97
0	29	97
1	102	97
2	617	97
3	5535	97
0	8367	93
0	102	1286
1	272	1280
2	689	1280
3	2133	1280
4	4257	1280
5	6593	1280
0	8559	1190

Stop Event

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

Compiler

Compiled 115 to 79 computations (31.3% saved)

preprocess111.0ms (1.2%)

Memory: -5.3MiB live, 111.2MiB allocated
Remove: (abs x)
Compiler: Compiled 178 to 106 computations (40.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	6	9
1	16	8
2	35	8
3	55	8
4	87	8
5	101	8
6	107	8
0	4	4
0	6	4
1	10	4
2	14	4
3	19	4
4	25	4
5	33	4
6	43	4
7	54	4
8	57	4
0	57	4

Iter	Nodes	Cost
0	24	126
0	38	126
1	61	126
2	89	126
3	126	126
4	153	126
5	176	126
6	198	126
7	221	126
8	226	126
0	226	126

Iter	Nodes	Cost
0	21	104
0	29	104
1	46	104
2	55	104
3	60	104
4	67	104
5	75	104
6	85	104
7	96	104
8	99	104
0	99	100

Iter	Nodes	Cost
0	15	65
0	21	65
1	37	57
2	61	49
3	96	49
4	107	49
5	118	49
6	128	49
7	142	49
8	146	49
0	146	49

Iter	Nodes	Cost
0	6	9
1	16	8
2	35	8
3	55	8
4	87	8
5	101	8
6	107	8
0	4	4
0	6	4
1	10	4
2	14	4
3	19	4
4	25	4
5	33	4
6	43	4
7	54	4
8	57	4
0	57	4

Iter	Nodes	Cost
0	24	126
0	38	126
1	61	126
2	89	126
3	126	126
4	153	126
5	176	126
6	198	126
7	221	126
8	226	126
0	226	126

Iter	Nodes	Cost
0	21	104
0	29	104
1	46	104
2	55	104
3	60	104
4	67	104
5	75	104
6	85	104
7	96	104
8	99	104
0	99	100

Iter	Nodes	Cost
0	15	65
0	21	65
1	37	57
2	61	49
3	96	49
4	107	49
5	118	49
6	128	49
7	142	49
8	146	49
0	146	49

start0.0ms (0%)

analyze3.0ms (0%)

sample3.1s (33.3%)

explain167.0ms (1.8%)

preprocess14.0ms (0.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0%)

localize85.0ms (0.9%)

series1.0ms (0%)

simplify581.0ms (6.2%)

rewrite214.0ms (2.3%)

eval65.0ms (0.7%)

prune9.0ms (0.1%)

simplify12.0ms (0.1%)

localize185.0ms (2%)

series19.0ms (0.2%)

simplify200.0ms (2.1%)

rewrite190.0ms (2%)

eval394.0ms (4.2%)

prune25.0ms (0.3%)

simplify6.0ms (0.1%)

localize183.0ms (1.9%)

series8.0ms (0.1%)

simplify172.0ms (1.8%)

rewrite171.0ms (1.8%)

eval36.0ms (0.4%)

prune10.0ms (0.1%)

simplify8.0ms (0.1%)

localize135.0ms (1.4%)

series5.0ms (0.1%)

simplify239.0ms (2.5%)

rewrite203.0ms (2.2%)

eval42.0ms (0.4%)

prune6.0ms (0.1%)

regimes25.0ms (0.3%)

regimes8.0ms (0.1%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes21.0ms (0.2%)

regimes5.0ms (0%)

simplify41.0ms (0.4%)

soundness2.7s (28.2%)

preprocess111.0ms (1.2%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	6	9
1	16	8
2	35	8
3	55	8
4	87	8
5	101	8
6	107	8
0	4	4
0	6	4
1	10	4
2	14	4
3	19	4
4	25	4
5	33	4
6	43	4
7	54	4
8	57	4
0	57	4

Iter	Nodes	Cost
0	24	126
0	38	126
1	61	126
2	89	126
3	126	126
4	153	126
5	176	126
6	198	126
7	221	126
8	226	126
0	226	126

Iter	Nodes	Cost
0	21	104
0	29	104
1	46	104
2	55	104
3	60	104
4	67	104
5	75	104
6	85	104
7	96	104
8	99	104
0	99	100

Iter	Nodes	Cost
0	15	65
0	21	65
1	37	57
2	61	49
3	96	49
4	107	49
5	118	49
6	128	49
7	142	49
8	146	49
0	146	49