Metrics for ENA, Section 1.4, Mentioned, A

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze3.0ms (0%)

Memory

3.8MiB live, 3.8MiB 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 (37.6%)

Memory

0.2MiB live, 2 946.9MiB allocated

Samples

2.2s	5 711×	2	valid
508.0ms	2 464×	1	valid
6.0ms	81×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 2.3s

ival-cos: 1.4s (61.8% of total)

adjust: 303.0ms (13.1% of total)

const: 275.0ms (11.9% of total)

ival-sub: 186.0ms (8.1% of total)

ival-<=: 96.0ms (4.2% of total)

ival-and: 12.0ms (0.5% of total)

exact: 6.0ms (0.3% of total)

ival-assert: 3.0ms (0.1% of total)

Bogosity

explain167.0ms (2%)

Memory

-19.4MiB live, 218.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
139	-	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(cos.f64 x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	139	0

Confusion

	Predicted +	Predicted -
+	139	0
-	0	117

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	139	0	0
-	0	0	117

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	117
1	139

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

116.0ms	360×	2	valid
12.0ms	152×	1	valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 110.0ms

ival-cos: 52.0ms (47.5% of total)

adjust: 44.0ms (40.2% of total)

ival-sub: 12.0ms (11% of total)

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

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

exact: 0.0ms (0% of total)

preprocess13.0ms (0.2%)

Memory

25.4MiB live, 25.4MiB 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	102	8
6	109	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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.5%	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Compiler

Compiled 4 to 4 computations (0% saved)

simplify3.0ms (0%)

Memory

5.9MiB live, 5.9MiB 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

localize62.0ms (0.7%)

Memory

-18.2MiB live, 99.1MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(cos.f64 x)
accuracy	31.66799108338649	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Samples

50.0ms	180×	2	valid
6.0ms	76×	1	valid

Compiler

Compiled 18 to 10 computations (44.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-cos: 35.0ms (77.4% of total)

adjust: 6.0ms (13.3% of total)

ival-sub: 4.0ms (8.8% 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

1.7MiB live, 1.7MiB 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))

simplify509.0ms (6.1%)

Memory

29.7MiB live, 331.9MiB 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	2425	144
7	3090	144
8	4387	144
9	5950	144
10	6859	144
11	7140	144
12	7179	144
13	7179	144
14	7601	144
15	7887	144
16	7928	144
17	7930	144
18	7930	144
19	7930	144
20	7930	144
21	7940	144
22	7940	144
23	7940	144
0	8845	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)

rewrite190.0ms (2.3%)

Memory

-6.2MiB live, 256.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
0	6	6
1	23	6
2	144	6
3	1181	6
0	8968	6

Stop Event

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

Counts

2 → 137

Calls

Call 1

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

Outputs
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eval20.0ms (0.2%)

Memory: -4.7MiB live, 44.5MiB allocated
Compiler: Compiled 3 413 to 442 computations (87% saved)

prune3.0ms (0%)

Memory

12.4MiB live, 12.4MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	3	162

Accuracy

100.0%

Counts

162 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.2%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 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))
▶	99.9%	#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))

Status

Accuracy

Program

▶

50.2%

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

▶

99.9%

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

Compiler

Compiled 21 to 17 computations (19% saved)

simplify7.0ms (0.1%)

Memory

16.6MiB live, 16.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
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	(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	(.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)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	76
0	22	76
1	38	76
2	60	76
3	93	76
4	116	76
5	133	76
6	149	76
7	166	76
8	170	76
0	170	76

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#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)
#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)
(-.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))

Outputs
#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)
#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)
(-.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))

localize162.0ms (1.9%)

Memory

-57.4MiB live, 171.1MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score
accuracy	0.08557743051330956	#s(approx (cos x) #s(literal 1 binary64))
accuracy	31.66799108338649	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
accuracy	0	(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
accuracy	0	(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
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	(*.f64 x x)
accuracy	0.00390625	(.f64 (.f64 x x) #s(literal 1/2 binary64))
accuracy	0.06239129719312811	#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))

Samples

61.0ms	180×	2	valid
14.0ms	76×	1	valid

Compiler

Compiled 124 to 27 computations (78.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 56.0ms

ival-cos: 28.0ms (50.4% of total)

adjust: 10.0ms (18% of total)

ival-mult: 8.0ms (14.4% of total)

ival-sub: 4.0ms (7.2% of total)

const: 4.0ms (7.2% of total)

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

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

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

exact: 0.0ms (0% of total)

series7.0ms (0.1%)

Memory

11.1MiB live, 11.1MiB allocated

Counts

9 → 108

Calls

Call 1

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

Outputs
#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 #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 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 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 (* (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 (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 (* (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 (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 (* 1/2 (pow x 2)) (taylor 0 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 2) (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 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 2) (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 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 2) (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 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 (* 1/2 x) (taylor 0 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 (* x (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 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 (* x (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 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 (* x (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 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 1/2 (taylor 0 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 (+ 1/2 (* -1/24 (pow x 2))) (taylor 0 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 (+ 1/2 (* -1/24 (pow x 2))) (taylor 0 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 (+ 1/2 (* -1/24 (pow x 2))) (taylor 0 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 (* 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 (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>) () ())) ())
#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 (* (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 (- 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>) () ())) ())
#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>) () ())) ())
#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>) () ())) ())

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

-inf

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

1.0ms

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

simplify173.0ms (2.1%)

Memory

15.8MiB live, 130.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	698
1	146	698
2	375	698
3	995	698
4	2550	698
5	5964	698
0	8176	647

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

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

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

rewrite238.0ms (2.8%)

Memory

-3.5MiB live, 303.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	67
0	22	67
1	77	67
2	460	67
3	3772	67
0	11975	67

Stop Event

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

Counts

9 → 290

Calls

Call 1

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

Outputs
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eval71.0ms (0.8%)

Memory: 10.4MiB live, 122.2MiB allocated
Compiler: Compiled 7 206 to 1 153 computations (84% saved)

prune59.0ms (0.7%)

Memory

-39.6MiB live, 49.5MiB allocated

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	414	2	416
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	415	4	419

Accuracy

100.0%

Counts

419 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.2%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
▶	4.1%	(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 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))
▶	99.9%	#s(approx (- 1 (cos x)) (.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x))

Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify5.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 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	#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	15	64
0	18	64
1	30	64
2	38	64
3	43	64
4	50	64
5	58	64
6	68	64
7	79	64
8	82	64
0	82	60

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
(+.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
(+.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)

localize92.0ms (1.1%)

Memory

-8.8MiB live, 177.0MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	0.08557743051330956	#s(approx (cos x) #s(literal 1 binary64))
accuracy	0	(.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x)
accuracy	0	(.f64 #s(approx (+ ( -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x)
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	0.0664102901437474	#s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64))

Samples

64.0ms	180×	2	valid
16.0ms	76×	1	valid

Compiler

Compiled 70 to 23 computations (67.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 65.0ms

ival-cos: 28.0ms (43.3% of total)

adjust: 12.0ms (18.6% of total)

ival-mult: 11.0ms (17% of total)

ival-add: 5.0ms (7.7% of total)

ival-sub: 4.0ms (6.2% of total)

const: 4.0ms (6.2% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0%)

Memory

12.1MiB live, 12.1MiB allocated

Counts

6 → 72

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 (+.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>) () ())

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 2 (taylor 0 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 (+ 2 (* -1/2 (pow x 2))) (taylor 0 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 (+ 2 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) (taylor 0 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 (+ 2 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) (taylor 0 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 (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 (cos x)) (taylor inf 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 (cos x)) (taylor inf 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 (cos x)) (taylor inf 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 (cos x)) (taylor inf 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 (* -1/24 (pow x 4)) (taylor inf 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 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor inf 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 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor inf 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 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor inf 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 (* -1/24 (pow x 3)) (taylor inf 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 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor inf 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 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor inf 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 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor inf 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 (* -1/24 (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 (+.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 (- 1 (cos x)) (taylor -inf 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 (cos x)) (taylor -inf 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 (cos x)) (taylor -inf 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 (cos x)) (taylor -inf 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 (* -1/24 (pow x 4)) (taylor -inf 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 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor -inf 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 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor -inf 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 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor -inf 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 (* -1/24 (pow x 3)) (taylor -inf 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 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf 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 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf 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 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf 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 (* -1/24 (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 (+.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>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

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

1.0ms

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) (+ (cos x) 1) (cos x))

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) (+ (cos x) 1) (cos x))

simplify113.0ms (1.4%)

Memory

32.5MiB live, 221.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	498
1	154	498
2	383	498
3	1020	498
4	2596	498
5	6032	498
0	8046	453

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

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

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))
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))
(- 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 (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)
(- 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 (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)

rewrite264.0ms (3.2%)

Memory

-33.7MiB live, 265.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	61
0	18	61
1	69	61
2	424	61
3	3513	61
0	10914	57

Stop Event

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

Counts

6 → 85

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

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

eval16.0ms (0.2%)

Memory: -0.6MiB live, 36.0MiB allocated
Compiler: Compiled 2 017 to 299 computations (85.2% saved)

prune5.0ms (0.1%)

Memory

12.6MiB live, 12.6MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	0	0	0
Picked	1	1	2
Done	0	2	2
Total	157	4	161

Accuracy

100.0%

Counts

161 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.2%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 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))
✓	99.9%	#s(approx (- 1 (cos x)) (.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x))
▶	4.1%	#s(approx (+ (cos x) 1) #s(literal 2 binary64))

Compiler

Compiled 24 to 21 computations (12.5% saved)

simplify3.0ms (0%)

Memory

1.9MiB live, 1.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
cost-diff	0	#s(approx (+ (cos x) 1) #s(literal 2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
0	6	7
1	9	7
0	9	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

localize13.0ms (0.2%)

Memory

-22.7MiB live, 16.3MiB allocated

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
accuracy	0.07792378852281104	#s(approx (+ (cos x) 1) #s(literal 2 binary64))

Samples

10.0ms

256×

valid

Compiler

Compiled 10 to 10 computations (0% saved)

Precisions

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

ival-cos: 3.0ms (59.4% of total)

ival-add: 1.0ms (19.8% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Counts

1 → 12

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>) () ())

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 (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 (+ (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>) () ())) ())

Calls

3 calls:

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

simplify221.0ms (2.6%)

Memory

11.6MiB live, 98.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	72
1	44	72
2	95	72
3	206	72
4	364	72
5	490	72
6	599	72
7	821	72
8	1382	72
9	2196	72
10	3423	72
11	3908	72
12	3997	72
13	4030	72
14	4707	72
15	4971	72
16	4971	72
17	4971	72
18	4971	72
19	4971	72
20	4973	72
0	4973	66

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

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 (cos x))
(+ 1 (cos x))
(+ 1 (cos x))
(+ 1 (cos x))
(+ 1 (cos x))
(+ 1 (cos x))
(+ 1 (cos x))
(+ 1 (cos x))

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 (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 (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))

rewrite193.0ms (2.3%)

Memory

-17.7MiB live, 173.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
0	6	6
1	22	6
2	134	6
3	1235	6
0	8194	6

Stop Event

1×	iter limit
1×	node limit
1×	saturated

Counts

1 → 1

Calls

Call 1

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

Outputs
#<batchref>

eval2.0ms (0%)

Memory: 4.0MiB live, 4.0MiB allocated
Compiler: Compiled 80 to 20 computations (75% saved)

prune3.0ms (0%)

Memory

6.9MiB live, 6.9MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	13	4	17

Accuracy

100.0%

Counts

17 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.2%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 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))
✓	99.9%	#s(approx (- 1 (cos x)) (.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x))
✓	4.1%	#s(approx (+ (cos x) 1) #s(literal 2 binary64))

Compiler

Compiled 62 to 43 computations (30.6% saved)

regimes8.0ms (0.1%)

Memory

15.7MiB live, 15.7MiB 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))
#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 #s(literal 1 binary64) (cos.f64 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	(cos.f64 x)
2.0ms	(-.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)

regimes19.0ms (0.2%)

Memory

-22.8MiB live, 13.1MiB allocated

Counts

5 → 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))

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:

15.0ms	x
2.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))
2.0ms	(cos.f64 x)

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
99.9%	1	`(cos.f64 x)`

Compiler

Compiled 7 to 7 computations (0% saved)

regimes6.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB 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	(cos.f64 x)
2.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
99.9%	1	`(cos.f64 x)`

Compiler

Compiled 7 to 7 computations (0% saved)

regimes5.0ms (0.1%)

Memory

10.8MiB live, 10.8MiB 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:

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

Results

Accuracy	Segments	Branch
50.2%	1	`x`
50.2%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
50.2%	1	`(cos.f64 x)`

Compiler

Compiled 7 to 7 computations (0% saved)

regimes5.0ms (0.1%)

Memory

9.3MiB live, 9.3MiB 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	(cos.f64 x)
1.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Results

Accuracy	Segments	Branch
4.1%	1	`x`
4.1%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
4.1%	1	`(cos.f64 x)`

Compiler

Compiled 7 to 7 computations (0% saved)

simplify95.0ms (1.1%)

Memory

-12.5MiB live, 67.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	55
1	41	55
2	52	55
3	62	55
4	76	55
5	88	55
6	141	55
7	314	55
8	4014	55
9	6067	55
10	7357	55

Stop Event

1×	node limit

Calls

Call 1

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

soundness2.4s (28.4%)

Memory

-12.7MiB live, 620.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	67
0	22	67
1	77	67
2	460	67
3	3772	67
0	11975	67
0	59	698
1	146	698
2	375	698
3	995	698
4	2550	698
5	5964	698
0	8176	647
0	63	498
1	154	498
2	383	498
3	1020	498
4	2596	498
5	6032	498
0	8046	453
0	41	144
1	101	144
2	246	144
3	588	144
4	1237	144
5	1916	144
6	2425	144
7	3090	144
8	4387	144
9	5950	144
10	6859	144
11	7140	144
12	7179	144
13	7179	144
14	7601	144
15	7887	144
16	7928	144
17	7930	144
18	7930	144
19	7930	144
20	7930	144
21	7940	144
22	7940	144
23	7940	144
0	8845	132

Stop Event

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

Compiler

Compiled 72 to 54 computations (25% saved)

preprocess78.0ms (0.9%)

Memory: 34.8MiB live, 111.7MiB allocated
Remove: (abs x)
Compiler: Compiled 132 to 92 computations (30.3% 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	102	8
6	109	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	15	76
0	22	76
1	38	76
2	60	76
3	93	76
4	116	76
5	133	76
6	149	76
7	166	76
8	170	76
0	170	76

Iter	Nodes	Cost
0	6	9
1	16	8
2	35	8
3	55	8
4	87	8
5	102	8
6	109	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	15	76
0	22	76
1	38	76
2	60	76
3	93	76
4	116	76
5	133	76
6	149	76
7	166	76
8	170	76
0	170	76

start0.0ms (0%)

analyze3.0ms (0%)

sample3.1s (37.6%)

explain167.0ms (2%)

preprocess13.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize62.0ms (0.7%)

series1.0ms (0%)

simplify509.0ms (6.1%)

rewrite190.0ms (2.3%)

eval20.0ms (0.2%)

prune3.0ms (0%)

simplify7.0ms (0.1%)

localize162.0ms (1.9%)

series7.0ms (0.1%)

simplify173.0ms (2.1%)

rewrite238.0ms (2.8%)

eval71.0ms (0.8%)

prune59.0ms (0.7%)

simplify5.0ms (0.1%)

localize92.0ms (1.1%)

series4.0ms (0%)

simplify113.0ms (1.4%)

rewrite264.0ms (3.2%)

eval16.0ms (0.2%)

prune5.0ms (0.1%)

simplify3.0ms (0%)

localize13.0ms (0.2%)

series1.0ms (0%)

simplify221.0ms (2.6%)

rewrite193.0ms (2.3%)

eval2.0ms (0%)

prune3.0ms (0%)

regimes8.0ms (0.1%)

regimes19.0ms (0.2%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

simplify95.0ms (1.1%)

soundness2.4s (28.4%)

preprocess78.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	6	9
1	16	8
2	35	8
3	55	8
4	87	8
5	102	8
6	109	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	15	76
0	22	76
1	38	76
2	60	76
3	93	76
4	116	76
5	133	76
6	149	76
7	166	76
8	170	76
0	170	76