Metrics for ENA, Section 1.4, Mentioned, A

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze3.0ms (0%)

Memory

3.7MiB live, 3.7MiB 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 (32.6%)

Memory

-80.9MiB live, 3 131.7MiB allocated

Samples

2.2s	5 708×	2	valid
437.0ms	2 475×	1	valid
5.0ms	73×	0	valid

Precisions

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

ival-cos: 1.4s (57.8% of total)

adjust: 289.0ms (12.3% of total)

const: 278.0ms (11.8% of total)

ival-sub: 275.0ms (11.7% of total)

ival-<=: 129.0ms (5.5% of total)

ival-and: 11.0ms (0.5% of total)

exact: 5.0ms (0.2% of total)

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

Bogosity

explain137.0ms (1.4%)

Memory

-32.8MiB live, 164.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
134	1	(2.682744773283621e-162)	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(cos.f64 x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	135	0

Confusion

	Predicted +	Predicted -
+	134	0
-	1	121

Precision

0.9925925925925926

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	134	0	0
-	1	0	121

Precision?

0.9925925925925926

Recall?

1.0

Freqs

test

number	freq
0	121
1	135

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

83.0ms	348×	2	valid
23.0ms	162×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 24 to 16 computations (33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 86.0ms

ival-cos: 68.0ms (79.5% of total)

adjust: 9.0ms (10.5% of total)

ival-sub: 7.0ms (8.2% of total)

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

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

exact: 0.0ms (0% of total)

preprocess14.0ms (0.2%)

Memory

6.0MiB live, 6.0MiB allocated

Algorithm

1×	egg-herbie

Rules

24×	`lower-+.f64`
24×	`lower-+.f32`
20×	`sub-neg`
18×	`lower--.f32`
16×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 4 to 4 computations (0% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.5%	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Compiler

Compiled 4 to 4 computations (0% saved)

simplify5.0ms (0%)

Memory

2.5MiB live, 2.5MiB 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))

Rules

24×	`lower-+.f64`
24×	`lower-+.f32`
18×	`lower--.f32`
16×	`sub-neg`
16×	`lower--.f64`

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

localize89.0ms (0.9%)

Memory

-6.2MiB live, 73.8MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(cos.f64 x)
accuracy	31.042093126159422	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Samples

65.0ms	174×	2	valid
18.0ms	81×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 10 to 6 computations (40% saved)

Precisions

Click to see histograms. Total time spent on operations: 63.0ms

ival-cos: 53.0ms (83.8% of total)

adjust: 6.0ms (9.5% of total)

ival-sub: 4.0ms (6.3% of total)

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

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

exact: 0.0ms (0% of total)

series1.0ms (0%)

Memory

2.9MiB live, 2.9MiB 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))

simplify526.0ms (5.5%)

Memory

4.3MiB live, 225.5MiB allocated

Algorithm

1×	egg-herbie

Rules

32 720×	`lower-fma.f64`
32 720×	`lower-fma.f32`
3 926×	`lower-*.f64`
3 926×	`lower-*.f32`
3 120×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 24

Calls

Call 1

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

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

rewrite203.0ms (2.1%)

Memory

-17.8MiB live, 345.5MiB allocated

Rules

4 830×	`lower-*.f64`
4 830×	`lower-*.f32`
4 620×	`lower-/.f64`
4 620×	`lower-/.f32`
3 866×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

2 → 314

Calls

Call 1

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

Outputs
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eval38.0ms (0.4%)

Memory: 37.7MiB live, 107.6MiB allocated
Compiler: Compiled 9 533 to 916 computations (90.4% saved)

prune9.0ms (0.1%)

Memory

1.1MiB live, 34.2MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	334	4	338
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	335	4	339

Accuracy

100.0%

Counts

339 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.2%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
▶	100.0%	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))
▶	100.0%	#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
▶	99.9%	#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))

Compiler

Compiled 28 to 23 computations (17.9% saved)

simplify16.0ms (0.2%)

Memory

-19.2MiB live, 22.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 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	(/.f64 x #s(literal 2 binary64))
cost-diff	0	(tan.f64 (/.f64 x #s(literal 2 binary64)))
cost-diff	0	(sin.f64 x)
cost-diff	0	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))
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)))

Rules

96×	`lower-*.f32`
86×	`lower-*.f64`
72×	`lower-fma.f32`
70×	`lower-fma.f64`
60×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	94
0	31	94
1	48	94
2	70	94
3	103	94
4	126	94
5	143	94
6	159	94
7	176	94
8	180	94
0	180	94

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

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

localize116.0ms (1.2%)

Memory

42.6MiB live, 300.3MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0.10356277706585662	#s(approx (cos x) #s(literal 1 binary64))
accuracy	31.042093126159422	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
accuracy	0	(/.f64 x #s(literal 2 binary64))
accuracy	0	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))
accuracy	0	(tan.f64 (/.f64 x #s(literal 2 binary64)))
accuracy	0	(sin.f64 x)
accuracy	0	(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) 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	0.00390625	(.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	0.07770303314335703	#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))

Samples

73.0ms	174×	2	valid
27.0ms	81×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 78 to 19 computations (75.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 77.0ms

ival-cos: 29.0ms (37.9% of total)

ival-mult: 17.0ms (22.2% of total)

adjust: 13.0ms (17% of total)

ival-div: 5.0ms (6.5% of total)

ival-sub: 4.0ms (5.2% of total)

const: 4.0ms (5.2% of total)

ival-sin: 2.0ms (2.6% of total)

ival-tan: 2.0ms (2.6% of total)

ival-add: 1.0ms (1.3% of total)

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

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

exact: 0.0ms (0% of total)

series108.0ms (1.1%)

Memory

-22.6MiB live, 74.3MiB allocated

Counts

13 → 156

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

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

Calls

3 calls:

Time

Variable

Point

Expression

100.0ms

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

2.0ms

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

2.0ms

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

simplify161.0ms (1.7%)

Memory

1.8MiB live, 276.4MiB allocated

Algorithm

1×	egg-herbie

Rules

15 162×	`lower-fma.f64`
15 162×	`lower-fma.f32`
4 386×	`lower-*.f64`
4 386×	`lower-*.f32`
2 218×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	100	1068
1	268	1062
2	676	1062
3	2086	1062
4	4152	1062
5	6395	1062
0	8204	993

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 155

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))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(- 1 (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))
(/ (* (sin x) (sin (* 1/2 x))) (cos (* 1/2 x)))
(/ (* (sin x) (sin (* 1/2 x))) (cos (* 1/2 x)))
(/ (* (sin x) (sin (* 1/2 x))) (cos (* 1/2 x)))
(/ (* (sin x) (sin (* 1/2 x))) (cos (* 1/2 x)))
(sin x)
(sin x)
(sin x)
(sin x)
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(* -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))
(/ (* (sin x) (sin (* 1/2 x))) (cos (* 1/2 x)))
(/ (* (sin x) (sin (* 1/2 x))) (cos (* 1/2 x)))
(/ (* (sin x) (sin (* 1/2 x))) (cos (* 1/2 x)))
(/ (* (sin x) (sin (* 1/2 x))) (cos (* 1/2 x)))
(sin x)
(sin x)
(sin x)
(sin x)
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)

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

rewrite275.0ms (2.9%)

Memory

12.8MiB live, 236.5MiB allocated

Rules

7 024×	`lower-*.f32`
7 014×	`lower-*.f64`
6 686×	`lower-fma.f32`
6 684×	`lower-fma.f64`
3 478×	`lower-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	83
0	31	83
1	96	83
2	513	83
3	3993	80
0	11844	80

Stop Event

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

Counts

13 → 497

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

Outputs
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eval153.0ms (1.6%)

Memory: -29.0MiB live, 189.3MiB allocated
Compiler: Compiled 10 978 to 1 740 computations (84.2% saved)

prune50.0ms (0.5%)

Memory

0.5MiB live, 53.0MiB allocated

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	671	3	674
Fresh	0	0	0
Picked	2	2	4
Done	0	0	0
Total	673	5	678

Accuracy

100.0%

Counts

678 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	51.2%	(-.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 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x))
✓	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 56 to 40 computations (28.6% saved)

simplify175.0ms (1.8%)

Memory

7.8MiB live, 195.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (cos x) #s(literal 1 binary64))
cost-diff	0	(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
cost-diff	0	(.f64 (.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (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 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x))
cost-diff	128	(neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))
cost-diff	1408	(.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))) x)
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))

Rules

16 180×	`lower-fma.f32`
16 174×	`lower-fma.f64`
2 468×	`lower-*.f32`
2 456×	`lower-*.f64`
1 188×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	235
0	46	230
1	86	230
2	143	230
3	320	226
4	898	197
5	2518	197
6	4590	197
7	6099	197
8	6660	197
9	6810	197
10	6875	197
11	7098	197
0	8025	189

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- 1 (cos x)) (.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x))
(.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x)
(.f64 #s(approx (+ ( -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x)
#s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x))
(.f64 (.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x)
(.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))) x)
(fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))))
(*.f64 x x)
x
(/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)))
(.f64 #s(literal 1/576 binary64) (.f64 x x))
#s(literal 1/576 binary64)
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
#s(literal -1/24 binary64)
#s(literal -1/2 binary64)
(neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))
(/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
#s(literal -1/4 binary64)
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
#s(literal 1/24 binary64)
#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))
#s(literal 1 binary64)

Outputs
#s(approx (- 1 (cos x)) (.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x))
(.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x)
(.f64 #s(approx (+ ( -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x)
#s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x))
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) #s(literal -1/4 binary64)) x) (/.f64 x (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal -1/2 binary64)))))
(.f64 (.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x)
(.f64 (.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) #s(literal -1/4 binary64)) x) (/.f64 x (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal -1/2 binary64))))
(.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))) x)
(.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/576 binary64) #s(literal -1/4 binary64)) (/.f64 x (fma.f64 (.f64 x x) #s(literal -1/24 binary64) #s(literal -1/2 binary64))))
(fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))))
(fma.f64 (/.f64 #s(literal -1/576 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))
(*.f64 x x)
x
(/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal -1/576 binary64) x) (/.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))
(.f64 #s(literal 1/576 binary64) (.f64 x x))
#s(literal 1/576 binary64)
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal -1/2 binary64))
#s(literal -1/24 binary64)
#s(literal -1/2 binary64)
(neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal -1/2 binary64)))
#s(literal -1/4 binary64)
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
#s(literal 1/24 binary64)
#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))
#s(literal 1 binary64)

localize277.0ms (2.9%)

Memory

-37.0MiB live, 428.8MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	0.10356277706585662	#s(approx (cos x) #s(literal 1 binary64))
accuracy	0.00390625	(.f64 (.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x)
accuracy	0.0078125	(/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
accuracy	0.015625	(/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)))
accuracy	0.19207001953688402	(.f64 #s(literal 1/576 binary64) (.f64 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	0.00390625	(.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x)
accuracy	0.0837733937827108	#s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64))

Samples

188.0ms	174×	2	valid
59.0ms	81×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 197 to 29 computations (85.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 168.0ms

ival-mult: 37.0ms (22.1% of total)

ival-cos: 36.0ms (21.5% of total)

adjust: 30.0ms (17.9% of total)

ival-sub: 28.0ms (16.7% of total)

ival-add: 13.0ms (7.8% of total)

const: 12.0ms (7.2% of total)

ival-div: 7.0ms (4.2% of total)

ival-neg: 3.0ms (1.8% of total)

exact: 1.0ms (0.6% of total)

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

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

series14.0ms (0.1%)

Memory

32.0MiB live, 32.0MiB allocated

Counts

13 → 156

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 (fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))) x) (patch (.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))) x) #<representation binary64>) () ())
#s(alt (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))) (patch (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (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 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (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 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))) x) x) (patch (.f64 (.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))) x) x) #<representation binary64>) () ())
#s(alt (+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) (patch (+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/576 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/576 binary64) (.f64 x x)) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (patch (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) (patch (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())

Outputs
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt #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>) () ())) ())
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#s(alt (* 1/576 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/576 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/576 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/576 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/576 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/576 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/576 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/576 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/576 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/576 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/576 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/576 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt -1/24 (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (patch (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 (pow x 2))) 1/24) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (patch (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (/ 1 (pow x 2))) (+ 1/24 (/ 6 (pow x 4)))) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (patch (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* 1/2 (/ 1 (pow x 2))) (* 72 (/ 1 (pow x 6)))) (+ 1/24 (/ 6 (pow x 4)))) (taylor -inf x) (#s(alt (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (patch (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ -6 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) (patch (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* 72 (/ 1 (pow x 2))) 6) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) (patch (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* 72 (/ 1 (pow x 2))) (+ 6 (/ 864 (pow x 4)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) (patch (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6)))) (+ 6 (/ 864 (pow x 4)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) (patch (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

((- 1 (cos x)) (* (* (+ (* -1/24 (* x x)) 1/2) x) x) (* (+ (* -1/24 (* x x)) 1/2) x) (+ (* -1/24 (* x x)) 1/2) (* (+ (* (* x x) (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2))) (neg (/ -1/4 (+ (* 1/24 (* x x)) 1/2)))) x) (neg (/ -1/4 (+ (* 1/24 (* x x)) 1/2))) (- 1 (cos x)) (* (* (+ (* (* x x) (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2))) (neg (/ -1/4 (+ (* 1/24 (* x x)) 1/2)))) x) x) (+ (cos x) 1) (cos x) (* 1/576 (* x x)) (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (/ -1/4 (+ (* 1/24 (* x x)) 1/2)))

3.0ms

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) (* (+ (* (* x x) (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2))) (neg (/ -1/4 (+ (* 1/24 (* x x)) 1/2)))) x) (neg (/ -1/4 (+ (* 1/24 (* x x)) 1/2))) (- 1 (cos x)) (* (* (+ (* (* x x) (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2))) (neg (/ -1/4 (+ (* 1/24 (* x x)) 1/2)))) x) x) (+ (cos x) 1) (cos x) (* 1/576 (* x x)) (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (/ -1/4 (+ (* 1/24 (* x x)) 1/2)))

2.0ms

-inf

((- 1 (cos x)) (* (* (+ (* -1/24 (* x x)) 1/2) x) x) (* (+ (* -1/24 (* x x)) 1/2) x) (+ (* -1/24 (* x x)) 1/2) (* (+ (* (* x x) (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2))) (neg (/ -1/4 (+ (* 1/24 (* x x)) 1/2)))) x) (neg (/ -1/4 (+ (* 1/24 (* x x)) 1/2))) (- 1 (cos x)) (* (* (+ (* (* x x) (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2))) (neg (/ -1/4 (+ (* 1/24 (* x x)) 1/2)))) x) x) (+ (cos x) 1) (cos x) (* 1/576 (* x x)) (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (/ -1/4 (+ (* 1/24 (* x x)) 1/2)))

simplify182.0ms (1.9%)

Memory

-3.2MiB live, 222.3MiB allocated

Algorithm

1×	egg-herbie

Rules

16 444×	`lower-fma.f64`
16 444×	`lower-fma.f32`
4 016×	`lower-+.f64`
4 016×	`lower-+.f32`
3 930×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	136	1294
1	341	1294
2	891	1294
3	2263	1294
4	5003	1294
0	8356	1219

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

Calls

Call 1

Inputs
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* -1/24 (pow x 2))))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* -1/24 (pow x 2)))
(* 1/2 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 (* (pow x 2) (- (* 1/288 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/288 (* -1/3456 (pow x 2)))) 1/24)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* 1/2 (pow x 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))))
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)))
(* 1/576 (pow x 2))
(* 1/576 (pow x 2))
(* 1/576 (pow x 2))
(* 1/576 (pow x 2))
(* -1/288 (pow x 2))
(* (pow x 2) (- (* 1/3456 (pow x 2)) 1/288))
(* (pow x 2) (- (* (pow x 2) (+ 1/3456 (* -1/41472 (pow x 2)))) 1/288))
(* (pow x 2) (- (* (pow x 2) (+ 1/3456 (* (pow x 2) (- (* 1/497664 (pow x 2)) 1/41472)))) 1/288))
-1/2
(- (* 1/24 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/24 (* -1/288 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/3456 (pow x 2)) 1/288)))) 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))
(* -1/24 (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))
(/ 6 (pow x 2))
(/ (- 6 (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 6 (/ 864 (pow x 4))) (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 6 (/ 864 (pow x 4))) (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6))))) (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 (cos x))
(+ 1 (cos x))
(+ 1 (cos x))
(+ 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(* 1/576 (pow x 2))
(* 1/576 (pow x 2))
(* 1/576 (pow x 2))
(* 1/576 (pow x 2))
-1/24
(- (* 1/2 (/ 1 (pow x 2))) 1/24)
(- (* 1/2 (/ 1 (pow x 2))) (+ 1/24 (/ 6 (pow x 4))))
(- (+ (* 1/2 (/ 1 (pow x 2))) (* 72 (/ 1 (pow x 6)))) (+ 1/24 (/ 6 (pow x 4))))
(/ -6 (pow x 2))
(/ (- (* 72 (/ 1 (pow x 2))) 6) (pow x 2))
(/ (- (* 72 (/ 1 (pow x 2))) (+ 6 (/ 864 (pow x 4)))) (pow x 2))
(/ (- (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6)))) (+ 6 (/ 864 (pow x 4)))) (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))
(* -1/24 (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))))))
(/ 6 (pow x 2))
(/ (- 6 (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 6 (/ 864 (pow x 4))) (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 6 (/ 864 (pow x 4))) (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6))))) (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 (cos x))
(+ 1 (cos x))
(+ 1 (cos x))
(+ 1 (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(* 1/576 (pow x 2))
(* 1/576 (pow x 2))
(* 1/576 (pow x 2))
(* 1/576 (pow x 2))
-1/24
(- (* 1/2 (/ 1 (pow x 2))) 1/24)
(- (* 1/2 (/ 1 (pow x 2))) (+ 1/24 (/ 6 (pow x 4))))
(- (+ (* 1/2 (/ 1 (pow x 2))) (* 72 (/ 1 (pow x 6)))) (+ 1/24 (/ 6 (pow x 4))))
(/ -6 (pow x 2))
(/ (- (* 72 (/ 1 (pow x 2))) 6) (pow x 2))
(/ (- (* 72 (/ 1 (pow x 2))) (+ 6 (/ 864 (pow x 4)))) (pow x 2))
(/ (- (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6)))) (+ 6 (/ 864 (pow x 4)))) (pow x 2))

Outputs
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) (.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(* 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 (* (pow x 2) (- (* 1/288 (pow x 2)) 1/24)))
(fma.f64 (fma.f64 #s(literal 1/288 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/288 (* -1/3456 (pow x 2)))) 1/24)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/3456 binary64) (.f64 x x) #s(literal 1/288 binary64)) (.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) (.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
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 (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
#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 (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))
(* 1/576 (pow x 2))
(.f64 #s(literal 1/576 binary64) (.f64 x x))
(* 1/576 (pow x 2))
(.f64 #s(literal 1/576 binary64) (.f64 x x))
(* 1/576 (pow x 2))
(.f64 #s(literal 1/576 binary64) (.f64 x x))
(* 1/576 (pow x 2))
(.f64 #s(literal 1/576 binary64) (.f64 x x))
(* -1/288 (pow x 2))
(.f64 #s(literal -1/288 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/3456 (pow x 2)) 1/288))
(.f64 (.f64 (fma.f64 #s(literal 1/3456 binary64) (*.f64 x x) #s(literal -1/288 binary64)) x) x)
(* (pow x 2) (- (* (pow x 2) (+ 1/3456 (* -1/41472 (pow x 2)))) 1/288))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/41472 binary64) (.f64 x x) #s(literal 1/3456 binary64)) (.f64 x x) #s(literal -1/288 binary64)) x) x)
(* (pow x 2) (- (* (pow x 2) (+ 1/3456 (* (pow x 2) (- (* 1/497664 (pow x 2)) 1/41472)))) 1/288))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/497664 binary64) (.f64 x x) #s(literal -1/41472 binary64)) (.f64 x x) #s(literal 1/3456 binary64)) (*.f64 x x) #s(literal -1/288 binary64)) x) x)
-1/2
#s(literal -1/2 binary64)
(- (* 1/24 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(- (* (pow x 2) (+ 1/24 (* -1/288 (pow x 2)))) 1/2)
(fma.f64 (fma.f64 #s(literal -1/288 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64))
(- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/3456 (pow x 2)) 1/288)))) 1/2)
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/3456 binary64) (.f64 x x) #s(literal -1/288 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(* -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 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 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))
(* -1/24 (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)
(/ 6 (pow x 2))
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(/ (- 6 (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 6 binary64) (/.f64 #s(literal 72 binary64) (*.f64 x x))) x) x)
(/ (- (+ 6 (/ 864 (pow x 4))) (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (/.f64 #s(literal 864 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 72 binary64) (.f64 x x)) #s(literal 6 binary64))) (.f64 x x))
(/ (- (+ 6 (/ 864 (pow x 4))) (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 864 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 72 binary64) (.f64 x x)) #s(literal 6 binary64))) (/.f64 #s(literal 10368 binary64) (pow.f64 x #s(literal 6 binary64)))) (.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 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)))
(+ 1 (cos x))
(+.f64 (cos.f64 x) #s(literal 1 binary64))
(+ 1 (cos x))
(+.f64 (cos.f64 x) #s(literal 1 binary64))
(+ 1 (cos x))
(+.f64 (cos.f64 x) #s(literal 1 binary64))
(+ 1 (cos x))
(+.f64 (cos.f64 x) #s(literal 1 binary64))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(* 1/576 (pow x 2))
(.f64 #s(literal 1/576 binary64) (.f64 x x))
(* 1/576 (pow x 2))
(.f64 #s(literal 1/576 binary64) (.f64 x x))
(* 1/576 (pow x 2))
(.f64 #s(literal 1/576 binary64) (.f64 x x))
(* 1/576 (pow x 2))
(.f64 #s(literal 1/576 binary64) (.f64 x x))
-1/24
#s(literal -1/24 binary64)
(- (* 1/2 (/ 1 (pow x 2))) 1/24)
(-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 1/24 binary64))
(- (* 1/2 (/ 1 (pow x 2))) (+ 1/24 (/ 6 (pow x 4))))
(-.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 1/24 binary64)) (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 4 binary64))))
(- (+ (* 1/2 (/ 1 (pow x 2))) (* 72 (/ 1 (pow x 6)))) (+ 1/24 (/ 6 (pow x 4))))
(-.f64 (-.f64 (/.f64 #s(literal -6 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 72 binary64) (pow.f64 x #s(literal 6 binary64)))))
(/ -6 (pow x 2))
(/.f64 #s(literal -6 binary64) (*.f64 x x))
(/ (- (* 72 (/ 1 (pow x 2))) 6) (pow x 2))
(/.f64 (/.f64 (-.f64 (/.f64 #s(literal 72 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ (- (* 72 (/ 1 (pow x 2))) (+ 6 (/ 864 (pow x 4)))) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 72 binary64) (.f64 x x)) #s(literal 6 binary64)) (/.f64 #s(literal 864 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 x x))
(/ (- (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6)))) (+ 6 (/ 864 (pow x 4)))) (pow x 2))
(/.f64 (-.f64 (-.f64 (-.f64 (/.f64 #s(literal 72 binary64) (.f64 x x)) #s(literal 6 binary64)) (/.f64 #s(literal 864 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal -10368 binary64) (pow.f64 x #s(literal 6 binary64)))) (.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 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 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))
(* -1/24 (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)
(/ 6 (pow x 2))
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(/ (- 6 (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 6 binary64) (/.f64 #s(literal 72 binary64) (*.f64 x x))) x) x)
(/ (- (+ 6 (/ 864 (pow x 4))) (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (/.f64 #s(literal 864 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 72 binary64) (.f64 x x)) #s(literal 6 binary64))) (.f64 x x))
(/ (- (+ 6 (/ 864 (pow x 4))) (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 864 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 72 binary64) (.f64 x x)) #s(literal 6 binary64))) (/.f64 #s(literal 10368 binary64) (pow.f64 x #s(literal 6 binary64)))) (.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 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)))
(+ 1 (cos x))
(+.f64 (cos.f64 x) #s(literal 1 binary64))
(+ 1 (cos x))
(+.f64 (cos.f64 x) #s(literal 1 binary64))
(+ 1 (cos x))
(+.f64 (cos.f64 x) #s(literal 1 binary64))
(+ 1 (cos x))
(+.f64 (cos.f64 x) #s(literal 1 binary64))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(* 1/576 (pow x 2))
(.f64 #s(literal 1/576 binary64) (.f64 x x))
(* 1/576 (pow x 2))
(.f64 #s(literal 1/576 binary64) (.f64 x x))
(* 1/576 (pow x 2))
(.f64 #s(literal 1/576 binary64) (.f64 x x))
(* 1/576 (pow x 2))
(.f64 #s(literal 1/576 binary64) (.f64 x x))
-1/24
#s(literal -1/24 binary64)
(- (* 1/2 (/ 1 (pow x 2))) 1/24)
(-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 1/24 binary64))
(- (* 1/2 (/ 1 (pow x 2))) (+ 1/24 (/ 6 (pow x 4))))
(-.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 1/24 binary64)) (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 4 binary64))))
(- (+ (* 1/2 (/ 1 (pow x 2))) (* 72 (/ 1 (pow x 6)))) (+ 1/24 (/ 6 (pow x 4))))
(-.f64 (-.f64 (/.f64 #s(literal -6 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 72 binary64) (pow.f64 x #s(literal 6 binary64)))))
(/ -6 (pow x 2))
(/.f64 #s(literal -6 binary64) (*.f64 x x))
(/ (- (* 72 (/ 1 (pow x 2))) 6) (pow x 2))
(/.f64 (/.f64 (-.f64 (/.f64 #s(literal 72 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ (- (* 72 (/ 1 (pow x 2))) (+ 6 (/ 864 (pow x 4)))) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 72 binary64) (.f64 x x)) #s(literal 6 binary64)) (/.f64 #s(literal 864 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 x x))
(/ (- (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6)))) (+ 6 (/ 864 (pow x 4)))) (pow x 2))
(/.f64 (-.f64 (-.f64 (-.f64 (/.f64 #s(literal 72 binary64) (.f64 x x)) #s(literal 6 binary64)) (/.f64 #s(literal 864 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal -10368 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 x x))

rewrite302.0ms (3.2%)

Memory

28.3MiB live, 183.6MiB allocated

Rules

9 246×	`lower-fma.f32`
9 240×	`lower-fma.f64`
4 096×	`lower-/.f32`
4 092×	`lower-/.f64`
3 774×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	185
0	46	181
1	168	178
2	1225	130
0	9277	123

Stop Event

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

Counts

13 → 198

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 (fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))) x)
(neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x))
(.f64 (.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x)
(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (cos x) #s(literal 1 binary64))
(.f64 #s(literal 1/576 binary64) (.f64 x x))
(/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)))
(/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))

Outputs
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eval119.0ms (1.3%)

Memory: -5.9MiB live, 32.8MiB allocated
Compiler: Compiled 9 504 to 1 257 computations (86.8% saved)

prune70.0ms (0.7%)

Memory

-29.0MiB live, 37.3MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	352	2	354
Fresh	0	0	0
Picked	2	1	3
Done	0	2	2
Total	354	5	359

Accuracy

100.0%

Counts

359 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	51.2%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
▶	100.0%	#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x))
✓	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 48 to 36 computations (25% saved)

simplify149.0ms (1.6%)

Memory

-11.1MiB live, 27.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))))
cost-diff	0	#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x))
cost-diff	128	(neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))
cost-diff	6144	(.f64 (.f64 (fma.f64 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x)
cost-diff	0	#s(approx (+ (cos x) 1) #s(literal 2 binary64))

Rules

1 708×	`lower-fma.f32`
1 704×	`lower-fma.f64`
1 272×	`lower-*.f32`
1 264×	`lower-*.f64`
944×	`unsub-neg`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	205
0	40	200
1	77	200
2	123	200
3	245	195
4	474	195
5	777	195
6	1172	195
7	1868	195
8	2589	195
9	2919	195
10	3047	195
11	3065	195
12	3069	195
13	3217	195
14	3281	195
15	3291	195
16	3449	195
17	4081	195
18	4081	195
19	4081	195
0	4081	195

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (+ (cos x) 1) #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x))
(.f64 (.f64 (fma.f64 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x)
(.f64 (fma.f64 (.f64 x x) #s(approx (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x)
(fma.f64 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))))
(*.f64 x x)
x
#s(approx (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x)))
(.f64 #s(literal -1/288 binary64) (.f64 x x))
#s(literal -1/288 binary64)
(neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))
(/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
#s(literal -1/4 binary64)
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)

Outputs
#s(approx (+ (cos x) 1) #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x))
#s(approx (- 1 (cos x)) (.f64 (fma.f64 #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (.f64 x x) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))) (*.f64 x x)))
(.f64 (.f64 (fma.f64 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x)
(.f64 (fma.f64 #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (.f64 x x) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))) (*.f64 x x))
(.f64 (fma.f64 (.f64 x x) #s(approx (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(approx (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) x))
(fma.f64 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))))
(fma.f64 #s(approx (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (.f64 x x) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))
(*.f64 x x)
x
#s(approx (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x)))
(.f64 #s(literal -1/288 binary64) (.f64 x x))
#s(literal -1/288 binary64)
(neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)))
#s(literal -1/4 binary64)
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)

localize173.0ms (1.8%)

Memory

6.8MiB live, 82.4MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(.f64 (.f64 (fma.f64 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x)
accuracy	0.0078125	(/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))
accuracy	0.0804551281885406	#s(approx (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x)))
accuracy	0.19207001953688402	(.f64 #s(literal -1/288 binary64) (.f64 x x))
accuracy	0.09583377183457051	#s(approx (+ (cos x) 1) #s(literal 2 binary64))

Samples

111.0ms	174×	2	valid
45.0ms	81×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 153 to 29 computations (81% saved)

Precisions

Click to see histograms. Total time spent on operations: 135.0ms

ival-cos: 48.0ms (35.4% of total)

ival-sub: 23.0ms (17% of total)

adjust: 21.0ms (15.5% of total)

ival-mult: 15.0ms (11.1% of total)

const: 12.0ms (8.9% of total)

ival-add: 9.0ms (6.6% of total)

ival-div: 5.0ms (3.7% of total)

ival-neg: 2.0ms (1.5% of total)

exact: 1.0ms (0.7% of total)

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

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

series8.0ms (0.1%)

Memory

4.7MiB live, 4.7MiB allocated

Counts

8 → 96

Calls

Call 1

Inputs
#s(alt #s(approx (+ (cos x) 1) #s(literal 2 binary64)) (patch #s(approx (+ (cos x) 1) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (fma.f64 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))) x) x) (patch (.f64 (.f64 (fma.f64 (.f64 x x) #s(approx (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x) #<representation binary64>) () ())
#s(alt (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))) (patch (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (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 (.f64 x x) #s(approx (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))) (patch (fma.f64 (.f64 x x) #s(approx (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -1/288 binary64) (.f64 x x)) (patch (.f64 #s(literal -1/288 binary64) (.f64 x x)) #<representation binary64>) () ())
#s(alt #s(approx (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (patch #s(approx (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) (patch (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 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 (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 (fma.f64 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))) x) x) (patch (.f64 (.f64 (fma.f64 (.f64 x x) #s(approx (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (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 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))) x) x) (patch (.f64 (.f64 (fma.f64 (.f64 x x) #s(approx (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (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 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))) x) x) (patch (.f64 (.f64 (fma.f64 (.f64 x x) #s(approx (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (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 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))) x) x) (patch (.f64 (.f64 (fma.f64 (.f64 x x) #s(approx (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor 0 x) (#s(alt (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))) (patch (neg.f64 (/.f64 #s(literal -1/4 binary64) (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 (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))) (patch (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (/ (- (* 72 (/ 1 (pow x 2))) (+ 6 (/ 864 (pow x 4)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) (patch (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6)))) (+ 6 (/ 864 (pow x 4)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) (patch (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

((+ (cos x) 1) (* (* (+ (* (* x x) (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2))) (neg (/ -1/4 (+ (* 1/24 (* x x)) 1/2)))) x) x) (neg (/ -1/4 (+ (* 1/24 (* x x)) 1/2))) (- 1 (cos x)) (+ (* (* x x) (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2))) (neg (/ -1/4 (+ (* 1/24 (* x x)) 1/2)))) (* -1/288 (* x x)) (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (/ -1/4 (+ (* 1/24 (* x x)) 1/2)))

1.0ms

-inf

((+ (cos x) 1) (* (* (+ (* (* x x) (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2))) (neg (/ -1/4 (+ (* 1/24 (* x x)) 1/2)))) x) x) (neg (/ -1/4 (+ (* 1/24 (* x x)) 1/2))) (- 1 (cos x)) (+ (* (* x x) (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2))) (neg (/ -1/4 (+ (* 1/24 (* x x)) 1/2)))) (* -1/288 (* x x)) (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (/ -1/4 (+ (* 1/24 (* x x)) 1/2)))

1.0ms

((+ (cos x) 1) (* (* (+ (* (* x x) (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2))) (neg (/ -1/4 (+ (* 1/24 (* x x)) 1/2)))) x) x) (neg (/ -1/4 (+ (* 1/24 (* x x)) 1/2))) (- 1 (cos x)) (+ (* (* x x) (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2))) (neg (/ -1/4 (+ (* 1/24 (* x x)) 1/2)))) (* -1/288 (* x x)) (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (/ -1/4 (+ (* 1/24 (* x x)) 1/2)))

simplify220.0ms (2.3%)

Memory

7.3MiB live, 84.2MiB allocated

Algorithm

1×	egg-herbie

Rules

14 332×	`lower-fma.f64`
14 332×	`lower-fma.f32`
4 006×	`lower-+.f64`
4 006×	`lower-+.f32`
3 096×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	121	848
1	302	848
2	791	848
3	1935	848
4	4364	848
5	7550	848
0	8182	800

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

Inputs
2
(+ 2 (* -1/2 (pow x 2)))
(+ 2 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/288 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/288 (* -1/3456 (pow x 2)))) 1/24)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* -1/24 (pow x 2)))
(* -1/288 (pow x 2))
(* -1/288 (pow x 2))
(* -1/288 (pow x 2))
(* -1/288 (pow x 2))
(* -1/288 (pow x 2))
(* (pow x 2) (- (* 1/3456 (pow x 2)) 1/288))
(* (pow x 2) (- (* (pow x 2) (+ 1/3456 (* -1/41472 (pow x 2)))) 1/288))
(* (pow x 2) (- (* (pow x 2) (+ 1/3456 (* (pow x 2) (- (* 1/497664 (pow x 2)) 1/41472)))) 1/288))
-1/2
(- (* 1/24 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/24 (* -1/288 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/3456 (pow x 2)) 1/288)))) 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))
(/ 6 (pow x 2))
(/ (- 6 (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 6 (/ 864 (pow x 4))) (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 6 (/ 864 (pow x 4))) (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6))))) (pow x 2))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(* -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))
(* -1/288 (pow x 2))
(* -1/288 (pow x 2))
(* -1/288 (pow x 2))
(* -1/288 (pow x 2))
-1/24
(- (* 1/2 (/ 1 (pow x 2))) 1/24)
(- (* 1/2 (/ 1 (pow x 2))) (+ 1/24 (/ 6 (pow x 4))))
(- (+ (* 1/2 (/ 1 (pow x 2))) (* 72 (/ 1 (pow x 6)))) (+ 1/24 (/ 6 (pow x 4))))
(/ -6 (pow x 2))
(/ (- (* 72 (/ 1 (pow x 2))) 6) (pow x 2))
(/ (- (* 72 (/ 1 (pow x 2))) (+ 6 (/ 864 (pow x 4)))) (pow x 2))
(/ (- (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6)))) (+ 6 (/ 864 (pow x 4)))) (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))
(/ 6 (pow x 2))
(/ (- 6 (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 6 (/ 864 (pow x 4))) (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 6 (/ 864 (pow x 4))) (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6))))) (pow x 2))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(* -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))
(* -1/288 (pow x 2))
(* -1/288 (pow x 2))
(* -1/288 (pow x 2))
(* -1/288 (pow x 2))
-1/24
(- (* 1/2 (/ 1 (pow x 2))) 1/24)
(- (* 1/2 (/ 1 (pow x 2))) (+ 1/24 (/ 6 (pow x 4))))
(- (+ (* 1/2 (/ 1 (pow x 2))) (* 72 (/ 1 (pow x 6)))) (+ 1/24 (/ 6 (pow x 4))))
(/ -6 (pow x 2))
(/ (- (* 72 (/ 1 (pow x 2))) 6) (pow x 2))
(/ (- (* 72 (/ 1 (pow x 2))) (+ 6 (/ 864 (pow x 4)))) (pow x 2))
(/ (- (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6)))) (+ 6 (/ 864 (pow x 4)))) (pow x 2))

Outputs
2
#s(literal 2 binary64)
(+ 2 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/288 (pow x 2)) 1/24)))
(fma.f64 (fma.f64 #s(literal 1/288 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/288 (* -1/3456 (pow x 2)))) 1/24)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/3456 binary64) (.f64 x x) #s(literal 1/288 binary64)) (.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.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 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) x (/.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) (*.f64 x x) #s(literal -1/24 binary64)) x (/.f64 #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))
(* -1/288 (pow x 2))
(.f64 #s(literal -1/288 binary64) (.f64 x x))
(* -1/288 (pow x 2))
(.f64 #s(literal -1/288 binary64) (.f64 x x))
(* -1/288 (pow x 2))
(.f64 #s(literal -1/288 binary64) (.f64 x x))
(* -1/288 (pow x 2))
(.f64 #s(literal -1/288 binary64) (.f64 x x))
(* -1/288 (pow x 2))
(.f64 #s(literal -1/288 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/3456 (pow x 2)) 1/288))
(.f64 (.f64 (fma.f64 #s(literal 1/3456 binary64) (*.f64 x x) #s(literal -1/288 binary64)) x) x)
(* (pow x 2) (- (* (pow x 2) (+ 1/3456 (* -1/41472 (pow x 2)))) 1/288))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/41472 binary64) (.f64 x x) #s(literal 1/3456 binary64)) (.f64 x x) #s(literal -1/288 binary64)) x) x)
(* (pow x 2) (- (* (pow x 2) (+ 1/3456 (* (pow x 2) (- (* 1/497664 (pow x 2)) 1/41472)))) 1/288))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/497664 binary64) (.f64 x x) #s(literal -1/41472 binary64)) (.f64 x x) #s(literal 1/3456 binary64)) (*.f64 x x) #s(literal -1/288 binary64)) x) x)
-1/2
#s(literal -1/2 binary64)
(- (* 1/24 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(- (* (pow x 2) (+ 1/24 (* -1/288 (pow x 2)))) 1/2)
(fma.f64 (fma.f64 #s(literal -1/288 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64))
(- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/3456 (pow x 2)) 1/288)))) 1/2)
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/3456 binary64) (.f64 x x) #s(literal -1/288 binary64)) (.f64 x x) #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))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(/ 6 (pow x 2))
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(/ (- 6 (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 6 binary64) (/.f64 #s(literal 72 binary64) (*.f64 x x))) x) x)
(/ (- (+ 6 (/ 864 (pow x 4))) (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (/.f64 #s(literal 864 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 72 binary64) (.f64 x x)) #s(literal 6 binary64))) (.f64 x x))
(/ (- (+ 6 (/ 864 (pow x 4))) (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6))))) (pow x 2))
(-.f64 (/.f64 (-.f64 (/.f64 #s(literal -10368 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (/.f64 #s(literal 72 binary64) (.f64 x x)) #s(literal 6 binary64))) (.f64 x x)) (/.f64 #s(literal -864 binary64) (pow.f64 x #s(literal 6 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 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))
(* -1/288 (pow x 2))
(.f64 #s(literal -1/288 binary64) (.f64 x x))
(* -1/288 (pow x 2))
(.f64 #s(literal -1/288 binary64) (.f64 x x))
(* -1/288 (pow x 2))
(.f64 #s(literal -1/288 binary64) (.f64 x x))
(* -1/288 (pow x 2))
(.f64 #s(literal -1/288 binary64) (.f64 x x))
-1/24
#s(literal -1/24 binary64)
(- (* 1/2 (/ 1 (pow x 2))) 1/24)
(-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 1/24 binary64))
(- (* 1/2 (/ 1 (pow x 2))) (+ 1/24 (/ 6 (pow x 4))))
(-.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 1/24 binary64)) (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 4 binary64))))
(- (+ (* 1/2 (/ 1 (pow x 2))) (* 72 (/ 1 (pow x 6)))) (+ 1/24 (/ 6 (pow x 4))))
(-.f64 (-.f64 (+.f64 (/.f64 #s(literal 72 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/24 binary64))
(/ -6 (pow x 2))
(/.f64 #s(literal -6 binary64) (*.f64 x x))
(/ (- (* 72 (/ 1 (pow x 2))) 6) (pow x 2))
(/.f64 (/.f64 (-.f64 (/.f64 #s(literal 72 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ (- (* 72 (/ 1 (pow x 2))) (+ 6 (/ 864 (pow x 4)))) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 72 binary64) (.f64 x x)) #s(literal 6 binary64)) (/.f64 #s(literal 864 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 x x))
(/ (- (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6)))) (+ 6 (/ 864 (pow x 4)))) (pow x 2))
(-.f64 (/.f64 #s(literal -864 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 (-.f64 (/.f64 #s(literal -10368 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (/.f64 #s(literal 72 binary64) (.f64 x x)) #s(literal 6 binary64))) (.f64 x x)))
(+ 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))
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(/ 6 (pow x 2))
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(/ (- 6 (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 6 binary64) (/.f64 #s(literal 72 binary64) (*.f64 x x))) x) x)
(/ (- (+ 6 (/ 864 (pow x 4))) (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 (/.f64 #s(literal 864 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 72 binary64) (.f64 x x)) #s(literal 6 binary64))) (.f64 x x))
(/ (- (+ 6 (/ 864 (pow x 4))) (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6))))) (pow x 2))
(-.f64 (/.f64 (-.f64 (/.f64 #s(literal -10368 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (/.f64 #s(literal 72 binary64) (.f64 x x)) #s(literal 6 binary64))) (.f64 x x)) (/.f64 #s(literal -864 binary64) (pow.f64 x #s(literal 6 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 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))
(* -1/288 (pow x 2))
(.f64 #s(literal -1/288 binary64) (.f64 x x))
(* -1/288 (pow x 2))
(.f64 #s(literal -1/288 binary64) (.f64 x x))
(* -1/288 (pow x 2))
(.f64 #s(literal -1/288 binary64) (.f64 x x))
(* -1/288 (pow x 2))
(.f64 #s(literal -1/288 binary64) (.f64 x x))
-1/24
#s(literal -1/24 binary64)
(- (* 1/2 (/ 1 (pow x 2))) 1/24)
(-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 1/24 binary64))
(- (* 1/2 (/ 1 (pow x 2))) (+ 1/24 (/ 6 (pow x 4))))
(-.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 1/24 binary64)) (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 4 binary64))))
(- (+ (* 1/2 (/ 1 (pow x 2))) (* 72 (/ 1 (pow x 6)))) (+ 1/24 (/ 6 (pow x 4))))
(-.f64 (-.f64 (+.f64 (/.f64 #s(literal 72 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (/.f64 #s(literal 6 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/24 binary64))
(/ -6 (pow x 2))
(/.f64 #s(literal -6 binary64) (*.f64 x x))
(/ (- (* 72 (/ 1 (pow x 2))) 6) (pow x 2))
(/.f64 (/.f64 (-.f64 (/.f64 #s(literal 72 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ (- (* 72 (/ 1 (pow x 2))) (+ 6 (/ 864 (pow x 4)))) (pow x 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 72 binary64) (.f64 x x)) #s(literal 6 binary64)) (/.f64 #s(literal 864 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 x x))
(/ (- (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6)))) (+ 6 (/ 864 (pow x 4)))) (pow x 2))
(-.f64 (/.f64 #s(literal -864 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 (-.f64 (/.f64 #s(literal -10368 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (/.f64 #s(literal 72 binary64) (.f64 x x)) #s(literal 6 binary64))) (.f64 x x)))

rewrite247.0ms (2.6%)

Memory

11.8MiB live, 244.6MiB allocated

Rules

6 948×	`lower-fma.f32`
6 944×	`lower-fma.f64`
4 936×	`lower-*.f32`
4 928×	`lower-*.f64`
3 556×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	156
0	40	152
1	149	152
2	1016	148
0	8614	148

Stop Event

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

Counts

8 → 234

Calls

Call 1

Inputs
#s(approx (+ (cos x) 1) #s(literal 2 binary64))
(.f64 (.f64 (fma.f64 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x)
(neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x))
(fma.f64 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))))
(.f64 #s(literal -1/288 binary64) (.f64 x x))
#s(approx (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x)))
(/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)))

Outputs
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eval46.0ms (0.5%)

Memory: -5.2MiB live, 121.9MiB allocated
Compiler: Compiled 10 960 to 1 430 computations (87% saved)

prune9.0ms (0.1%)

Memory

-7.5MiB live, 30.5MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	329	1	330
Fresh	0	0	0
Picked	1	1	2
Done	0	3	3
Total	330	5	335

Accuracy

100.0%

Counts

335 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	51.2%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
	100.0%	#s(approx (- 1 (cos x)) (.f64 (fma.f64 #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (.f64 x x) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))) (*.f64 x x)))
✓	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 169 to 86 computations (49.1% saved)

regimes33.0ms (0.3%)

Memory

-4.4MiB live, 38.9MiB allocated

Counts

11 → 1

Calls

Call 1

Inputs
#s(approx (+ (cos x) 1) #s(literal 2 binary64))
(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
#s(approx (- 1 (cos x)) (.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x))
#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 (fma.f64 #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (.f64 x x) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))) (*.f64 x x)))
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x))
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 x x)) (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (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))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))

Outputs

#s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(approx (/ (* 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (*.f64 #s(literal -1/288 binary64) (*.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x))

Calls

3 calls:

26.0ms	x
3.0ms	(cos.f64 x)
3.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Results

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

Compiler

Compiled 7 to 7 computations (0% saved)

regimes9.0ms (0.1%)

Memory

-15.0MiB live, 23.1MiB 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))
#s(approx (- 1 (cos x)) (.f64 (fma.f64 #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (.f64 x x) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))) (*.f64 x x)))

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

Calls

3 calls:

4.0ms	x
2.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))
2.0ms	(cos.f64 x)

Results

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

Compiler

Compiled 7 to 7 computations (0% saved)

regimes6.0ms (0.1%)

Memory

17.5MiB live, 17.5MiB 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:

2.0ms	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)

regimes7.0ms (0.1%)

Memory

-16.8MiB live, 21.6MiB 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:

3.0ms	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

21.5MiB live, 21.5MiB allocated

Counts

3 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
51.2%	1	`x`
51.2%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
51.2%	1	`(cos.f64 x)`

Compiler

Compiled 7 to 7 computations (0% saved)

regimes5.0ms (0.1%)

Memory

-19.7MiB live, 19.0MiB 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:

3.0ms	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)

simplify29.0ms (0.3%)

Memory

12.8MiB live, 92.3MiB allocated

Algorithm

1×	egg-herbie

Rules

24×	`-commutative-binary64-.f64`
10×	`+-commutative-binary64-+.f64`
10×	`sub-neg-binary64-neg.f64-+.f64--.f64`
8×	`neg-sub0-binary64--.f64-neg.f64`
8×	`neg-mul-1-binary64-*.f64-neg.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	96
1	62	96
2	71	96
3	78	96
4	81	96

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #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))
#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 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))))) x) x))
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(approx (/ ( 1/576 (* x x)) (+ (* -1/24 (* x x)) -1/2)) (.f64 #s(literal -1/288 binary64) (.f64 x x))) (/.f64 (neg.f64 #s(literal -1/4 binary64)) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #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))
#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))

soundness2.3s (24.6%)

Memory

5.1MiB live, 711.1MiB allocated

Rules

32 720×	`lower-fma.f64`
32 720×	`lower-fma.f32`
16 444×	`lower-fma.f64`
16 444×	`lower-fma.f32`
15 162×	`lower-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	83
0	31	83
1	96	83
2	513	83
3	3993	80
0	11844	80
0	41	144
1	101	144
2	246	144
3	588	144
4	1237	144
5	1916	144
6	2187	144
7	2836	144
8	4071	144
9	5644	144
10	6543	144
11	6823	144
12	6862	144
13	6862	144
14	7274	144
15	7556	144
16	7597	144
17	7599	144
18	7599	144
19	7599	144
20	7599	144
21	7609	144
22	7609	144
23	7609	144
0	8514	132
0	136	1294
1	341	1294
2	891	1294
3	2263	1294
4	5003	1294
0	8356	1219
0	100	1068
1	268	1062
2	676	1062
3	2086	1062
4	4152	1062
5	6395	1062
0	8204	993

Stop Event

1×	fuel
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 117 to 82 computations (29.9% saved)

preprocess71.0ms (0.7%)

Memory: 14.1MiB live, 128.8MiB allocated
Remove: (abs x)
Compiler: Compiled 280 to 174 computations (37.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

Iter	Nodes	Cost
0	20	94
0	31	94
1	48	94
2	70	94
3	103	94
4	126	94
5	143	94
6	159	94
7	176	94
8	180	94
0	180	94

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

Iter	Nodes	Cost
0	20	94
0	31	94
1	48	94
2	70	94
3	103	94
4	126	94
5	143	94
6	159	94
7	176	94
8	180	94
0	180	94

start0.0ms (0%)

analyze3.0ms (0%)

sample3.1s (32.6%)

explain137.0ms (1.4%)

preprocess14.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify5.0ms (0%)

localize89.0ms (0.9%)

series1.0ms (0%)

simplify526.0ms (5.5%)

rewrite203.0ms (2.1%)

eval38.0ms (0.4%)

prune9.0ms (0.1%)

simplify16.0ms (0.2%)

localize116.0ms (1.2%)

series108.0ms (1.1%)

simplify161.0ms (1.7%)

rewrite275.0ms (2.9%)

eval153.0ms (1.6%)

prune50.0ms (0.5%)

simplify175.0ms (1.8%)

localize277.0ms (2.9%)

series14.0ms (0.1%)

simplify182.0ms (1.9%)

rewrite302.0ms (3.2%)

eval119.0ms (1.3%)

prune70.0ms (0.7%)

simplify149.0ms (1.6%)

localize173.0ms (1.8%)

series8.0ms (0.1%)

simplify220.0ms (2.3%)

rewrite247.0ms (2.6%)

eval46.0ms (0.5%)

prune9.0ms (0.1%)

regimes33.0ms (0.3%)

regimes9.0ms (0.1%)

regimes6.0ms (0.1%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

simplify29.0ms (0.3%)

soundness2.3s (24.6%)

preprocess71.0ms (0.7%)

end0.0ms (0%)

Profiling

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

Iter	Nodes	Cost
0	20	94
0	31	94
1	48	94
2	70	94
3	103	94
4	126	94
5	143	94
6	159	94
7	176	94
8	180	94
0	180	94