Metrics for ENA, Section 1.4, Mentioned, A

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze3.0ms (0%)

Memory

4.7MiB live, 4.7MiB 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)

sample2.6s (32.1%)

Memory

20.1MiB live, 2 873.9MiB allocated

Samples

2.0s	5 767×	2	valid
289.0ms	2 412×	1	valid
5.0ms	77×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.9s

ival-cos: 1.1s (56.9% of total)

adjust: 288.0ms (15.2% of total)

const: 210.0ms (11.1% of total)

ival-sub: 155.0ms (8.2% of total)

ival-<=: 142.0ms (7.5% of total)

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

exact: 4.0ms (0.2% of total)

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

Bogosity

explain157.0ms (1.9%)

Memory

-24.1MiB live, 191.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
134	1	(6.002392005440498e-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

91.0ms	348×	2	valid
12.0ms	160×	1	valid
0.0ms	4×	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: 70.0ms (81.1% of total)

adjust: 9.0ms (10.4% of total)

ival-sub: 7.0ms (8.1% 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

32.9MiB live, 32.9MiB 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)

eval2.0ms (0%)

Memory: -36.7MiB live, 0.6MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.1%	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Compiler

Compiled 4 to 4 computations (0% saved)

simplify5.0ms (0.1%)

Memory

15.5MiB live, 15.5MiB 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

localize56.0ms (0.7%)

Memory

-13.0MiB live, 106.6MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(cos.f64 x)
accuracy	30.028985303671902	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Samples

38.0ms	174×	2	valid
11.0ms	80×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 10 to 6 computations (40% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-cos: 25.0ms (74.7% of total)

adjust: 4.0ms (11.9% of total)

ival-sub: 4.0ms (11.9% of total)

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

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

exact: 0.0ms (0% of total)

series1.0ms (0%)

Memory

2.5MiB live, 2.5MiB allocated

Counts

2 → 24

Calls

Call 1

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

Inputs

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

#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())

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

Calls

3 calls:

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

simplify552.0ms (6.7%)

Memory

48.2MiB live, 348.1MiB 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)

rewrite244.0ms (3%)

Memory

-7.3MiB live, 274.4MiB 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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eval97.0ms (1.2%)

Memory: 17.1MiB live, 87.1MiB allocated
Compiler: Compiled 9 533 to 916 computations (90.4% saved)

prune12.0ms (0.2%)

Memory

-21.8MiB live, 25.8MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	335	3	338
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	336	3	339

Accuracy

100.0%

Counts

339 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.2%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
▶	100.0%	#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
▶	99.6%	#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))

Status

Accuracy

Program

▶

52.2%

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

▶

100.0%

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

▶

99.6%

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

Compiler

Compiled 21 to 17 computations (19% saved)

simplify8.0ms (0.1%)

Memory

18.0MiB live, 18.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

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

Rules

92×	`lower-*.f32`
84×	`lower-*.f64`
72×	`lower-fma.f32`
70×	`lower-fma.f64`
60×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize126.0ms (1.5%)

Memory

-16.7MiB live, 205.9MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score
accuracy	0.3116564758023605	#s(approx (cos x) #s(literal 1 binary64))
accuracy	30.028985303671902	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
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	0.0078125	(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
accuracy	0.01171875	(.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	0.2626188859692903	#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))

Samples

60.0ms	174×	2	valid
25.0ms	80×	1	valid
10.0ms	2×	0	valid

Compiler

Compiled 60 to 14 computations (76.7% saved)

Precisions

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

ival-cos: 26.0ms (41.2% of total)

ival-add: 13.0ms (20.6% of total)

adjust: 10.0ms (15.9% of total)

ival-mult: 7.0ms (11.1% of total)

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

const: 3.0ms (4.8% of total)

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

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

exact: 0.0ms (0% of total)

series7.0ms (0.1%)

Memory

24.8MiB live, 24.8MiB allocated

Counts

9 → 108

Calls

Call 1

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

Outputs
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) (taylor 0 x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))) (taylor 0 x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) (taylor 0 x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))) (taylor 0 x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/24 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/24 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/24 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) (taylor 0 x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* -1/24 (pow x 4)) (taylor inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* -1/24 (pow x 3)) (taylor inf x) (#s(alt (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor inf x) (#s(alt (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor inf x) (#s(alt (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor inf x) (#s(alt (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1/24 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor inf x) (#s(alt (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor inf x) (#s(alt (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor inf x) (#s(alt (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) (patch #s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* -1/24 (pow x 4)) (taylor -inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor -inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor -inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor -inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* -1/24 (pow x 3)) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1/24 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24)) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos x)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (patch (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt #s(approx (cos x) #s(literal 1 binary64)) (patch #s(approx (cos x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

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

1.0ms

-inf

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

1.0ms

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

simplify231.0ms (2.8%)

Memory

-24.2MiB live, 240.0MiB allocated

Algorithm

1×	egg-herbie

Rules

9 614×	`lower-fma.f64`
9 614×	`lower-fma.f32`
3 170×	`lower-*.f64`
3 170×	`lower-*.f32`
1 448×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	698
1	146	698
2	367	698
3	990	698
4	2488	698
5	5880	698
0	8285	647

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

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

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

rewrite177.0ms (2.2%)

Memory

14.2MiB live, 284.0MiB allocated

Rules

6 496×	`lower-*.f32`
6 488×	`lower-*.f64`
6 218×	`lower-fma.f32`
6 216×	`lower-fma.f64`
3 166×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	67
0	22	67
1	77	67
2	458	67
3	3741	67
0	11070	67

Stop Event

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

Counts

9 → 290

Calls

Call 1

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

Outputs
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eval51.0ms (0.6%)

Memory: -16.6MiB live, 103.5MiB allocated
Compiler: Compiled 7 206 to 1 152 computations (84% saved)

prune13.0ms (0.2%)

Memory

0.4MiB live, 38.5MiB allocated

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	413	3	416
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	414	5	419

Accuracy

100.0%

Counts

419 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.2%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
▶	4.3%	(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
▶	100.0%	#s(approx (- 1 (cos x)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))))
✓	100.0%	#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
▶	99.6%	#s(approx (- 1 (cos x)) (.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x))

Compiler

Compiled 37 to 31 computations (16.2% saved)

simplify7.0ms (0.1%)

Memory

15.2MiB live, 15.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

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

Rules

50×	`lower-*.f32`
42×	`lower-*.f64`
36×	`lower-+.f32`
34×	`lower-+.f64`
32×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize204.0ms (2.5%)

Memory

-22.3MiB live, 219.4MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(+.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	0.3116564758023605	#s(approx (cos x) #s(literal 1 binary64))
accuracy	0	(pow.f64 x #s(literal 4 binary64))
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0	#s(approx (- 1 (cos x)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))))
accuracy	0.109375	(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
accuracy	0	#s(approx (- 1 (cos x)) (.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x))
accuracy	0.0078125	(.f64 #s(approx (+ ( -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x)
accuracy	0.01171875	(.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x)
accuracy	0.2673702184448668	#s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64))

Samples

109.0ms	174×	2	valid
49.0ms	80×	1	valid
30.0ms	2×	0	valid

Compiler

Compiled 72 to 20 computations (72.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 129.0ms

adjust: 60.0ms (46.4% of total)

ival-cos: 33.0ms (25.5% of total)

ival-mult: 20.0ms (15.5% of total)

ival-add: 6.0ms (4.6% of total)

const: 4.0ms (3.1% of total)

ival-sub: 3.0ms (2.3% of total)

ival-pow: 3.0ms (2.3% of total)

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

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

exact: 0.0ms (0% of total)

series12.0ms (0.1%)

Memory

4.0MiB live, 40.3MiB allocated

Counts

11 → 132

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

inf

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

2.0ms

-inf

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

1.0ms

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

simplify218.0ms (2.7%)

Memory

-10.6MiB live, 113.0MiB allocated

Algorithm

1×	egg-herbie

Rules

10 130×	`lower-fma.f64`
10 130×	`lower-fma.f32`
3 178×	`lower-*.f64`
3 178×	`lower-*.f32`
1 448×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

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

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

rewrite183.0ms (2.2%)

Memory

47.3MiB live, 269.2MiB allocated

Rules

7 608×	`lower-fma.f32`
7 606×	`lower-fma.f64`
4 772×	`lower-*.f32`
4 764×	`lower-*.f64`
2 106×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	97
0	29	97
1	102	97
2	617	97
3	5534	97
0	8366	93

Stop Event

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

Counts

11 → 189

Calls

Call 1

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

Outputs
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eval61.0ms (0.7%)

Memory: -17.8MiB live, 85.9MiB allocated
Compiler: Compiled 5 441 to 724 computations (86.7% saved)

prune9.0ms (0.1%)

Memory

-10.0MiB live, 26.1MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	319	2	321
Fresh	0	0	0
Picked	2	1	3
Done	0	2	2
Total	321	5	326

Accuracy

100.0%

Counts

326 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.2%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
▶	100.0%	#s(approx (- 1 (cos x)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal -1/24 binary64))))
✓	100.0%	#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
✓	99.6%	#s(approx (- 1 (cos x)) (.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x))
▶	4.3%	#s(approx (+ (cos x) 1) #s(literal 2 binary64))

Compiler

Compiled 39 to 30 computations (23.1% saved)

simplify7.0ms (0.1%)

Memory

12.8MiB live, 12.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

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

Rules

84×	`lower-*.f32`
76×	`lower-*.f64`
60×	`lower-fma.f32`
58×	`lower-fma.f64`
44×	`lower-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize188.0ms (2.3%)

Memory

-15.0MiB live, 223.0MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0	#s(approx (- 1 (cos x)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal -1/24 binary64))))
accuracy	0.109375	(.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/24 binary64))
accuracy	0.14128876953688402	(.f64 (.f64 x x) (*.f64 x x))
accuracy	0.29212771239422625	#s(approx (+ (cos x) 1) #s(literal 2 binary64))

Samples

163.0ms	174×	2	valid
14.0ms	80×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 51 to 16 computations (68.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 147.0ms

ival-cos: 98.0ms (66.6% of total)

ival-mult: 24.0ms (16.3% of total)

adjust: 10.0ms (6.8% of total)

ival-add: 5.0ms (3.4% of total)

const: 5.0ms (3.4% of total)

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

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

11.6MiB live, 11.6MiB allocated

Counts

6 → 72

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify138.0ms (1.7%)

Memory

9.9MiB live, 168.4MiB allocated

Algorithm

1×	egg-herbie

Rules

10 310×	`lower-fma.f64`
10 310×	`lower-fma.f32`
4 134×	`lower-*.f64`
4 134×	`lower-*.f32`
2 360×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

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

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

rewrite191.0ms (2.3%)

Memory

-12.6MiB live, 231.9MiB allocated

Rules

7 996×	`lower-fma.f32`
7 994×	`lower-fma.f64`
5 428×	`lower-*.f32`
5 420×	`lower-*.f64`
1 898×	`lower-pow.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	58
0	21	50
1	72	42
2	474	42
3	5101	42
0	9184	42

Stop Event

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

Counts

6 → 129

Calls

Call 1

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

Outputs
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eval27.0ms (0.3%)

Memory: -26.1MiB live, 55.4MiB allocated
Compiler: Compiled 3 955 to 537 computations (86.4% saved)

prune6.0ms (0.1%)

Memory

20.1MiB live, 20.1MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	201	5	206

Accuracy

100.0%

Counts

206 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.2%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
✓	100.0%	#s(approx (- 1 (cos x)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal -1/24 binary64))))
✓	100.0%	#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
✓	99.6%	#s(approx (- 1 (cos x)) (.f64 (.f64 #s(approx (+ (* -1/24 (* x x)) 1/2) #s(literal 1/2 binary64)) x) x))
✓	4.3%	#s(approx (+ (cos x) 1) #s(literal 2 binary64))

Compiler

Compiled 103 to 62 computations (39.8% saved)

regimes10.0ms (0.1%)

Memory

-14.0MiB live, 23.1MiB allocated

Counts

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 7 to 7 computations (0% saved)

regimes7.0ms (0.1%)

Memory

19.2MiB live, 19.2MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 7 to 7 computations (0% saved)

regimes7.0ms (0.1%)

Memory

-19.9MiB live, 18.5MiB 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:

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

Results

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

Compiler

Compiled 7 to 7 computations (0% saved)

regimes6.0ms (0.1%)

Memory

16.0MiB live, 15.9MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 7 to 7 computations (0% saved)

regimes5.0ms (0.1%)

Memory

12.8MiB live, 12.8MiB allocated

Counts

3 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
52.2%	1	`x`
52.2%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
52.2%	1	`(cos.f64 x)`

Compiler

Compiled 7 to 7 computations (0% saved)

regimes24.0ms (0.3%)

Memory

-27.2MiB live, 11.2MiB 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:

21.0ms	x
1.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))
1.0ms	(cos.f64 x)

Results

Accuracy	Segments	Branch
4.3%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
4.3%	1	`x`
4.3%	1	`(cos.f64 x)`

Compiler

Compiled 7 to 7 computations (0% saved)

simplify48.0ms (0.6%)

Memory

19.5MiB live, 63.6MiB allocated

Algorithm

1×	egg-herbie

Rules

16×	`-commutative-binary64-.f64`
4×	`+-commutative-binary64-+.f64`
4×	`sub-neg-binary64-neg.f64-+.f64--.f64`
2×	`1-exp-binary32-exp.f32`
2×	`1-exp-binary64-exp.f64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness2.3s (28.1%)

Memory

-36.9MiB live, 505.7MiB allocated

Rules

32 720×	`lower-fma.f64`
32 720×	`lower-fma.f32`
10 130×	`lower-fma.f64`
10 130×	`lower-fma.f32`
9 614×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	698
1	146	698
2	367	698
3	990	698
4	2488	698
5	5880	698
0	8285	647
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	15	67
0	22	67
1	77	67
2	458	67
3	3741	67
0	11070	67
0	63	832
1	154	832
2	375	832
3	1011	832
4	2546	832
5	5941	832
0	8123	772
0	21	97
0	29	97
1	102	97
2	617	97
3	5534	97
0	8366	93

Stop Event

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

Compiler

Compiled 119 to 83 computations (30.3% saved)

preprocess153.0ms (1.9%)

Memory: 16.8MiB live, 94.5MiB allocated
Remove: (abs x)
Compiler: Compiled 178 to 106 computations (40.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

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

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

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

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

start0.0ms (0%)

analyze3.0ms (0%)

sample2.6s (32.1%)

explain157.0ms (1.9%)

preprocess14.0ms (0.2%)

eval2.0ms (0%)

prune0.0ms (0%)

simplify5.0ms (0.1%)

localize56.0ms (0.7%)

series1.0ms (0%)

simplify552.0ms (6.7%)

rewrite244.0ms (3%)

eval97.0ms (1.2%)

prune12.0ms (0.2%)

simplify8.0ms (0.1%)

localize126.0ms (1.5%)

series7.0ms (0.1%)

simplify231.0ms (2.8%)

rewrite177.0ms (2.2%)

eval51.0ms (0.6%)

prune13.0ms (0.2%)

simplify7.0ms (0.1%)

localize204.0ms (2.5%)

series12.0ms (0.1%)

simplify218.0ms (2.7%)

rewrite183.0ms (2.2%)

eval61.0ms (0.7%)

prune9.0ms (0.1%)

simplify7.0ms (0.1%)

localize188.0ms (2.3%)

series5.0ms (0.1%)

simplify138.0ms (1.7%)

rewrite191.0ms (2.3%)

eval27.0ms (0.3%)

prune6.0ms (0.1%)

regimes10.0ms (0.1%)

regimes7.0ms (0.1%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

regimes24.0ms (0.3%)

simplify48.0ms (0.6%)

soundness2.3s (28.1%)

preprocess153.0ms (1.9%)

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

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

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