Metrics for cos2 (problem 3.4.1)

analyze2.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
50%	50%	50%	0%	0%	0%	0%	2
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 10 to 7 computations (30% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

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

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

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample2.2s (21.6%)

Results

1.2s	1995×	2	valid
408.0ms	4207×	0	valid
357.0ms	2054×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 1.6s

ival-cos: 1.1s (73.3% of total)

ival-mult: 107.0ms (6.9% of total)

ival-div: 105.0ms (6.7% of total)

ival-sub: 95.0ms (6.1% of total)

backward-pass: 94.0ms (6% of total)

const: 15.0ms (1% of total)

Bogosity

preprocess116.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

1096×	`fnmadd-define`
1018×	`sum3-define`
1016×	`fma-define`
936×	`sum5-define`
904×	`sum3-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	40	22
2	113	21
3	311	21
4	845	21
5	1951	21
6	3654	21
7	3863	21
0	6	7
1	16	7
2	28	7
3	46	7
4	85	7
5	145	7
6	236	7
7	465	7
8	1142	7
9	2534	7
10	4043	7
11	4063	7
0	4063	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

Outputs
(/ (- 1 (cos x)) (* x x))
(/ (- 1 (cos x)) (square x))
(/ (- 1 (cos (neg x))) (* (neg x) (neg x)))
(/ (- 1 (cos x)) (square x))
(neg (/ (- 1 (cos (neg x))) (* (neg x) (neg x))))
(/ (+ (cos x) -1) (square x))

Symmetry

(abs x)

explain190.0ms (1.9%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
65	0	-	1	(7.627770520680113e-158)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`
63	1	(2.9929323001348095e+46)	0	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
0	0	-	0	-	`x`
0	0	-	0	-	`(*.f64 x x)`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(cos.f64 x)`

Results

75.0ms	124×	2	valid
52.0ms	274×	0	valid
30.0ms	114×	1	valid

Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions

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

ival-cos: 49.0ms (56% of total)

ival-mult: 15.0ms (17.2% of total)

backward-pass: 11.0ms (12.6% of total)

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

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

const: 1.0ms (1.1% of total)

eval0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.6%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify65.0ms (0.6%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(cos.f64 x)
✓	cost-diff	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	cost-diff	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Rules

1096×	`fnmadd-define`
1018×	`sum3-define`
1016×	`fma-define`
880×	`sum5-define`
550×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
1	16	17
2	28	17
3	46	17
4	85	17
5	145	17
6	236	17
7	465	17
8	1142	17
9	2534	17
10	4043	17
11	4063	17
0	4063	17

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize76.0ms (0.7%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	78.8%	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	accuracy	75.9%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Results

32.0ms	62×	2	valid
20.0ms	137×	0	valid
12.0ms	57×	1	valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

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

ival-cos: 25.0ms (61.2% of total)

ival-sub: 6.0ms (14.7% of total)

backward-pass: 4.0ms (9.8% of total)

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

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

const: 1.0ms (2.4% of total)

series3.0ms (0%)

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (/ (- 1 (cos x)) (* x x))>
#<alt (- 1 (cos x))>
#<alt (cos x)>
#<alt (* x x)>

Outputs
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/ (- 1 (cos x)) (* x x))
0.0ms	x	@	inf	(* x x)
0.0ms	x	@	-inf	(/ (- 1 (cos x)) (* x x))
0.0ms	x	@	0	(/ (- 1 (cos x)) (* x x))
0.0ms	x	@	0	(cos x)

rewrite403.0ms (4%)

Algorithm

1×	batch-egg-rewrite

Rules

2562×	`-lowering-.f32`
2562×	`-lowering-.f64`
2250×	`fma-lowering-fma.f32`
2250×	`fma-lowering-fma.f64`
1948×	`prod-diff`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	37	15
2	270	15
3	2919	15
0	8614	15

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 463

Calls

Call 1

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

Outputs
(+.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 x x)) (+.f64 (.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (cos.f64 x)) (/.f64 (/.f64 (cos.f64 x) x) x)))
(+.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 x x)) (fma.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (/.f64 (cos.f64 x) x) x)))
(+.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x)) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) x)) (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 (cos.f64 x) x) x)))
(+.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x)) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (cos.f64 x) x) (/.f64 (/.f64 (cos.f64 x) x) x)))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (/.f64 (cos.f64 x) x) x))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (cos.f64 x) x) x)))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (cos.f64 x) x) x))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (cos.f64 x) x) x)) #s(literal 1 binary64)))
(+.f64 (/.f64 (/.f64 (cos.f64 x) x) x) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (cos.f64 x) x) x)) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)) (neg.f64 (.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (cos.f64 x)))) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (cos.f64 x) (.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (cos.f64 x))))
(+.f64 (fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x))))) (fma.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))))
(+.f64 (fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)) (neg.f64 (.f64 (/.f64 (/.f64 (cos.f64 x) x) x) #s(literal -1 binary64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (cos.f64 x) x) x)) #s(literal -1 binary64) (*.f64 (/.f64 (/.f64 (cos.f64 x) x) x) #s(literal -1 binary64))))
(+.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64) (neg.f64 (.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (cos.f64 x)))) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (cos.f64 x) (.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (cos.f64 x))))
(+.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x))))) (fma.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))))
(+.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64) (neg.f64 (.f64 (/.f64 (/.f64 (cos.f64 x) x) x) #s(literal -1 binary64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (cos.f64 x) x) x)) #s(literal -1 binary64) (*.f64 (/.f64 (/.f64 (cos.f64 x) x) x) #s(literal -1 binary64))))
(+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)) (neg.f64 (.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (cos.f64 x)))) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (cos.f64 x) (.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (cos.f64 x))))
(+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x))))) (fma.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))))
(+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)) (neg.f64 (.f64 (/.f64 (/.f64 (cos.f64 x) x) x) #s(literal -1 binary64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (cos.f64 x) x) x)) #s(literal -1 binary64) (*.f64 (/.f64 (/.f64 (cos.f64 x) x) x) #s(literal -1 binary64))))
(+.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x) (neg.f64 (.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (cos.f64 x)))) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (cos.f64 x) (.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (cos.f64 x))))
(+.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x))))) (fma.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))))
(+.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x) (neg.f64 (.f64 (/.f64 (/.f64 (cos.f64 x) x) x) #s(literal -1 binary64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (cos.f64 x) x) x)) #s(literal -1 binary64) (.f64 (/.f64 (/.f64 (cos.f64 x) x) x) #s(literal -1 binary64))))
(+.f64 (fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)) (neg.f64 (.f64 (/.f64 (/.f64 (cos.f64 x) x) x) #s(literal 1 binary64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (cos.f64 x) x) x)) #s(literal 1 binary64) (*.f64 (/.f64 (/.f64 (cos.f64 x) x) x) #s(literal 1 binary64))))
(+.f64 (fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)) (neg.f64 (.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x))))) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))))
(+.f64 (fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)) (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (cos.f64 x) x) x)) #s(literal -1 binary64)))) (fma.f64 (/.f64 (/.f64 (cos.f64 x) x) x) #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (cos.f64 x) x) x)) #s(literal -1 binary64))))
(+.f64 (fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)) (neg.f64 (.f64 (/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal -1 binary64) x)))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x))) (/.f64 #s(literal -1 binary64) x) (*.f64 (/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal -1 binary64) x))))
(+.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64) (neg.f64 (.f64 (/.f64 (/.f64 (cos.f64 x) x) x) #s(literal 1 binary64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (cos.f64 x) x) x)) #s(literal 1 binary64) (*.f64 (/.f64 (/.f64 (cos.f64 x) x) x) #s(literal 1 binary64))))
(+.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64) (neg.f64 (.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x))))) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))))
(+.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64) (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (cos.f64 x) x) x)) #s(literal -1 binary64)))) (fma.f64 (/.f64 (/.f64 (cos.f64 x) x) x) #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (cos.f64 x) x) x)) #s(literal -1 binary64))))
(+.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64) (neg.f64 (.f64 (/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal -1 binary64) x)))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x))) (/.f64 #s(literal -1 binary64) x) (*.f64 (/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal -1 binary64) x))))
(+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)) (neg.f64 (.f64 (/.f64 (/.f64 (cos.f64 x) x) x) #s(literal 1 binary64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (cos.f64 x) x) x)) #s(literal 1 binary64) (*.f64 (/.f64 (/.f64 (cos.f64 x) x) x) #s(literal 1 binary64))))
(+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)) (neg.f64 (.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x))))) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))))
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(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)) (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 9 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))) (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))))
(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
(pow.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
(.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
(.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))) #s(literal 1 binary64)))
(.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(.f64 (sin.f64 x) (.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(*.f64 #s(literal -1 binary64) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
(.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))))
(.f64 (+.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 x) #s(literal -1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) #s(literal -1 binary64)))
(.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))))
(.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (/.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
(.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
(.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (+.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))))) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (-.f64 (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 1 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 x) #s(literal -1 binary64))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 9 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 6 binary64))))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(cos.f64 x)
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(neg.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(*.f64 #s(literal 1 binary64) (cos.f64 x))
(*.f64 (cos.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 x))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (*.f64 x x) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal -1 binary64))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 x x)
(*.f64 x (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(*.f64 x (/.f64 x #s(literal 1 binary64)))
(*.f64 x (pow.f64 (/.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 x (pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) #s(literal 1 binary64)))
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(.f64 #s(literal -1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal 1 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 (.f64 #s(literal 1 binary64) x) x)
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) x)
(*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64)))
(*.f64 (pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) #s(literal 1 binary64)) x)
(*.f64 (pow.f64 (exp.f64 (log.f64 x)) #s(literal 1 binary64)) (pow.f64 (exp.f64 (log.f64 x)) #s(literal 1 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)

simplify189.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

2236×	`sum3-define`
2048×	`fma-lowering-fma.f32`
2048×	`fma-lowering-fma.f64`
1796×	`sum4-define`
1484×	`fmm-def`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	278
1	113	224
2	316	224
3	821	224
4	1931	224
5	2947	224
6	3532	224
7	4854	224
0	8003	224

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval61.0ms (0.6%)

Compiler: Compiled 13229 to 1215 computations (90.8% saved)

prune89.0ms (0.9%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	493	18	511
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	493	19	512

Accuracy

100.0%

Counts

512 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	30.4%	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x x)) (*.f64 x x))
	30.2%	(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	53.5%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))))) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
	14.6%	(/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 (.f64 (.f64 x x) x) x))
	21.8%	(/.f64 (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) (/.f64 (cos.f64 x) x))) (.f64 (*.f64 x x) x))
▶	53.6%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
✓	53.6%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
	25.4%	(/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (*.f64 x x))
	53.5%	(/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
	75.1%	(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 x x))
	53.6%	(/.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) (+.f64 (cos.f64 x) #s(literal -1 binary64))))
	53.5%	(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (/.f64 (cos.f64 x) x) x))
	53.8%	(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
	47.3%	(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
▶	75.6%	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
	53.6%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
	75.4%	(.f64 (sin.f64 x) (/.f64 (sin.f64 x) (.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
▶	54.7%	(neg.f64 (/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x) x))
▶	48.7%	#s(literal 1/2 binary64)

Compiler

Compiled 481 to 294 computations (38.9% saved)

simplify161.0ms (1.6%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	128	(-.f64 (.f64 x x) (.f64 x (*.f64 x (cos.f64 x))))
✓	cost-diff	640	(/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x x))
✓	cost-diff	640	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x x)) (*.f64 x x))
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	cost-diff	256	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
✓	cost-diff	0	(+.f64 (cos.f64 x) #s(literal -1 binary64))
✓	cost-diff	0	(/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x)
✓	cost-diff	0	(/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x) x)
✓	cost-diff	64	(neg.f64 (/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x) x))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(sin.f64 x)
✓	cost-diff	0	(/.f64 (sin.f64 x) (*.f64 x x))
✓	cost-diff	0	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))

Rules

2348×	`-lowering-.f32`
2348×	`-lowering-.f64`
1982×	`fma-lowering-fma.f32`
1982×	`fma-lowering-fma.f64`
1740×	`sum5-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	115
1	77	115
2	245	111
3	1035	111
4	2927	111
5	6259	111
0	8176	111

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize302.0ms (3%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(*.f64 x (cos.f64 x))
✓	accuracy	76.6%	(-.f64 (.f64 x x) (.f64 x (*.f64 x (cos.f64 x))))
✓	accuracy	75.9%	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x x)) (*.f64 x x))
✓	accuracy	45.1%	(/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x x))
✓	accuracy	99.4%	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	accuracy	99.1%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	accuracy	78.8%	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	accuracy	75.9%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	99.9%	(/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x) x)
✓	accuracy	78.8%	(+.f64 (cos.f64 x) #s(literal -1 binary64))
✓	accuracy	76.9%	(/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x)
✓	accuracy	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	99.8%	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
✓	accuracy	76.6%	(/.f64 (sin.f64 x) (*.f64 x x))

Results

109.0ms	62×	2	valid
83.0ms	137×	0	valid
39.0ms	19×	3	valid
29.0ms	38×	1	valid

Compiler

Compiled 158 to 26 computations (83.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 122.0ms

ival-div: 33.0ms (27.1% of total)

ival-cos: 33.0ms (27.1% of total)

backward-pass: 15.0ms (12.3% of total)

ival-mult: 14.0ms (11.5% of total)

ival-sin: 8.0ms (6.6% of total)

ival-sub: 6.0ms (4.9% of total)

ival-tan: 6.0ms (4.9% of total)

ival-add: 3.0ms (2.5% of total)

ival-neg: 2.0ms (1.6% of total)

const: 1.0ms (0.8% of total)

series14.0ms (0.1%)

Counts

18 → 216

Calls

Call 1

Inputs
#<alt (* (/ (sin x) (* x x)) (tan (/ x 2)))>
#<alt (/ (sin x) (* x x))>
#<alt (sin x)>
#<alt (* x x)>
#<alt (neg (/ (/ (+ (cos x) -1) x) x))>
#<alt (/ (/ (+ (cos x) -1) x) x)>
#<alt (/ (+ (cos x) -1) x)>
#<alt (+ (cos x) -1)>
#<alt (/ (- 1 (cos x)) (/ 1 (/ 1 (* x x))))>
#<alt (/ 1 (/ 1 (* x x)))>
#<alt (- 1 (cos x))>
#<alt (cos x)>
#<alt (/ (/ (- (* x x) (* x (* x (cos x)))) (* x x)) (* x x))>
#<alt (/ (- (* x x) (* x (* x (cos x)))) (* x x))>
#<alt (- (* x x) (* x (* x (cos x))))>
#<alt (tan (/ x 2))>
#<alt (/ 1 (* x x))>
#<alt (* x (cos x))>

Outputs
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* -1/6 (pow x 2))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) x)>
#<alt (/ (sin x) (pow x 2))>
#<alt (/ (sin x) (pow x 2))>
#<alt (/ (sin x) (pow x 2))>
#<alt (/ (sin x) (pow x 2))>
#<alt (/ (sin x) (pow x 2))>
#<alt (/ (sin x) (pow x 2))>
#<alt (/ (sin x) (pow x 2))>
#<alt (/ (sin x) (pow x 2))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt -1/2>
#<alt (- (* 1/24 (pow x 2)) 1/2)>
#<alt (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)>
#<alt (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2)>
#<alt (/ (- (cos x) 1) (pow x 2))>
#<alt (/ (- (cos x) 1) (pow x 2))>
#<alt (/ (- (cos x) 1) (pow x 2))>
#<alt (/ (- (cos x) 1) (pow x 2))>
#<alt (/ (- (cos x) 1) (pow x 2))>
#<alt (/ (- (cos x) 1) (pow x 2))>
#<alt (/ (- (cos x) 1) (pow x 2))>
#<alt (/ (- (cos x) 1) (pow x 2))>
#<alt (* -1/2 x)>
#<alt (* x (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))>
#<alt (/ (- (cos x) 1) x)>
#<alt (/ (- (cos x) 1) x)>
#<alt (/ (- (cos x) 1) x)>
#<alt (/ (- (cos x) 1) x)>
#<alt (/ (- (cos x) 1) x)>
#<alt (/ (- (cos x) 1) x)>
#<alt (/ (- (cos x) 1) x)>
#<alt (/ (- (cos x) 1) x)>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))>
#<alt (- (cos x) 1)>
#<alt (- (cos x) 1)>
#<alt (- (cos x) 1)>
#<alt (- (cos x) 1)>
#<alt (- (cos x) 1)>
#<alt (- (cos x) 1)>
#<alt (- (cos x) 1)>
#<alt (- (cos x) 1)>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (* 1/2 (pow x 4))>
#<alt (* (pow x 4) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 4) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 4) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (* (pow x 2) (- 1 (cos x)))>
#<alt (* (pow x 2) (- 1 (cos x)))>
#<alt (* (pow x 2) (- 1 (cos x)))>
#<alt (* (pow x 2) (- 1 (cos x)))>
#<alt (* (pow x 2) (- 1 (cos x)))>
#<alt (* (pow x 2) (- 1 (cos x)))>
#<alt (* (pow x 2) (- 1 (cos x)))>
#<alt (* (pow x 2) (- 1 (cos x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* x (cos x))>
#<alt (* x (cos x))>
#<alt (* x (cos x))>
#<alt (* x (cos x))>
#<alt (* x (cos x))>
#<alt (* x (cos x))>
#<alt (* x (cos x))>
#<alt (* x (cos x))>

Calls

54 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(* (/ (sin x) (* x x)) (tan (/ x 2)))
1.0ms	x	@	-inf	(/ (+ (cos x) -1) x)
1.0ms	x	@	inf	(* (/ (sin x) (* x x)) (tan (/ x 2)))
1.0ms	x	@	-inf	(* (/ (sin x) (* x x)) (tan (/ x 2)))
1.0ms	x	@	inf	(/ (/ (- (* x x) (* x (* x (cos x)))) (* x x)) (* x x))

rewrite370.0ms (3.7%)

Algorithm

1×	batch-egg-rewrite

Rules

3696×	`/-lowering-/.f32`
3696×	`/-lowering-/.f64`
2840×	`-lowering-.f32`
2840×	`-lowering-.f64`
1680×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	98
1	175	94
2	1450	93
0	8563	93

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 1400

Calls

Call 1

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

Outputs
(/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (*.f64 x x) (sin.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) (sin.f64 x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x x) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 (.f64 x x) (sin.f64 x)) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (cos.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (/.f64 (sin.f64 x) x) (sin.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)) (*.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sin.f64 x) (*.f64 x x))) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (.f64 x x))) (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) x) (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 x (sin.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (sin.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 x (sin.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (*.f64 x x) (sin.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) x)))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (.f64 (/.f64 (.f64 x x) (sin.f64 x)) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sin.f64 x) (*.f64 x x))))
(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 x x))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (*.f64 x x) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 (/.f64 (sin.f64 x) x) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 x (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x)) (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 x x)))
(/.f64 (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (/.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (.f64 x x))))
(/.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 x (sin.f64 x))) (*.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) x))
(/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (neg.f64 (.f64 (/.f64 (.f64 x x) (sin.f64 x)) (cos.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (neg.f64 (/.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sin.f64 x) (*.f64 x x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 x (sin.f64 x))) x)
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) x)
(/.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (*.f64 x x) (sin.f64 x))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) x) x)
(/.f64 (/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (neg.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 x x) (sin.f64 x))))
(/.f64 (neg.f64 (.f64 (sin.f64 x) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (neg.f64 (.f64 (*.f64 x x) (cos.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (cos.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (neg.f64 (.f64 (/.f64 (sin.f64 x) x) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (neg.f64 (.f64 x (cos.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (neg.f64 (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x))) (neg.f64 (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 x x))))
(/.f64 (neg.f64 (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))) (neg.f64 (/.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (.f64 x x)))))
(/.f64 (neg.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 x (sin.f64 x)))) (neg.f64 (*.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) x)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))))) (.f64 x x))
(/.f64 (neg.f64 (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))) (.f64 x x))
(/.f64 (neg.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 x (sin.f64 x)))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))) (.f64 x x))
(/.f64 (neg.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (*.f64 x x) (sin.f64 x)))) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (neg.f64 (/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) x)) (-.f64 #s(literal 0 binary64) x))
(pow.f64 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal -1 binary64))
(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)))
(.f64 (sin.f64 x) (.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sin.f64 x) (.f64 x x)))
(.f64 #s(literal 1 binary64) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (.f64 x x) (sin.f64 x))))
(.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 (*.f64 x x) (sin.f64 x)) (cos.f64 (/.f64 x #s(literal 2 binary64))))))
(.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sin.f64 x) (.f64 x x)))))
(.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) x))
(.f64 (.f64 (sin.f64 x) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (cos.f64 (/.f64 x #s(literal 2 binary64))))))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (cos.f64 (/.f64 x #s(literal 2 binary64))))))
(.f64 (.f64 (/.f64 (sin.f64 x) x) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 x (cos.f64 (/.f64 x #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x))))
(.f64 (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))))
(.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 x (sin.f64 x))) (/.f64 #s(literal 1 binary64) (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) x)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(.f64 (.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(.f64 (.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(*.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 x (sin.f64 x))) (/.f64 #s(literal 1 binary64) x))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(.f64 (.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (.f64 x x) (sin.f64 x))) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(.f64 (/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) x) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (sin.f64 x))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) (/.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(neg.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(/.f64 (sin.f64 x) (*.f64 x x))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 x x) (sin.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 x x) (sin.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (/.f64 (sin.f64 x) #s(literal -1 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (/.f64 (sin.f64 x) x) x)
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (sin.f64 x) x)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 (sin.f64 x) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (sin.f64 x) x))) x)
(/.f64 (neg.f64 (/.f64 (sin.f64 x) #s(literal -1 binary64))) (*.f64 x x))
(pow.f64 (/.f64 (*.f64 x x) (sin.f64 x)) #s(literal -1 binary64))
(.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (.f64 x x) (sin.f64 x)))))
(.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (sin.f64 x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal -1 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (/.f64 #s(literal -1 binary64) (.f64 x x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sin.f64 x) x))
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 #s(literal 1 binary64) x))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 (sin.f64 x) x)) (/.f64 #s(literal -1 binary64) x))
(.f64 (/.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (.f64 x x)))
(.f64 (pow.f64 (/.f64 (.f64 x x) (sin.f64 x)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (*.f64 x x) (sin.f64 x)) #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(sin.f64 x)
(neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(/.f64 (sin.f64 x) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) #s(literal -1 binary64))
(*.f64 (sin.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 x (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 x x) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
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(pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 x x)))) #s(literal -1 binary64))
(.f64 x (-.f64 x (.f64 x (cos.f64 x))))
(.f64 #s(literal -1 binary64) (.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 x (*.f64 x (cos.f64 x)))))
(.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (.f64 x x))))
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(.f64 (-.f64 x (.f64 x (cos.f64 x))) x)
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (pow.f64 (.f64 x (.f64 x (cos.f64 x))) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (cos.f64 x))) (.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (.f64 x x)))))))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64)) (.f64 x x)))))
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(.f64 (.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (.f64 x x))) (-.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (.f64 x x))) (+.f64 (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (cos.f64 x))) (.f64 x (.f64 x (cos.f64 x)))))) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (.f64 x x))) (+.f64 (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (cos.f64 x))) (.f64 x (*.f64 x (cos.f64 x)))))))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(neg.f64 (tan.f64 (/.f64 x #s(literal -2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (neg.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64))
(*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(*.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))))
(exp.f64 (*.f64 #s(literal -2 binary64) (log.f64 x)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal -2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(/.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
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(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x x)))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))))
(/.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) x) x)
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) x))) x)
(pow.f64 x #s(literal -2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64))
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(.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)))
(.f64 #s(literal -1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal 1 binary64)))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal -1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (cos.f64 x))))
(/.f64 (*.f64 x (cos.f64 x)) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (cos.f64 x))) #s(literal -1 binary64))
(*.f64 x (cos.f64 x))
(*.f64 (cos.f64 x) x)
(.f64 (.f64 x (cos.f64 x)) #s(literal 1 binary64))

simplify240.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

3600×	`-lowering-.f32`
3600×	`-lowering-.f64`
3324×	`+-lowering-+.f64`
3324×	`+-lowering-+.f32`
2144×	`sum4-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	117	1561
1	343	1311
2	967	1305
3	3203	1305
4	5815	1305
5	7329	1305
0	8046	1305

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ 1 x)
(/ (+ 1 (* -1/6 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) x)
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
-1/2
(- (* 1/24 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2)
(/ (- (cos x) 1) (pow x 2))
(/ (- (cos x) 1) (pow x 2))
(/ (- (cos x) 1) (pow x 2))
(/ (- (cos x) 1) (pow x 2))
(/ (- (cos x) 1) (pow x 2))
(/ (- (cos x) 1) (pow x 2))
(/ (- (cos x) 1) (pow x 2))
(/ (- (cos x) 1) (pow x 2))
(* -1/2 x)
(* x (- (* 1/24 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(/ (- (cos x) 1) x)
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
(- (cos x) 1)
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 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 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
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)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(* 1/2 (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 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(* 1/2 (pow x 4))
(* (pow x 4) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 4) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 4) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* (pow x 2) (- 1 (cos x)))
(* (pow x 2) (- 1 (cos x)))
(* (pow x 2) (- 1 (cos x)))
(* (pow x 2) (- 1 (cos x)))
(* (pow x 2) (- 1 (cos x)))
(* (pow x 2) (- 1 (cos x)))
(* (pow x 2) (- 1 (cos x)))
(* (pow x 2) (- 1 (cos x)))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
x
(* x (+ 1 (* -1/2 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))

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

eval215.0ms (2.1%)

Compiler: Compiled 42702 to 3204 computations (92.5% saved)

prune197.0ms (2%)

Pruning

30 alts after pruning (26 fresh and 4 done)

	Pruned	Kept	Total
New	1778	24	1802
Fresh	11	2	13
Picked	2	3	5
Done	0	1	1
Total	1791	30	1821

Accuracy

100.0%

Counts

1821 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
	30.3%	(/.f64 (/.f64 (-.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x x)) (.f64 x x))
	30.4%	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (/.f64 x (/.f64 #s(literal 1 binary64) x))) (.f64 x x))
✓	30.4%	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x x)) (*.f64 x x))
	54.7%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	14.7%	(/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (.f64 x x))) (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x))))
▶	30.4%	(/.f64 (/.f64 (.f64 (-.f64 x (.f64 x (cos.f64 x))) x) (.f64 x x)) (.f64 x x))
	14.4%	(/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x x)) (.f64 x x))
	30.4%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (.f64 x x))) #s(literal -1 binary64)))) (*.f64 x x))
	53.5%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (cos.f64 x) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
	54.2%	(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) (*.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) x))) x)
▶	44.1%	(/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x (*.f64 x x)))
	53.6%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
	53.6%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))))
✓	53.6%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
	25.4%	(/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (*.f64 x x))
	75.1%	(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 x x))
	22.6%	(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
	44.1%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (-.f64 x (*.f64 x (cos.f64 x)))))
	54.4%	(/.f64 #s(literal -1 binary64) (/.f64 x (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x)))
	53.5%	(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
▶	47.3%	(-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
	53.8%	(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (cos.f64 x) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
✓	75.6%	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
▶	53.6%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
▶	75.6%	(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)))
	24.6%	(neg.f64 (/.f64 (/.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) x) x))
	54.7%	(neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (+.f64 (cos.f64 x) #s(literal -1 binary64)))) x))
	54.6%	(neg.f64 (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x))) x))
	54.7%	(neg.f64 (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (cos.f64 x) #s(literal -1 binary64))) x))
✓	48.7%	#s(literal 1/2 binary64)

Compiler

Compiled 782 to 468 computations (40.2% saved)

simplify122.0ms (1.2%)

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(-.f64 x (*.f64 x (cos.f64 x)))
✓	cost-diff	0	(.f64 (-.f64 x (.f64 x (cos.f64 x))) x)
✓	cost-diff	512	(/.f64 (.f64 (-.f64 x (.f64 x (cos.f64 x))) x) (*.f64 x x))
✓	cost-diff	512	(/.f64 (/.f64 (.f64 (-.f64 x (.f64 x (cos.f64 x))) x) (.f64 x x)) (.f64 x x))
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(*.f64 x (cos.f64 x))
✓	cost-diff	0	(-.f64 x (*.f64 x (cos.f64 x)))
✓	cost-diff	256	(/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x (*.f64 x x)))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	cost-diff	128	(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) #s(literal 1/24 binary64))
✓	cost-diff	0	(-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
✓	cost-diff	0	(tan.f64 (/.f64 x #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 x x))
✓	cost-diff	0	(sin.f64 x)
✓	cost-diff	0	(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)))

Rules

1478×	`fma-lowering-fma.f32`
1478×	`fma-lowering-fma.f64`
1408×	`sum3-define`
1404×	`-lowering-.f32`
1404×	`-lowering-.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	127
1	73	124
2	212	120
3	444	120
4	1048	120
5	3249	120
6	7369	120
0	8005	120

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize263.0ms (2.6%)

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(*.f64 x (cos.f64 x))
✓	accuracy	84.0%	(-.f64 x (*.f64 x (cos.f64 x)))
✓	accuracy	75.9%	(/.f64 (/.f64 (.f64 (-.f64 x (.f64 x (cos.f64 x))) x) (.f64 x x)) (.f64 x x))
✓	accuracy	45.1%	(/.f64 (.f64 (-.f64 x (.f64 x (cos.f64 x))) x) (*.f64 x x))
✓	accuracy	99.8%	(.f64 x (.f64 x x))
✓	accuracy	99.8%	(*.f64 x (cos.f64 x))
✓	accuracy	84.0%	(-.f64 x (*.f64 x (cos.f64 x)))
✓	accuracy	61.0%	(/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x (*.f64 x x)))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	99.4%	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	accuracy	78.8%	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	accuracy	75.1%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
✓	accuracy	100.0%	(-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal 1/24 binary64))
✓	accuracy	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	99.8%	(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)))
✓	accuracy	76.6%	(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 x x))

Results

79.0ms	59×	2	valid
67.0ms	137×	0	valid
38.0ms	42×	1	valid
36.0ms	18×	3	valid

Compiler

Compiled 164 to 25 computations (84.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 116.0ms

ival-cos: 31.0ms (26.8% of total)

ival-mult: 19.0ms (16.4% of total)

ival-div: 17.0ms (14.7% of total)

backward-pass: 17.0ms (14.7% of total)

ival-tan: 8.0ms (6.9% of total)

ival-sin: 8.0ms (6.9% of total)

ival-sub: 7.0ms (6% of total)

...c/correct-round.rkt:119:19: 7.0ms (6% of total)

const: 1.0ms (0.9% of total)

series8.0ms (0.1%)

Counts

18 → 216

Calls

Call 1

Inputs
#<alt (* (sin x) (/ (tan (/ x 2)) (* x x)))>
#<alt (sin x)>
#<alt (/ (tan (/ x 2)) (* x x))>
#<alt (tan (/ x 2))>
#<alt (- 1/2 (* (* x x) 1/24))>
#<alt (* (* x x) 1/24)>
#<alt (* x x)>
#<alt (* (/ 1 (* x x)) (- 1 (cos x)))>
#<alt (/ 1 (* x x))>
#<alt (- 1 (cos x))>
#<alt (/ (- x (* x (cos x))) (* x (* x x)))>
#<alt (- x (* x (cos x)))>
#<alt (* x (cos x))>
#<alt (cos x)>
#<alt (/ (/ (* (- x (* x (cos x))) x) (* x x)) (* x x))>
#<alt (/ (* (- x (* x (cos x))) x) (* x x))>
#<alt (* (- x (* x (cos x))) x)>
#<alt (* x (* x x))>

Outputs
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (* 1/24 (pow x 2))) x)>
#<alt (/ (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))) x)>
#<alt (/ (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))) x)>
#<alt (/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (* -1/24 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* -1/24 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (* 1/2 (pow x 3))>
#<alt (* (pow x 3) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 3) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (* x (- 1 (cos x)))>
#<alt (* x (- 1 (cos x)))>
#<alt (* x (- 1 (cos x)))>
#<alt (* x (- 1 (cos x)))>
#<alt (* x (+ 1 (* -1 (cos x))))>
#<alt (* x (+ 1 (* -1 (cos x))))>
#<alt (* x (+ 1 (* -1 (cos x))))>
#<alt (* x (+ 1 (* -1 (cos x))))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* x (cos x))>
#<alt (* x (cos x))>
#<alt (* x (cos x))>
#<alt (* x (cos x))>
#<alt (* x (cos x))>
#<alt (* x (cos x))>
#<alt (* x (cos x))>
#<alt (* x (cos x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (+ 1 (* -1 (cos x)))>
#<alt (+ 1 (* -1 (cos x)))>
#<alt (+ 1 (* -1 (cos x)))>
#<alt (+ 1 (* -1 (cos x)))>
#<alt (* 1/2 (pow x 4))>
#<alt (* (pow x 4) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 4) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 4) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (* (pow x 2) (- 1 (cos x)))>
#<alt (* (pow x 2) (- 1 (cos x)))>
#<alt (* (pow x 2) (- 1 (cos x)))>
#<alt (* (pow x 2) (- 1 (cos x)))>
#<alt (* (pow x 2) (+ 1 (* -1 (cos x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (cos x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (cos x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (cos x))))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>

Calls

54 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/ (- x (* x (cos x))) (* x (* x x)))
0.0ms	x	@	-inf	(/ (- x (* x (cos x))) (* x (* x x)))
0.0ms	x	@	inf	(/ (tan (/ x 2)) (* x x))
0.0ms	x	@	inf	(* (- x (* x (cos x))) x)
0.0ms	x	@	inf	(* (* x x) 1/24)

rewrite339.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

4496×	`-lowering-.f32`
4496×	`-lowering-.f64`
3310×	`/-lowering-/.f32`
3310×	`/-lowering-/.f64`
1566×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	100
1	149	94
2	1218	90
0	8705	90

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 1396

Calls

Call 1

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

Outputs
(neg.f64 (.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x))) (sin.f64 x)))
(neg.f64 (.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x)))))
(neg.f64 (.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(neg.f64 (/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(neg.f64 (/.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1 binary64)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (*.f64 x x)))
(/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) x) (sin.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))))))
(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 x x))
(/.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1 binary64)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (/.f64 (sin.f64 x) x) (/.f64 x (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) x) x)
(/.f64 (*.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) x) (sin.f64 x)) x)
(/.f64 (neg.f64 (sin.f64 x)) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1 binary64)) (tan.f64 (/.f64 x #s(literal 2 binary64))))) (*.f64 x x))
(/.f64 (neg.f64 (/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) x)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (*.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) x) (sin.f64 x))) (-.f64 #s(literal 0 binary64) x))
(pow.f64 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal -1 binary64))
(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)))
(.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (sin.f64 x)))
(.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)) (sin.f64 x))
(.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)) (/.f64 (sin.f64 x) #s(literal 1 binary64)))
(.f64 (/.f64 (sin.f64 x) (/.f64 (.f64 x x) (tan.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal 1 binary64))
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(.f64 (.f64 (-.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 x (cos.f64 x)) #s(literal 3 binary64))) x) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))) (.f64 x x))))
(.f64 (.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) x) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x))) (*.f64 x x))))
(.f64 (/.f64 #s(literal -1 binary64) x) (-.f64 (.f64 x (cos.f64 x)) x))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (cos.f64 x)) x)) x) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 x #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)))
(.f64 (/.f64 x (-.f64 #s(literal 0 binary64) x)) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x (cos.f64 x)) x)))
(.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) x) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x (cos.f64 x)) x)))
(.f64 (/.f64 (.f64 x (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (.f64 x x)))
(.f64 (/.f64 (-.f64 (.f64 x (cos.f64 x)) x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (-.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 x (cos.f64 x)) #s(literal 3 binary64))) x) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))))
(.f64 (/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) x) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(.f64 (/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))) x) (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))))
(.f64 (/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x))) x) (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) (.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(.f64 (pow.f64 (/.f64 x (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 x (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)) #s(literal -1/2 binary64)))
(.f64 (.f64 x (.f64 x (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
(.f64 (.f64 (.f64 x (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)) x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x))
(.f64 (.f64 #s(literal 1 binary64) (.f64 x (-.f64 (.f64 x (cos.f64 x)) x))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 x (cos.f64 x)) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(+.f64 (.f64 x x) (.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(+.f64 (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (cos.f64 x))) (*.f64 x x))
(-.f64 #s(literal 0 binary64) (.f64 x (-.f64 (.f64 x (cos.f64 x)) x)))
(fma.f64 x x (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(neg.f64 (.f64 x (-.f64 (.f64 x (cos.f64 x)) x)))
(/.f64 x (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))) (.f64 (-.f64 (.f64 x (.f64 x x)) (pow.f64 (*.f64 x (cos.f64 x)) #s(literal 3 binary64))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x))) (.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))) (.f64 x (-.f64 (.f64 x (.f64 x x)) (pow.f64 (*.f64 x (cos.f64 x)) #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x))) (.f64 x (.f64 (.f64 x x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))))
(/.f64 (.f64 (-.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 x (cos.f64 x)) #s(literal 3 binary64))) x) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
(/.f64 (.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) x) (.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (.f64 x (-.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 x (cos.f64 x)) #s(literal 3 binary64)))) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
(/.f64 (.f64 x (.f64 (.f64 x x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) (.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 x (cos.f64 x)) #s(literal 3 binary64))) x)) (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))))
(/.f64 (neg.f64 (.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) x)) (.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 x))) x))
(/.f64 (neg.f64 (.f64 x (-.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 x (cos.f64 x)) #s(literal 3 binary64))))) (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))))
(/.f64 (neg.f64 (.f64 x (.f64 (.f64 x x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))) (.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 x))) x))
(/.f64 (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (pow.f64 (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (cos.f64 x))) #s(literal 3 binary64))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (cos.f64 x))) (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (cos.f64 x)))) (.f64 (.f64 x x) (.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) (cos.f64 x)))))))
(/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (cos.f64 x))) (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (cos.f64 x))))) (-.f64 (.f64 x x) (.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) (cos.f64 x)))))
(.f64 x (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(.f64 (.f64 x (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (.f64 x (-.f64 (*.f64 x (cos.f64 x)) x)))
(.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 (.f64 x (cos.f64 x)) x))
(.f64 (-.f64 (.f64 x (cos.f64 x)) x) (-.f64 #s(literal 0 binary64) x))
(.f64 (.f64 (-.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 x (cos.f64 x)) #s(literal 3 binary64))) x) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))))
(.f64 (.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) x) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(.f64 (.f64 x (-.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 x (cos.f64 x)) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))))
(.f64 (.f64 x (.f64 (.f64 x x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) x))
(.f64 (/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 1 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(-.f64 #s(literal 0 binary64) (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x))))
(neg.f64 (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x))))
(neg.f64 (/.f64 x (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(/.f64 x (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
(/.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(/.f64 (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x x))) #s(literal -1 binary64))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) x))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))

simplify251.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

3990×	`-lowering-.f32`
3990×	`-lowering-.f64`
3024×	`+-lowering-+.f64`
3024×	`+-lowering-+.f32`
2184×	`sum4-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	1580
1	361	1334
2	1025	1320
3	3421	1320
4	6006	1320
5	7196	1320
0	8011	1320

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(/ 1/2 x)
(/ (+ 1/2 (* 1/24 (pow x 2))) x)
(/ (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))) x)
(/ (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))) x)
(/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))
(/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))
(/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))
(/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))
(/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))
(/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))
(/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))
(/ (sin (* 1/2 x)) (* (pow x 2) (cos (* 1/2 x))))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* -1/24 (pow x 2)))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(* 1/24 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (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 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(* 1/2 (pow x 3))
(* (pow x 3) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 3) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 3) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* x (- 1 (cos x)))
(* x (- 1 (cos x)))
(* x (- 1 (cos x)))
(* x (- 1 (cos x)))
(* x (+ 1 (* -1 (cos x))))
(* x (+ 1 (* -1 (cos x))))
(* x (+ 1 (* -1 (cos x))))
(* x (+ 1 (* -1 (cos x))))
x
(* x (+ 1 (* -1/2 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
1
(+ 1 (* -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)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(* 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 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(+ 1 (* -1 (cos x)))
(* 1/2 (pow x 4))
(* (pow x 4) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 4) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 4) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* (pow x 2) (- 1 (cos x)))
(* (pow x 2) (- 1 (cos x)))
(* (pow x 2) (- 1 (cos x)))
(* (pow x 2) (- 1 (cos x)))
(* (pow x 2) (+ 1 (* -1 (cos x))))
(* (pow x 2) (+ 1 (* -1 (cos x))))
(* (pow x 2) (+ 1 (* -1 (cos x))))
(* (pow x 2) (+ 1 (* -1 (cos x))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)

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

eval229.0ms (2.3%)

Compiler: Compiled 40448 to 2701 computations (93.3% saved)

prune148.0ms (1.5%)

Pruning

31 alts after pruning (25 fresh and 6 done)

	Pruned	Kept	Total
New	1913	14	1927
Fresh	10	11	21
Picked	1	4	5
Done	2	2	4
Total	1926	31	1957

Accuracy

100.0%

Counts

1957 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	30.3%	(/.f64 (/.f64 (-.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x x)) (.f64 x x))
	53.5%	(/.f64 (/.f64 (-.f64 (.f64 x (cos.f64 x)) x) (-.f64 #s(literal 0 binary64) x)) (.f64 x x))
	30.4%	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (/.f64 x (/.f64 #s(literal 1 binary64) x))) (.f64 x x))
▶	54.7%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	14.4%	(/.f64 (/.f64 (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) (.f64 x x))) x) (.f64 x x)) (.f64 x x))
	14.5%	(/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 x x)) (.f64 x x))
	53.6%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x))) (.f64 x x))
▶	54.2%	(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) (*.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) x))) x)
	10.5%	(/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 x (cos.f64 x)) x))) (.f64 (.f64 x (.f64 x x)) (.f64 x x)))
✓	44.1%	(/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x (*.f64 x x)))
	53.6%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
✓	53.6%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
▶	25.4%	(/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (*.f64 x x))
	54.7%	(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (cos.f64 x))) x)
▶	75.7%	(/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
	44.1%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (-.f64 x (*.f64 x (cos.f64 x)))))
	54.4%	(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)))
	53.5%	(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
✓	47.3%	(-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
	53.8%	(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (cos.f64 x)))
	54.0%	(*.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
	53.5%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
✓	53.6%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
	22.6%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
✓	75.6%	(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)))
	49.4%	(*.f64 (sin.f64 x) (/.f64 #s(literal 1/2 binary64) x))
	44.1%	(.f64 x (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 (cos.f64 x) (.f64 x (*.f64 x x)))))
	24.6%	(neg.f64 (/.f64 (/.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) x) x))
	54.7%	(neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (+.f64 (cos.f64 x) #s(literal -1 binary64)))) x))
▶	54.6%	(neg.f64 (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x))) x))
✓	48.7%	#s(literal 1/2 binary64)

Compiler

Compiled 771 to 442 computations (42.7% saved)

simplify132.0ms (1.3%)

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	128	(*.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) x))
✓	cost-diff	256	(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)
✓	cost-diff	512	(-.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) (*.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) x)))
✓	cost-diff	512	(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) (*.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) x))) x)
✓	cost-diff	0	(/.f64 #s(literal -1 binary64) x)
✓	cost-diff	256	(-.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x)))
✓	cost-diff	256	(/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x))) x)
✓	cost-diff	320	(neg.f64 (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x))) x))
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
✓	cost-diff	0	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	128	(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
✓	cost-diff	384	(/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (*.f64 x x))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(/.f64 (*.f64 x x) (tan.f64 (/.f64 x #s(literal 2 binary64))))
✓	cost-diff	0	(sin.f64 x)
✓	cost-diff	0	(/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (tan.f64 (/.f64 x #s(literal 2 binary64)))))

Rules

2282×	`-lowering-.f32`
2282×	`-lowering-.f64`
1072×	`/-lowering-/.f32`
1072×	`/-lowering-/.f64`
924×	`fmsub-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	29	134
1	76	133
2	159	129
3	477	126
4	1469	124
5	4607	124
6	6904	124
0	8026	124

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (sin x) (/ (* x x) (tan (/ x 2))))
(sin x)
x
(/ (* x x) (tan (/ x 2)))
(* x x)
(tan (/ x 2))
(/ x 2)
2
(/ (- 1 1) (* x x))
(- 1 1)
1
(* x x)
x
(/ (/ (- 1 (cos x)) x) x)
(/ (- 1 (cos x)) x)
(- 1 (cos x))
1
(cos x)
x
(neg (/ (- (/ -1 x) (/ (cos x) (- 0 x))) x))
(/ (- (/ -1 x) (/ (cos x) (- 0 x))) x)
(- (/ -1 x) (/ (cos x) (- 0 x)))
(/ -1 x)
-1
x
(/ (cos x) (- 0 x))
(cos x)
(- 0 x)
0
(/ (- (* (/ 1 (* x x)) x) (* 1 (/ (cos x) x))) x)
(- (* (/ 1 (* x x)) x) (* 1 (/ (cos x) x)))
(* (/ 1 (* x x)) x)
(/ 1 (* x x))
1
(* x x)
x
(* 1 (/ (cos x) x))
(/ (cos x) x)
(cos x)

Outputs
(/ (sin x) (/ (* x x) (tan (/ x 2))))
(/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(sin x)
(sin.f64 x)
x
(/ (* x x) (tan (/ x 2)))
(/.f64 (*.f64 x x) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(* x x)
(*.f64 x x)
(tan (/ x 2))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ x 2)
(/.f64 x #s(literal 2 binary64))
2
#s(literal 2 binary64)
(/ (- 1 1) (* x x))
#s(literal 0 binary64)
(- 1 1)
#s(literal 0 binary64)
1
#s(literal 1 binary64)
(* x x)
(*.f64 x x)
x
(/ (/ (- 1 (cos x)) x) x)
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
1
#s(literal 1 binary64)
(cos x)
(cos.f64 x)
x
(neg (/ (- (/ -1 x) (/ (cos x) (- 0 x))) x))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- (/ -1 x) (/ (cos x) (- 0 x))) x)
(/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x) x)
(- (/ -1 x) (/ (cos x) (- 0 x)))
(/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
-1
#s(literal -1 binary64)
x
(/ (cos x) (- 0 x))
(/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x))
(cos x)
(cos.f64 x)
(- 0 x)
(-.f64 #s(literal 0 binary64) x)
0
#s(literal 0 binary64)
(/ (- (* (/ 1 (* x x)) x) (* 1 (/ (cos x) x))) x)
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(- (* (/ 1 (* x x)) x) (* 1 (/ (cos x) x)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
(* (/ 1 (* x x)) x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 (* x x))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
1
#s(literal 1 binary64)
(* x x)
(*.f64 x x)
x
(* 1 (/ (cos x) x))
(/.f64 (cos.f64 x) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(cos x)
(cos.f64 x)

localize341.0ms (3.4%)

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(/.f64 (cos.f64 x) x)
✓	accuracy	99.4%	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	accuracy	55.4%	(-.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) (*.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) x)))
✓	accuracy	54.8%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	99.9%	(/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x))) x)
✓	accuracy	99.8%	(/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x))
✓	accuracy	55.4%	(-.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x)))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	99.9%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
✓	accuracy	78.8%	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	accuracy	76.9%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	76.2%	(/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (*.f64 x x))
✓	accuracy	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	99.5%	(/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
✓	accuracy	77.0%	(/.f64 (*.f64 x x) (tan.f64 (/.f64 x #s(literal 2 binary64))))

Results

96.0ms	60×	2	valid
86.0ms	21×	3	valid
72.0ms	137×	0	valid
38.0ms	38×	1	valid

Compiler

Compiled 183 to 30 computations (83.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 176.0ms

ival-div: 51.0ms (29% of total)

backward-pass: 43.0ms (24.4% of total)

ival-cos: 30.0ms (17.1% of total)

ival-mult: 17.0ms (9.7% of total)

ival-sub: 12.0ms (6.8% of total)

ival-sin: 9.0ms (5.1% of total)

ival-tan: 6.0ms (3.4% of total)

ival-neg: 5.0ms (2.8% of total)

const: 1.0ms (0.6% of total)

series15.0ms (0.2%)

Counts

22 → 252

Calls

Call 1

Inputs
#<alt (/ (sin x) (/ (* x x) (tan (/ x 2))))>
#<alt (sin x)>
#<alt (/ (* x x) (tan (/ x 2)))>
#<alt (* x x)>
#<alt (/ (- 1 1) (* x x))>
#<alt (- 1 1)>
#<alt (/ (/ (- 1 (cos x)) x) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (- 1 (cos x))>
#<alt (cos x)>
#<alt (neg (/ (- (/ -1 x) (/ (cos x) (- 0 x))) x))>
#<alt (/ (- (/ -1 x) (/ (cos x) (- 0 x))) x)>
#<alt (- (/ -1 x) (/ (cos x) (- 0 x)))>
#<alt (/ -1 x)>
#<alt (/ (- (* (/ 1 (* x x)) x) (* 1 (/ (cos x) x))) x)>
#<alt (- (* (/ 1 (* x x)) x) (* 1 (/ (cos x) x)))>
#<alt (* (/ 1 (* x x)) x)>
#<alt (* 1 (/ (cos x) x))>
#<alt (tan (/ x 2))>
#<alt (/ (cos x) (- 0 x))>
#<alt (/ 1 (* x x))>
#<alt (/ (cos x) x)>

Outputs
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* -1/6 (pow x 2))))>
#<alt (* x (+ 2 (* (pow x 2) (- (* -1/360 (pow x 2)) 1/6))))>
#<alt (* x (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/15120 (pow x 2)) 1/360)) 1/6))))>
#<alt (/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))>
#<alt (/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))>
#<alt (/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))>
#<alt (/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))>
#<alt (/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))>
#<alt (/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))>
#<alt (/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))>
#<alt (/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt -1/2>
#<alt (- (* 1/24 (pow x 2)) 1/2)>
#<alt (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)>
#<alt (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2)>
#<alt (* -1 (/ (+ 1 (* -1 (cos x))) (pow x 2)))>
#<alt (* -1 (/ (+ 1 (* -1 (cos x))) (pow x 2)))>
#<alt (* -1 (/ (+ 1 (* -1 (cos x))) (pow x 2)))>
#<alt (* -1 (/ (+ 1 (* -1 (cos x))) (pow x 2)))>
#<alt (* -1 (/ (- 1 (cos x)) (pow x 2)))>
#<alt (* -1 (/ (- 1 (cos x)) (pow x 2)))>
#<alt (* -1 (/ (- 1 (cos x)) (pow x 2)))>
#<alt (* -1 (/ (- 1 (cos x)) (pow x 2)))>
#<alt (* -1/2 x)>
#<alt (* x (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))>
#<alt (* -1 (/ (+ 1 (* -1 (cos x))) x))>
#<alt (* -1 (/ (+ 1 (* -1 (cos x))) x))>
#<alt (* -1 (/ (+ 1 (* -1 (cos x))) x))>
#<alt (* -1 (/ (+ 1 (* -1 (cos x))) x))>
#<alt (* -1 (/ (- 1 (cos x)) x))>
#<alt (* -1 (/ (- 1 (cos x)) x))>
#<alt (* -1 (/ (- 1 (cos x)) x))>
#<alt (* -1 (/ (- 1 (cos x)) x))>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (+ 1 (* -1 (cos x))) x)>
#<alt (/ (+ 1 (* -1 (cos x))) x)>
#<alt (/ (+ 1 (* -1 (cos x))) x)>
#<alt (/ (+ 1 (* -1 (cos x))) x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* -1/2 (pow x 2))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) x)>
#<alt (/ (cos x) x)>
#<alt (/ (cos x) x)>
#<alt (/ (cos x) x)>
#<alt (/ (cos x) x)>
#<alt (/ (cos x) x)>
#<alt (/ (cos x) x)>
#<alt (/ (cos x) x)>
#<alt (/ (cos x) x)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ -1 x)>
#<alt (/ (- (* 1/2 (pow x 2)) 1) x)>
#<alt (/ (- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1) x)>
#<alt (/ (- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1) x)>
#<alt (* -1 (/ (cos x) x))>
#<alt (* -1 (/ (cos x) x))>
#<alt (* -1 (/ (cos x) x))>
#<alt (* -1 (/ (cos x) x))>
#<alt (* -1 (/ (cos x) x))>
#<alt (* -1 (/ (cos x) x))>
#<alt (* -1 (/ (cos x) x))>
#<alt (* -1 (/ (cos x) x))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* -1/2 (pow x 2))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) x)>
#<alt (/ (cos x) x)>
#<alt (/ (cos x) x)>
#<alt (/ (cos x) x)>
#<alt (/ (cos x) x)>
#<alt (/ (cos x) x)>
#<alt (/ (cos x) x)>
#<alt (/ (cos x) x)>
#<alt (/ (cos x) x)>

Calls

63 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	(neg (/ (- (/ -1 x) (/ (cos x) (- 0 x))) x))
3.0ms	x	@	inf	(/ (- (* (/ 1 (* x x)) x) (* 1 (/ (cos x) x))) x)
1.0ms	x	@	-inf	(/ (- (* (/ 1 (* x x)) x) (* 1 (/ (cos x) x))) x)
1.0ms	x	@	-inf	(neg (/ (- (/ -1 x) (/ (cos x) (- 0 x))) x))
1.0ms	x	@	inf	(/ (* x x) (tan (/ x 2)))

rewrite403.0ms (4%)

Algorithm

1×	batch-egg-rewrite

Rules

2866×	`/-lowering-/.f32`
2866×	`/-lowering-/.f64`
1804×	`-lowering-.f32`
1804×	`-lowering-.f64`
1606×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	103
1	213	102
2	1869	100
0	9216	100

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 1855

Calls

Call 1

Inputs
(/ (sin x) (/ (* x x) (tan (/ x 2))))
(sin x)
(/ (* x x) (tan (/ x 2)))
(* x x)
(/ (- 1 1) (* x x))
(- 1 1)
(/ (/ (- 1 (cos x)) x) x)
(/ (- 1 (cos x)) x)
(- 1 (cos x))
(cos x)
(neg (/ (- (/ -1 x) (/ (cos x) (- 0 x))) x))
(/ (- (/ -1 x) (/ (cos x) (- 0 x))) x)
(- (/ -1 x) (/ (cos x) (- 0 x)))
(/ -1 x)
(/ (- (* (/ 1 (* x x)) x) (* 1 (/ (cos x) x))) x)
(- (* (/ 1 (* x x)) x) (* 1 (/ (cos x) x)))
(* (/ 1 (* x x)) x)
(* 1 (/ (cos x) x))
(tan (/ x 2))
(/ (cos x) (- 0 x))
(/ 1 (* x x))
(/ (cos x) x)

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)))) (/.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)))))
(neg.f64 (/.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 x x)))))
(/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (/.f64 #s(literal -1 binary64) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 x x))))
(/.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (*.f64 x x) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x))) (/.f64 (*.f64 x x) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 (sin.f64 x) #s(literal 1 binary64)) (/.f64 (.f64 x x) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 x x))
(/.f64 (/.f64 (sin.f64 x) x) (/.f64 x (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (neg.f64 (/.f64 (sin.f64 x) (*.f64 x x))) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (neg.f64 (.f64 (sin.f64 x) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (neg.f64 (.f64 (*.f64 x x) (cos.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)))) (/.f64 #s(literal -1 binary64) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 x x))))
(/.f64 (neg.f64 (.f64 (sin.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x))))
(/.f64 (neg.f64 (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (neg.f64 (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (neg.f64 (/.f64 (sin.f64 x) x)) (neg.f64 (/.f64 x (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(pow.f64 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)))
(.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sin.f64 x) (.f64 x x)))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (*.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (sin.f64 x)) #s(literal -1 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (/.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 (/.f64 x (tan.f64 (/.f64 x #s(literal 2 binary64)))) (sin.f64 x)) #s(literal -1 binary64)))
(.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)) (sin.f64 x))
(.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal -1 binary64)))
(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(.f64 (/.f64 (sin.f64 x) #s(literal 1 binary64)) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)))
(.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (.f64 x x))) (-.f64 #s(literal 0 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(+.f64 (.f64 (sin.f64 x) (cos.f64 #s(literal 0 binary64))) (.f64 (cos.f64 x) (sin.f64 #s(literal 0 binary64))))
(+.f64 (.f64 (sin.f64 #s(literal 0 binary64)) (cos.f64 x)) (.f64 (cos.f64 #s(literal 0 binary64)) (sin.f64 x)))
(-.f64 (.f64 (sin.f64 #s(literal 0 binary64)) (cos.f64 x)) (.f64 (cos.f64 #s(literal 0 binary64)) (sin.f64 (-.f64 #s(literal 0 binary64) x))))
(sin.f64 x)
(neg.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)))
(exp.f64 (.f64 (log.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal -1 binary64) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 x x))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 x x))))
(/.f64 (*.f64 x x) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 x x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 x x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 x x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 x x)) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (-.f64 #s(literal 0 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
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(*.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) x))
(*.f64 (cos.f64 x) (neg.f64 (/.f64 #s(literal -1 binary64) x)))
(*.f64 #s(literal -1 binary64) (/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x)))
(*.f64 (/.f64 (cos.f64 x) x) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) (cos.f64 x))
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)))
(.f64 (/.f64 (cos.f64 x) (.f64 x x)) x)
(.f64 (/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (.f64 x x))

simplify277.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

4018×	`-lowering-.f32`
4018×	`-lowering-.f64`
3672×	`+-lowering-+.f64`
3672×	`+-lowering-+.f32`
1912×	`sum4-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	143	1731
1	417	1500
2	1113	1497
3	3497	1475
4	6509	1475
0	8251	1475

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 252

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(* 2 x)
(* x (+ 2 (* -1/6 (pow x 2))))
(* x (+ 2 (* (pow x 2) (- (* -1/360 (pow x 2)) 1/6))))
(* x (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/15120 (pow x 2)) 1/360)) 1/6))))
(/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))
(/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))
(/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))
(/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))
(/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))
(/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))
(/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))
(/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
0
0
0
0
0
0
0
0
0
0
0
0
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
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)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
-1/2
(- (* 1/24 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2)
(* -1 (/ (+ 1 (* -1 (cos x))) (pow x 2)))
(* -1 (/ (+ 1 (* -1 (cos x))) (pow x 2)))
(* -1 (/ (+ 1 (* -1 (cos x))) (pow x 2)))
(* -1 (/ (+ 1 (* -1 (cos x))) (pow x 2)))
(* -1 (/ (- 1 (cos x)) (pow x 2)))
(* -1 (/ (- 1 (cos x)) (pow x 2)))
(* -1 (/ (- 1 (cos x)) (pow x 2)))
(* -1 (/ (- 1 (cos x)) (pow x 2)))
(* -1/2 x)
(* x (- (* 1/24 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(* -1 (/ (+ 1 (* -1 (cos x))) x))
(* -1 (/ (+ 1 (* -1 (cos x))) x))
(* -1 (/ (+ 1 (* -1 (cos x))) x))
(* -1 (/ (+ 1 (* -1 (cos x))) x))
(* -1 (/ (- 1 (cos x)) x))
(* -1 (/ (- 1 (cos x)) x))
(* -1 (/ (- 1 (cos x)) x))
(* -1 (/ (- 1 (cos x)) x))
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (+ 1 (* -1 (cos x))) x)
(/ (+ 1 (* -1 (cos x))) x)
(/ (+ 1 (* -1 (cos x))) x)
(/ (+ 1 (* -1 (cos x))) x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ (+ 1 (* -1/2 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ -1 x)
(/ (- (* 1/2 (pow x 2)) 1) x)
(/ (- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1) x)
(/ (- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1) x)
(* -1 (/ (cos x) x))
(* -1 (/ (cos x) x))
(* -1 (/ (cos x) x))
(* -1 (/ (cos x) x))
(* -1 (/ (cos x) x))
(* -1 (/ (cos x) x))
(* -1 (/ (cos x) x))
(* -1 (/ (cos x) x))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 x)
(/ (+ 1 (* -1/2 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)

Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) x))) (.f64 (.f64 x x) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) x))) (.f64 (.f64 x x) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) x))) (.f64 (.f64 x x) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) x))) (.f64 (.f64 x x) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) x))) (.f64 (.f64 x x) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) x))) (.f64 (.f64 x x) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) x))) (.f64 (.f64 x x) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) x))) (.f64 (.f64 x x) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal -1/6 binary64))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/120 binary64)))))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* -1/6 (pow x 2))))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal -1/6 binary64))))
(* x (+ 2 (* (pow x 2) (- (* -1/360 (pow x 2)) 1/6))))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal -1/360 binary64)))))))
(* x (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/15120 (pow x 2)) 1/360)) 1/6))))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/360 binary64) (.f64 (*.f64 x x) #s(literal -1/15120 binary64)))))))))
(/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))
(/.f64 (.f64 (.f64 x x) (cos.f64 (.f64 #s(literal 1/2 binary64) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))
(/.f64 (.f64 (.f64 x x) (cos.f64 (.f64 #s(literal 1/2 binary64) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))
(/.f64 (.f64 (.f64 x x) (cos.f64 (.f64 #s(literal 1/2 binary64) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))
(/.f64 (.f64 (.f64 x x) (cos.f64 (.f64 #s(literal 1/2 binary64) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))
(/.f64 (.f64 (.f64 x x) (cos.f64 (.f64 #s(literal 1/2 binary64) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))
(/.f64 (.f64 (.f64 x x) (cos.f64 (.f64 #s(literal 1/2 binary64) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))
(/.f64 (.f64 (.f64 x x) (cos.f64 (.f64 #s(literal 1/2 binary64) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (* (pow x 2) (cos (* 1/2 x))) (sin (* 1/2 x)))
(/.f64 (.f64 (.f64 x x) (cos.f64 (.f64 #s(literal 1/2 binary64) x))) (sin.f64 (.f64 #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)
(pow x 2)
(*.f64 x 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)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))))))
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (*.f64 x x))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/720 binary64)))))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (*.f64 x x) #s(literal -1/40320 binary64))))))))
(/ (- 1 (cos x)) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
(/ (- 1 (cos x)) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
(/ (- 1 (cos x)) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
(/ (- 1 (cos x)) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
(/ (- 1 (cos x)) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
(/ (- 1 (cos x)) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
(/ (- 1 (cos x)) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
(/ (- 1 (cos x)) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 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 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 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 (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
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))))))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
-1/2
#s(literal -1/2 binary64)
(- (* 1/24 (pow x 2)) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
(- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))
(- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) #s(literal 1/40320 binary64))))))))
(* -1 (/ (+ 1 (* -1 (cos x))) (pow x 2)))
(/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x) x)
(* -1 (/ (+ 1 (* -1 (cos x))) (pow x 2)))
(/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x) x)
(* -1 (/ (+ 1 (* -1 (cos x))) (pow x 2)))
(/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x) x)
(* -1 (/ (+ 1 (* -1 (cos x))) (pow x 2)))
(/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x) x)
(* -1 (/ (- 1 (cos x)) (pow x 2)))
(/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x) x)
(* -1 (/ (- 1 (cos x)) (pow x 2)))
(/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x) x)
(* -1 (/ (- 1 (cos x)) (pow x 2)))
(/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x) x)
(* -1 (/ (- 1 (cos x)) (pow x 2)))
(/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x) x)
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* x (- (* 1/24 (pow x 2)) 1/2))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))
(* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))
(* x (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/720 binary64) (.f64 (*.f64 x x) #s(literal 1/40320 binary64)))))))))
(* -1 (/ (+ 1 (* -1 (cos x))) x))
(/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x)
(* -1 (/ (+ 1 (* -1 (cos x))) x))
(/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x)
(* -1 (/ (+ 1 (* -1 (cos x))) x))
(/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x)
(* -1 (/ (+ 1 (* -1 (cos x))) x))
(/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x)
(* -1 (/ (- 1 (cos x)) x))
(/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x)
(* -1 (/ (- 1 (cos x)) x))
(/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x)
(* -1 (/ (- 1 (cos x)) x))
(/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x)
(* -1 (/ (- 1 (cos x)) x))
(/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))))))
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (*.f64 x x))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/720 binary64)))))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (*.f64 x x) #s(literal -1/40320 binary64))))))))
(/ (- 1 (cos x)) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
(/ (- 1 (cos x)) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
(/ (- 1 (cos x)) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
(/ (- 1 (cos x)) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
(/ (+ 1 (* -1 (cos x))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
(/ (+ 1 (* -1 (cos x))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
(/ (+ 1 (* -1 (cos x))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
(/ (+ 1 (* -1 (cos x))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* -1/2 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64))) x)
(/ (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/240 binary64))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64))))))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ (- (* 1/2 (pow x 2)) 1) x)
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal -1 binary64) x))
(/ (- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1) x)
(+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (*.f64 x x)))) (/.f64 #s(literal -1 binary64) x))
(/ (- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1) x)
(+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/720 binary64))))))) (/.f64 #s(literal -1 binary64) x))
(* -1 (/ (cos x) x))
(-.f64 #s(literal 0 binary64) (/.f64 (cos.f64 x) x))
(* -1 (/ (cos x) x))
(-.f64 #s(literal 0 binary64) (/.f64 (cos.f64 x) x))
(* -1 (/ (cos x) x))
(-.f64 #s(literal 0 binary64) (/.f64 (cos.f64 x) x))
(* -1 (/ (cos x) x))
(-.f64 #s(literal 0 binary64) (/.f64 (cos.f64 x) x))
(* -1 (/ (cos x) x))
(-.f64 #s(literal 0 binary64) (/.f64 (cos.f64 x) x))
(* -1 (/ (cos x) x))
(-.f64 #s(literal 0 binary64) (/.f64 (cos.f64 x) x))
(* -1 (/ (cos x) x))
(-.f64 #s(literal 0 binary64) (/.f64 (cos.f64 x) x))
(* -1 (/ (cos x) x))
(-.f64 #s(literal 0 binary64) (/.f64 (cos.f64 x) x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* -1/2 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64))) x)
(/ (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(/ (cos x) x)
(/.f64 (cos.f64 x) x)

eval322.0ms (3.2%)

Compiler: Compiled 51983 to 3498 computations (93.3% saved)

prune206.0ms (2%)

Pruning

31 alts after pruning (23 fresh and 8 done)

	Pruned	Kept	Total
New	2234	9	2243
Fresh	6	14	20
Picked	3	2	5
Done	0	6	6
Total	2243	31	2274

Accuracy

100.0%

Counts

2274 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	30.3%	(/.f64 (/.f64 (-.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x x)) (.f64 x x))
	53.5%	(/.f64 (/.f64 (-.f64 (.f64 x (cos.f64 x)) x) (-.f64 #s(literal 0 binary64) x)) (.f64 x x))
	30.4%	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (/.f64 x (/.f64 #s(literal 1 binary64) x))) (.f64 x x))
	53.5%	(/.f64 (/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x x)) x)
✓	54.7%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	14.4%	(/.f64 (/.f64 (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) (.f64 x x))) x) (.f64 x x)) (.f64 x x))
	24.6%	(/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x) x)
	54.7%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))) x)
	53.6%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x))) (.f64 x x))
	54.6%	(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) x)) x)
	26.3%	(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) (/.f64 #s(literal 1 binary64) x)) x)
	10.5%	(/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 x (cos.f64 x)) x))) (.f64 (.f64 x (.f64 x x)) (.f64 x x)))
✓	44.1%	(/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x (*.f64 x x)))
✓	53.6%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
✓	75.7%	(/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
	49.5%	(/.f64 (sin.f64 x) (*.f64 x #s(literal 2 binary64)))
	44.1%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (-.f64 x (*.f64 x (cos.f64 x)))))
	53.6%	(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
	53.5%	(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
✓	47.3%	(-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
	53.8%	(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (cos.f64 x)))
	54.0%	(*.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
	53.5%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
✓	53.6%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
	22.6%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
✓	75.6%	(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)))
	49.4%	(*.f64 (sin.f64 x) (/.f64 #s(literal 1/2 binary64) x))
	44.1%	(.f64 x (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 (cos.f64 x) (.f64 x (*.f64 x x)))))
	54.6%	(neg.f64 (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) (/.f64 x (cos.f64 x)))) x))
✓	48.7%	#s(literal 1/2 binary64)
	26.2%	#s(literal 0 binary64)

Compiler

Compiled 1222 to 426 computations (65.1% saved)

regimes63.0ms (0.6%)

Counts

66 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(literal 1/2 binary64)
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
(-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (*.f64 x x))
(/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x) x)
(neg.f64 (/.f64 (/.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) x) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) (/.f64 #s(literal 1 binary64) x)) x)
(/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x x)) (.f64 x x))
(/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 x x)) (.f64 x x))
(/.f64 (/.f64 (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) (.f64 x x))) x) (.f64 x x)) (.f64 x x))
(*.f64 (sin.f64 x) (/.f64 #s(literal 1/2 binary64) x))
(/.f64 (sin.f64 x) (*.f64 x #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(neg.f64 (/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x) x))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 #s(literal -1 binary64) (/.f64 x (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x)))
(/.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) (+.f64 (cos.f64 x) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (cos.f64 x))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) x)) x)
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))) x)
(neg.f64 (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (cos.f64 x) #s(literal -1 binary64))) x))
(neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (+.f64 (cos.f64 x) #s(literal -1 binary64)))) x))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (/.f64 (cos.f64 x) x) x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x (*.f64 x x)))
(/.f64 (/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x x)) x)
(neg.f64 (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) (/.f64 x (cos.f64 x)))) x))
(neg.f64 (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x))) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (cos.f64 x) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (cos.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (-.f64 x (*.f64 x (cos.f64 x)))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x))) (.f64 x x))
(/.f64 (/.f64 (-.f64 (.f64 x (cos.f64 x)) x) (-.f64 #s(literal 0 binary64) x)) (.f64 x x))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) (*.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) x))) x)
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (cos.f64 x) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (/.f64 (.f64 (-.f64 x (.f64 x (cos.f64 x))) x) (.f64 x x)) (.f64 x x))
(.f64 x (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 (cos.f64 x) (.f64 x (*.f64 x x)))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) (/.f64 (cos.f64 x) x))) (.f64 (*.f64 x x) x))
(/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 (.f64 (.f64 x x) x) x))
(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x x)) (*.f64 x x))
(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (/.f64 x (/.f64 #s(literal 1 binary64) x))) (.f64 x x))
(/.f64 (/.f64 (-.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x x)) (.f64 x x))
(/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (.f64 x x))) (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (.f64 x x))) #s(literal -1 binary64)))) (*.f64 x x))
(/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 x (cos.f64 x)) x))) (.f64 (.f64 x (.f64 x x)) (.f64 x x)))
(*.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))))
(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)))
(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (sin.f64 x) (/.f64 (*.f64 x x) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 x x))
(/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))))) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
(.f64 (sin.f64 x) (/.f64 (sin.f64 x) (.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x))))))

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

Calls

2 calls:

40.0ms	x
18.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Results

Accuracy	Segments	Branch
99.7%	2	`x`
99.3%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes21.0ms (0.2%)

Counts

57 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(literal 1/2 binary64)
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
(-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (*.f64 x x))
(/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x) x)
(neg.f64 (/.f64 (/.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) x) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) (/.f64 #s(literal 1 binary64) x)) x)
(/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x x)) (.f64 x x))
(/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 x x)) (.f64 x x))
(/.f64 (/.f64 (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) (.f64 x x))) x) (.f64 x x)) (.f64 x x))
(*.f64 (sin.f64 x) (/.f64 #s(literal 1/2 binary64) x))
(/.f64 (sin.f64 x) (*.f64 x #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(neg.f64 (/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x) x))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 #s(literal -1 binary64) (/.f64 x (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x)))
(/.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) (+.f64 (cos.f64 x) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (cos.f64 x))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) x)) x)
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))) x)
(neg.f64 (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (cos.f64 x) #s(literal -1 binary64))) x))
(neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (+.f64 (cos.f64 x) #s(literal -1 binary64)))) x))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (/.f64 (cos.f64 x) x) x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x (*.f64 x x)))
(/.f64 (/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x x)) x)
(neg.f64 (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) (/.f64 x (cos.f64 x)))) x))
(neg.f64 (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x))) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (cos.f64 x) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (cos.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (-.f64 x (*.f64 x (cos.f64 x)))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x))) (.f64 x x))
(/.f64 (/.f64 (-.f64 (.f64 x (cos.f64 x)) x) (-.f64 #s(literal 0 binary64) x)) (.f64 x x))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) (*.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) x))) x)
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (cos.f64 x) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (/.f64 (.f64 (-.f64 x (.f64 x (cos.f64 x))) x) (.f64 x x)) (.f64 x x))
(.f64 x (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 (cos.f64 x) (.f64 x (*.f64 x x)))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) (/.f64 (cos.f64 x) x))) (.f64 (*.f64 x x) x))
(/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 (.f64 (.f64 x x) x) x))
(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x x)) (*.f64 x x))
(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (/.f64 x (/.f64 #s(literal 1 binary64) x))) (.f64 x x))
(/.f64 (/.f64 (-.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x x)) (.f64 x x))
(/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (.f64 x x))) (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (.f64 x x))) #s(literal -1 binary64)))) (*.f64 x x))
(/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 x (cos.f64 x)) x))) (.f64 (.f64 x (.f64 x x)) (.f64 x x)))

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

Calls

1 calls:

18.0ms

Results

Accuracy	Segments	Branch
99.7%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes8.0ms (0.1%)

Counts

17 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(literal 1/2 binary64)
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
(-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (*.f64 x x))
(/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x) x)
(neg.f64 (/.f64 (/.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) x) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) (/.f64 #s(literal 1 binary64) x)) x)
(/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x x)) (.f64 x x))
(/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 x x)) (.f64 x x))
(/.f64 (/.f64 (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) (.f64 x x))) x) (.f64 x x)) (.f64 x x))
(*.f64 (sin.f64 x) (/.f64 #s(literal 1/2 binary64) x))
(/.f64 (sin.f64 x) (*.f64 x #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)

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

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
99.3%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes6.0ms (0.1%)

Counts

15 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(literal 1/2 binary64)
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
(-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (*.f64 x x))
(/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x) x)
(neg.f64 (/.f64 (/.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) x) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) (/.f64 #s(literal 1 binary64) x)) x)
(/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x x)) (.f64 x x))
(/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 x x)) (.f64 x x))
(/.f64 (/.f64 (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) (.f64 x x))) x) (.f64 x x)) (.f64 x x))
(*.f64 (sin.f64 x) (/.f64 #s(literal 1/2 binary64) x))
(/.f64 (sin.f64 x) (*.f64 x #s(literal 2 binary64)))

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

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
71.6%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Counts

9 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(literal 1/2 binary64)
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
(-.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (*.f64 x x))
(/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x) x)
(neg.f64 (/.f64 (/.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) x) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))

Outputs
#s(literal 1/2 binary64)
#s(literal 0 binary64)

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
71.5%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)

Outputs
#s(literal 0 binary64)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
26.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch19.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
18.0ms	8.772895316130977e-8	286964136.8317163

Results

12.0ms

160×

valid

Compiler

Compiled 203 to 159 computations (21.7% saved)

Precisions

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

ival-mult: 3.0ms (40.3% of total)

ival-cos: 2.0ms (26.9% of total)

ival-sub: 1.0ms (13.4% of total)

ival-div: 1.0ms (13.4% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch20.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
18.0ms	8.772895316130977e-8	286964136.8317163

Results

13.0ms

160×

valid

Compiler

Compiled 203 to 149 computations (26.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-cos: 4.0ms (49.9% of total)

ival-sub: 1.0ms (12.5% of total)

ival-div: 1.0ms (12.5% of total)

ival-mult: 1.0ms (12.5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch19.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
17.0ms	8.772895316130977e-8	286964136.8317163

Results

12.0ms

160×

valid

Compiler

Compiled 203 to 149 computations (26.6% saved)

Precisions

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

ival-div: 2.0ms (29.6% of total)

ival-cos: 2.0ms (29.6% of total)

ival-sub: 1.0ms (14.8% of total)

ival-mult: 1.0ms (14.8% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch14.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	1.3149278301411815e+67	1.0287438639794168e+68

Results

10.0ms

96×

valid

Compiler

Compiled 121 to 81 computations (33.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-cos: 4.0ms (70.4% of total)

ival-sub: 1.0ms (17.6% of total)

ival-div: 1.0ms (17.6% of total)

ival-mult: 1.0ms (17.6% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch18.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	3.648799600129264e+74	2.257182529372032e+79

Results

12.0ms

128×

valid

Compiler

Compiled 61 to 57 computations (6.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-cos: 4.0ms (47.6% of total)

ival-mult: 2.0ms (23.8% of total)

ival-sub: 1.0ms (11.9% of total)

ival-div: 1.0ms (11.9% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

22×	`unsub-neg_binary64`
22×	`neg-mul-1_binary64`
14×	`*-commutative_binary64`
14×	`+-commutative_binary64`
12×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	82
1	42	82
2	53	82
3	61	82
4	69	82
5	85	82
6	109	82

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal 5764607523034235/1152921504606846976 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x))) (*.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(if (<=.f64 x #s(literal 5764607523034235/1152921504606846976 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x))
(if (<=.f64 x #s(literal 5764607523034235/1152921504606846976 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x))) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x)))
(if (<=.f64 x #s(literal 102000000000000004524777371792440373446253513877115520177721581764608 binary64)) #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) (/.f64 #s(literal 1 binary64) x)) x))
(if (<=.f64 x #s(literal 130000000000000009331693572985691597674199002984591404980029211519262914510848 binary64)) #s(literal 1/2 binary64) #s(literal 0 binary64))
#s(literal 0 binary64)

Outputs
(if (<=.f64 x #s(literal 5764607523034235/1152921504606846976 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x))) (*.f64 (pow.f64 x #s(literal -2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(if (<=.f64 x #s(literal 5764607523034235/1152921504606846976 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x))
(if (<=.f64 x #s(literal 5764607523034235/1152921504606846976 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x))) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x)))
(if (<=.f64 x #s(literal 102000000000000004524777371792440373446253513877115520177721581764608 binary64)) #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) (/.f64 #s(literal 1 binary64) x)) x))
(if (<=.f64 x #s(literal 102000000000000004524777371792440373446253513877115520177721581764608 binary64)) #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 x (/.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal -1 binary64) x)) x))
(if (<=.f64 x #s(literal 130000000000000009331693572985691597674199002984591404980029211519262914510848 binary64)) #s(literal 1/2 binary64) #s(literal 0 binary64))
#s(literal 0 binary64)

soundness1.9s (18.9%)

Rules

4496×	`-lowering-.f32`
4496×	`-lowering-.f64`
4018×	`-lowering-.f32`
4018×	`-lowering-.f64`
3696×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	278
1	113	224
2	316	224
3	821	224
4	1931	224
5	2947	224
6	3532	224
7	4854	224
0	8003	224
0	24	98
1	175	94
2	1450	93
0	8563	93
0	29	103
1	213	102
2	1869	100
0	9216	100
0	6	15
1	37	15
2	270	15
3	2919	15
0	8614	15
0	143	1731
1	417	1500
2	1113	1497
3	3497	1475
4	6509	1475
0	8251	1475
0	24	100
1	149	94
2	1218	90
0	8705	90

Stop Event

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

Compiler

Compiled 175 to 98 computations (44% saved)

preprocess58.0ms (0.6%)

Compiler: Compiled 224 to 108 computations (51.8% saved)

analyze2.0ms (0%)

sample2.2s (21.6%)

preprocess116.0ms (1.1%)

explain190.0ms (1.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify65.0ms (0.6%)

localize76.0ms (0.7%)

series3.0ms (0%)

rewrite403.0ms (4%)

simplify189.0ms (1.9%)

eval61.0ms (0.6%)

prune89.0ms (0.9%)

simplify161.0ms (1.6%)

localize302.0ms (3%)

series14.0ms (0.1%)

rewrite370.0ms (3.7%)

simplify240.0ms (2.4%)

eval215.0ms (2.1%)

prune197.0ms (2%)

simplify122.0ms (1.2%)

localize263.0ms (2.6%)

series8.0ms (0.1%)

rewrite339.0ms (3.4%)

simplify251.0ms (2.5%)

eval229.0ms (2.3%)

prune148.0ms (1.5%)

simplify132.0ms (1.3%)

localize341.0ms (3.4%)

series15.0ms (0.2%)

rewrite403.0ms (4%)

simplify277.0ms (2.7%)

eval322.0ms (3.2%)

prune206.0ms (2%)

regimes63.0ms (0.6%)

regimes21.0ms (0.2%)

regimes8.0ms (0.1%)

regimes6.0ms (0.1%)

regimes4.0ms (0%)

regimes2.0ms (0%)

bsearch19.0ms (0.2%)

bsearch20.0ms (0.2%)

bsearch19.0ms (0.2%)

bsearch14.0ms (0.1%)

bsearch18.0ms (0.2%)

simplify10.0ms (0.1%)

soundness1.9s (18.9%)

preprocess58.0ms (0.6%)

end0.0ms (0%)

Profiling