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)

sample2.1s (21.8%)

Results

936.0ms	2022×	2	valid
350.0ms	4185×	0	valid
319.0ms	2049×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 1.3s

ival-cos: 894.0ms (68% of total)

ival-div: 120.0ms (9.1% of total)

ival-mult: 102.0ms (7.8% of total)

ival-sub: 95.0ms (7.2% of total)

backward-pass: 89.0ms (6.8% of total)

const: 16.0ms (1.2% of total)

Bogosity

preprocess111.0ms (1.2%)

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	25
1	38	25
2	111	24
3	309	24
4	835	24
5	1930	24
6	3633	24
7	3842	24
0	6	8
1	15	8
2	27	8
3	45	8
4	84	8
5	144	8
6	235	8
7	463	8
8	1139	8
9	2518	8
10	4027	8
11	4047	8
0	4047	8

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

Symmetry

(abs x)

explain160.0ms (1.7%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
85	0	-	1	(6.338893685905177e+166)	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
51	1	(1.2835221951565376e+161)	0	-	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x 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

67.0ms	100×	2	valid
27.0ms	262×	0	valid
27.0ms	150×	1	valid

Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 90.0ms

ival-cos: 66.0ms (73.3% of total)

ival-div: 6.0ms (6.7% of total)

ival-mult: 6.0ms (6.7% of total)

ival-sub: 6.0ms (6.7% of total)

backward-pass: 5.0ms (5.6% 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
▶	51.4%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify58.0ms (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	19
1	15	19
2	27	19
3	45	19
4	84	19
5	144	19
6	235	19
7	463	19
8	1139	19
9	2518	19
10	4027	19
11	4047	19
0	4047	19

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)

localize82.0ms (0.9%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	80.8%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
✓	accuracy	71.7%	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Results

46.0ms	50×	2	valid
14.0ms	75×	1	valid
13.0ms	131×	0	valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 59.0ms

ival-cos: 26.0ms (44.3% of total)

ival-mult: 23.0ms (39.1% of total)

ival-div: 4.0ms (6.8% of total)

backward-pass: 3.0ms (5.1% of total)

ival-sub: 3.0ms (5.1% of total)

const: 1.0ms (1.7% 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)

rewrite324.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

2600×	`-lowering-.f32`
2600×	`-lowering-.f64`
2226×	`fma-lowering-fma.f32`
2226×	`fma-lowering-fma.f64`
1948×	`prod-diff`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
1	36	17
2	268	17
3	2905	17
0	8648	17

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 462

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 (cos.f64 x) (.f64 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 (cos.f64 x) (*.f64 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 (cos.f64 x) (.f64 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 (cos.f64 x) (.f64 x 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 #s(literal 0 binary64) (cos.f64 x)) (.f64 x x)))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 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 #s(literal 1 binary64) (.f64 x x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (*.f64 x x)) #s(literal 1 binary64)))
(+.f64 (/.f64 (cos.f64 x) (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(+.f64 (/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 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 (cos.f64 x) (.f64 x x)) #s(literal -1 binary64)))) (fma.f64 (/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 x x)) #s(literal -1 binary64) (.f64 (/.f64 (cos.f64 x) (.f64 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 (cos.f64 x) (.f64 x x)) #s(literal -1 binary64)))) (fma.f64 (/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 x x)) #s(literal -1 binary64) (.f64 (/.f64 (cos.f64 x) (.f64 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 (cos.f64 x) (.f64 x x)) #s(literal -1 binary64)))) (fma.f64 (/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 x x)) #s(literal -1 binary64) (.f64 (/.f64 (cos.f64 x) (.f64 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 (cos.f64 x) (.f64 x x)) #s(literal -1 binary64)))) (fma.f64 (/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 x x)) #s(literal -1 binary64) (.f64 (/.f64 (cos.f64 x) (*.f64 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 x x)) #s(literal 1 binary64)))) (fma.f64 (/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 x x)) #s(literal 1 binary64) (.f64 (/.f64 (cos.f64 x) (.f64 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 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 x x)) #s(literal -1 binary64)))) (fma.f64 (/.f64 (cos.f64 x) (.f64 x x)) #s(literal -1 binary64) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 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 (cos.f64 x) (.f64 x x)) #s(literal 1 binary64)))) (fma.f64 (/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 x x)) #s(literal 1 binary64) (.f64 (/.f64 (cos.f64 x) (.f64 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 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 x x)) #s(literal -1 binary64)))) (fma.f64 (/.f64 (cos.f64 x) (.f64 x x)) #s(literal -1 binary64) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 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 (cos.f64 x) (.f64 x x)) #s(literal 1 binary64)))) (fma.f64 (/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 x x)) #s(literal 1 binary64) (.f64 (/.f64 (cos.f64 x) (.f64 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 #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 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) #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 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) #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 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))) (/.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) #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 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))) #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 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) #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 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 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) #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 (+.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 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 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)))))
(.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 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) #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)))))))
(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 x (/.f64 #s(literal 1 binary64) 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)

simplify197.0ms (2%)

Algorithm

1×	egg-herbie

Rules

2236×	`sum3-define`
2048×	`fma-lowering-fma.f32`
2048×	`fma-lowering-fma.f64`
1796×	`sum4-define`
1588×	`fmsub-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	278
1	113	266
2	315	266
3	818	266
4	1931	266
5	2941	266
6	3513	266
7	4835	266
0	8655	266

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

eval60.0ms (0.6%)

Compiler: Compiled 13161 to 1210 computations (90.8% saved)

prune93.0ms (1%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	492	18	510
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	492	19	511

Accuracy

100.0%

Counts

511 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	25.2%	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x x)) (*.f64 x x))
	50.8%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64)) (.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
	52.2%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	50.8%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
	16.4%	(/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (cos.f64 x))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)))
	45.1%	(/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x (*.f64 x x)))
▶	51.3%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
✓	51.4%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
	28.1%	(/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (*.f64 x x))
	80.1%	(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 x x))
▶	16.4%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x))))))
	51.4%	(/.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) (+.f64 (cos.f64 x) #s(literal -1 binary64))))
	51.4%	(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
▶	51.3%	(+.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 x (.f64 x #s(literal -1/40320 binary64))))))))
	51.7%	(+.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)))))
	51.1%	(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
▶	80.6%	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
	51.3%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
▶	51.7%	#s(literal 1/2 binary64)

Compiler

Compiled 503 to 296 computations (41.2% saved)

simplify164.0ms (1.7%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 x (.f64 x (*.f64 x x)))
✓	cost-diff	128	(-.f64 (.f64 x x) (.f64 x (*.f64 x (cos.f64 x))))
✓	cost-diff	640	(/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))))
✓	cost-diff	768	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x))))))
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	cost-diff	128	(/.f64 x (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	128	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(+.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))))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x 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)))))))
✓	cost-diff	0	(+.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 x (.f64 x #s(literal -1/40320 binary64))))))))
✓	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

1952×	`sum5-define`
1912×	`-lowering-.f32`
1912×	`-lowering-.f64`
1692×	`sum3-define`
1522×	`sum4-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	193
1	95	178
2	301	178
3	928	173
4	2617	173
5	5204	173
0	8412	173

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

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

localize292.0ms (3%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(*.f64 x (cos.f64 x))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x))))))
✓	accuracy	76.2%	(-.f64 (.f64 x x) (.f64 x (*.f64 x (cos.f64 x))))
✓	accuracy	34.7%	(/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	99.8%	(/.f64 x (/.f64 #s(literal 1 binary64) x))
✓	accuracy	80.8%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
✓	accuracy	71.7%	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	accuracy	100.0%	(+.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x #s(literal -1/40320 binary64))))
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal -1/40320 binary64)))
✓	accuracy	99.8%	(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x #s(literal -1/40320 binary64)))))
✓	accuracy	99.8%	(.f64 (.f64 x 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)))))))
✓	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	81.4%	(/.f64 (sin.f64 x) (*.f64 x x))

Results

131.0ms	77×	2	valid
57.0ms	131×	0	valid
28.0ms	14×	3	valid
24.0ms	34×	1	valid

Compiler

Compiled 220 to 33 computations (85% saved)

Precisions

Click to see histograms. Total time spent on operations: 167.0ms

backward-pass: 38.0ms (22.7% of total)

ival-cos: 34.0ms (20.3% of total)

ival-mult: 32.0ms (19.1% of total)

ival-div: 19.0ms (11.4% of total)

...c/correct-round.rkt:119:19: 17.0ms (10.2% of total)

ival-sin: 9.0ms (5.4% of total)

ival-tan: 6.0ms (3.6% of total)

ival-add: 6.0ms (3.6% of total)

ival-sub: 5.0ms (3% of total)

const: 1.0ms (0.6% of total)

series16.0ms (0.2%)

Counts

20 → 240

Calls

Call 1

Inputs
#<alt (* (/ (sin x) (* x x)) (tan (/ x 2)))>
#<alt (/ (sin x) (* x x))>
#<alt (sin x)>
#<alt (* x x)>
#<alt (+ 1/2 (* (* x x) (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))>
#<alt (* (* x x) (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320))))))>
#<alt (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))>
#<alt (/ (- 1 (cos x)) (/ x (/ 1 x)))>
#<alt (/ x (/ 1 x))>
#<alt (- 1 (cos x))>
#<alt (cos x)>
#<alt (/ 1 (/ (* x (* x (* x x))) (- (* x x) (* x (* x (cos x))))))>
#<alt (/ (* x (* x (* x x))) (- (* x x) (* x (* x (cos x)))))>
#<alt (- (* x x) (* x (* x (cos x))))>
#<alt (* x (* x (* x x)))>
#<alt (tan (/ x 2))>
#<alt (* (* x x) (+ 1/720 (* x (* x -1/40320))))>
#<alt (* x (* x -1/40320))>
#<alt (+ 1/720 (* x (* x -1/40320)))>
#<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 (* -1/40320 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* -1/40320 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* -1/24 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))>
#<alt (* -1/40320 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* -1/40320 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt -1/24>
#<alt (- (* 1/720 (pow x 2)) 1/24)>
#<alt (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)>
#<alt (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)>
#<alt (* -1/40320 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* -1/40320 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<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 2>
#<alt (+ 2 (* 1/6 (pow x 2)))>
#<alt (+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2)))))>
#<alt (+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2)))))))>
#<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 (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 (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<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 (* 1/720 (pow x 2))>
#<alt (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))>
#<alt (* -1/40320 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* -1/40320 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt 1/720>
#<alt (+ 1/720 (* -1/40320 (pow x 2)))>
#<alt (+ 1/720 (* -1/40320 (pow x 2)))>
#<alt (+ 1/720 (* -1/40320 (pow x 2)))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<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

60 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(* x (* x -1/40320))
1.0ms	x	@	inf	(* (/ (sin x) (* x x)) (tan (/ x 2)))
1.0ms	x	@	inf	(+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))
1.0ms	x	@	-inf	(* (/ (sin x) (* x x)) (tan (/ x 2)))
1.0ms	x	@	inf	(/ 1 (/ (* x (* x (* x x))) (- (* x x) (* x (* x (cos x))))))

rewrite448.0ms (4.7%)

Algorithm

1×	batch-egg-rewrite

Rules

3628×	`-lowering-.f32`
3628×	`-lowering-.f64`
3098×	`/-lowering-/.f32`
3098×	`/-lowering-/.f64`
1794×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	32	156
1	218	137
2	1790	137
0	8409	137

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 1112

Calls

Call 1

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

Outputs
(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (*.f64 x x) (sin.f64 x)))
(/.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) (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 (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 #s(literal 1 binary64) (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 (.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))) #s(literal 1 binary64)) (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (*.f64 x x) (sin.f64 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 0 binary64) (*.f64 x x))))
(/.f64 (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sin.f64 x) x)) (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) x))
(/.f64 (neg.f64 (.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))) #s(literal 1 binary64)) (/.f64 (.f64 x x) (sin.f64 x)))
(/.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 (sin.f64 x) x)) x)
(/.f64 (.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 (.f64 x x) (sin.f64 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 (sin.f64 x) (.f64 x 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 (neg.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) (neg.f64 (/.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 #s(literal 1 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 (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))) #s(literal 1 binary64))) (neg.f64 (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (*.f64 x x) (sin.f64 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 0 binary64) (*.f64 x x)))))
(/.f64 (neg.f64 (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sin.f64 x) x))) (neg.f64 (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) x)))
(/.f64 (neg.f64 (neg.f64 (.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))))) (neg.f64 (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))) (neg.f64 (/.f64 (.f64 x x) (sin.f64 x))))
(/.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 (sin.f64 x) x))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))) (neg.f64 (/.f64 (.f64 x x) (sin.f64 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 (sin.f64 x) (.f64 x x)))) (neg.f64 (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 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (tan.f64 (/.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 (/.f64 (sin.f64 x) (.f64 x x)) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)))
(.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sin.f64 x) (.f64 x x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 x (sin.f64 x))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sin.f64 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 (tan.f64 (/.f64 x #s(literal 2 binary64))) x) (/.f64 (sin.f64 x) x))
(*.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) x) (/.f64 (/.f64 (sin.f64 x) x) #s(literal 1 binary64)))
(.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x))))
(*.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) x)) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) x) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 x (sin.f64 x))))
(.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sin.f64 x))))
(.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 x #s(literal -1 binary64))) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) x)))
(*.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) x)) (/.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) x)) (/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) x))
(.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (.f64 x x)))
(*.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 x #s(literal -1 binary64))) (/.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) x)))
(.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(*.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 (/.f64 (sin.f64 x) x) (-.f64 #s(literal 0 binary64) x)))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) x) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) x)))
(*.f64 (/.f64 (/.f64 (sin.f64 x) x) #s(literal 1 binary64)) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) x))
(.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) #s(literal -1 binary64)) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)))
(*.f64 (/.f64 (/.f64 (sin.f64 x) x) #s(literal -1 binary64)) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) x)))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (sin.f64 x))) #s(literal -1 binary64)))
(-.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 (*.f64 x x) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) (sin.f64 x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (sin.f64 x)) x))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (*.f64 x x) (sin.f64 x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x x) (sin.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (*.f64 x x) (sin.f64 x)) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (/.f64 x (sin.f64 x)) x)))
(/.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 (neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x))) (*.f64 x x))
(/.f64 (neg.f64 (/.f64 (sin.f64 x) x)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (.f64 (sin.f64 x) #s(literal 1 binary64)) (.f64 x x))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)))) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (neg.f64 (neg.f64 (/.f64 (sin.f64 x) x))) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 (neg.f64 (.f64 (sin.f64 x) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(pow.f64 (/.f64 (*.f64 x x) (sin.f64 x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (*.f64 x x) (sin.f64 x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 x (sin.f64 x)) 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 x x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sin.f64 x) x))
(.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) (-.f64 #s(literal 0 binary64) 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 (sin.f64 x) x) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))
(*.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))))
(.f64 (/.f64 (sin.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(*.f64 (/.f64 (sin.f64 x) (/.f64 x #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) x)))
(sin.f64 x)
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal -1 binary64)))
(-.f64 (-.f64 x x) (-.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)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 (.f64 x (.f64 x x)) x)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -1 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal -1 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (.f64 x (.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x))) (/.f64 #s(literal -1 binary64) x))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 2 binary64)))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) (/.f64 x #s(literal -1 binary64)))
(*.f64 (/.f64 x #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(*.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (-.f64 #s(literal 0 binary64) x) (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (/.f64 x (pow.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 x (pow.f64 x #s(literal -1/2 binary64))))
(.f64 (/.f64 (.f64 x x) #s(literal -1 binary64)) (/.f64 x (-.f64 #s(literal 0 binary64) x)))
(*.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) x) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) x))
(*.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (-.f64 #s(literal 0 binary64) x)))
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(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/40320 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/40320 binary64))) #s(literal 1/720 binary64)))) (+.f64 #s(literal 1/373248000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/65548320768000 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x #s(literal -1/40320 binary64)))) (-.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/1625702400 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/40320 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/40320 binary64))) #s(literal 1/720 binary64)))) (+.f64 #s(literal 1/373248000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/65548320768000 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x #s(literal -1/40320 binary64)))) (-.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/1625702400 binary64))))))
(/.f64 (+.f64 #s(literal 1/373248000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/65548320768000 binary64)))) (+.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/40320 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal -1/40320 binary64))) #s(literal 1/720 binary64)))))
(/.f64 (+.f64 #s(literal 1/373248000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/65548320768000 binary64)))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/1625702400 binary64)) (-.f64 #s(literal 1/518400 binary64) (.f64 #s(literal 1/720 binary64) (.f64 x (*.f64 x #s(literal -1/40320 binary64)))))))
(/.f64 (-.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/1625702400 binary64))) (-.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x #s(literal -1/40320 binary64)))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/373248000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/65548320768000 binary64))))) (neg.f64 (+.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/40320 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal -1/40320 binary64))) #s(literal 1/720 binary64))))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/373248000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/65548320768000 binary64))))) (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/1625702400 binary64)) (-.f64 #s(literal 1/518400 binary64) (.f64 #s(literal 1/720 binary64) (.f64 x (*.f64 x #s(literal -1/40320 binary64))))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/1625702400 binary64)))) (neg.f64 (-.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x #s(literal -1/40320 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/1625702400 binary64)) #s(literal 1/518400 binary64)) (-.f64 (.f64 x (.f64 x #s(literal -1/40320 binary64))) #s(literal 1/720 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 1/518400 binary64) (-.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x #s(literal -1/40320 binary64))))) (.f64 (-.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x #s(literal -1/40320 binary64)))) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/1625702400 binary64)))) (.f64 (-.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x #s(literal -1/40320 binary64)))) (-.f64 #s(literal 1/720 binary64) (.f64 x (*.f64 x #s(literal -1/40320 binary64))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 #s(literal 1/373248000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/65548320768000 binary64)))))) (neg.f64 (neg.f64 (+.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/40320 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal -1/40320 binary64))) #s(literal 1/720 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/1625702400 binary64))))) (neg.f64 (neg.f64 (-.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x #s(literal -1/40320 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/1625702400 binary64)) #s(literal 1/518400 binary64))) (neg.f64 (-.f64 (.f64 x (.f64 x #s(literal -1/40320 binary64))) #s(literal 1/720 binary64))))
(pow.f64 (/.f64 (+.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/40320 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/40320 binary64))) #s(literal 1/720 binary64)))) (+.f64 #s(literal 1/373248000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/65548320768000 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x #s(literal -1/40320 binary64)))) (-.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/1625702400 binary64)))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal 1/373248000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/65548320768000 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/40320 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/40320 binary64))) #s(literal 1/720 binary64))))))
(.f64 (-.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/1625702400 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/720 binary64) (.f64 x (*.f64 x #s(literal -1/40320 binary64))))))
(*.f64 x (cos.f64 x))
(*.f64 (cos.f64 x) x)

simplify352.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

3684×	`+-lowering-+.f64`
3684×	`+-lowering-+.f32`
3562×	`-lowering-.f32`
3562×	`-lowering-.f64`
1784×	`sum4-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	135	1865
1	392	1800
2	1133	1774
3	3674	1763
4	6629	1755
0	8160	1755

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

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)))
(* -1/40320 (pow x 6))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/40320 (pow x 6))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))
(* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))
(* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))
(* -1/40320 (pow x 6))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/40320 (pow x 6))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
-1/24
(- (* 1/720 (pow x 2)) 1/24)
(- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)
(- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)
(* -1/40320 (pow x 4))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/40320 (pow x 4))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
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))
2
(+ 2 (* 1/6 (pow x 2)))
(+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2)))))))
(/ (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 (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)))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(* 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)))
(* 1/720 (pow x 2))
(* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))
(* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))
(* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))
(* -1/40320 (pow x 4))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* -1/40320 (pow x 4))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
1/720
(+ 1/720 (* -1/40320 (pow x 2)))
(+ 1/720 (* -1/40320 (pow x 2)))
(+ 1/720 (* -1/40320 (pow x 2)))
(* -1/40320 (pow x 2))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* -1/40320 (pow x 2))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
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 #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 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 (.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))))
(/ 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 x (.f64 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))
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(.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)))
(* 1/720 (pow x 2))
(.f64 x (.f64 x #s(literal 1/720 binary64)))
(* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
(* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
(* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
(* -1/40320 (pow x 4))
(.f64 x (.f64 #s(literal -1/40320 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
(* -1/40320 (pow x 4))
(.f64 x (.f64 #s(literal -1/40320 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
1/720
#s(literal 1/720 binary64)
(+ 1/720 (* -1/40320 (pow x 2)))
(+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))
(+ 1/720 (* -1/40320 (pow x 2)))
(+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))
(+ 1/720 (* -1/40320 (pow x 2)))
(+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))
(* (pow x 2) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))
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 (.f64 x 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 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))

eval211.0ms (2.2%)

Compiler: Compiled 41973 to 3327 computations (92.1% saved)

prune172.0ms (1.8%)

Pruning

22 alts after pruning (18 fresh and 4 done)

	Pruned	Kept	Total
New	1570	13	1583
Fresh	8	5	13
Picked	2	3	5
Done	0	1	1
Total	1580	22	1602

Accuracy

100.0%

Counts

1602 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	52.2%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	16.4%	(/.f64 (-.f64 (.f64 x x) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))) (.f64 x (.f64 x (.f64 x x))))
	45.1%	(/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x (*.f64 x x)))
	45.2%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 (.f64 x (.f64 x x)) x))
✓	51.4%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
	28.1%	(/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (*.f64 x x))
▶	31.2%	(/.f64 (.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)))))))) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
▶	80.7%	(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (*.f64 x x) (sin.f64 x)))
	50.7%	(/.f64 #s(literal 1 binary64) (/.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 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (.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 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 x (*.f64 x #s(literal -1/40320 binary64))))))))))))
	16.5%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
	80.1%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))
	52.0%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
	51.4%	(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (.f64 x x)))
▶	51.4%	(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
✓	51.3%	(+.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 x (.f64 x #s(literal -1/40320 binary64))))))))
	51.7%	(+.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)))))
▶	51.1%	(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
✓	80.6%	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
▶	52.1%	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x))) (/.f64 #s(literal 1 binary64) x))
	51.2%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 x (*.f64 x (cos.f64 x))))))
	80.0%	(.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	51.7%	#s(literal 1/2 binary64)

Compiler

Compiled 647 to 363 computations (43.9% saved)

simplify165.0ms (1.7%)

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)))
✓	cost-diff	384	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x))) (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(/.f64 (cos.f64 x) (*.f64 x x))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	cost-diff	256	(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.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))))))))
✓	cost-diff	128	(/.f64 x (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	640	(/.f64 (.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)))))))) (/.f64 x (/.f64 #s(literal 1 binary64) 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	(/.f64 (*.f64 x x) (sin.f64 x))
✓	cost-diff	0	(/.f64 x #s(literal 2 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 (*.f64 x x) (sin.f64 x)))

Rules

2518×	`-lowering-.f32`
2518×	`-lowering-.f64`
1526×	`/-lowering-/.f32`
1526×	`/-lowering-/.f64`
1490×	`+-lowering-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	263
1	104	245
2	333	226
3	996	222
4	2889	222
5	6972	222
0	8032	222

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize327.0ms (3.4%)

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x))) (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)))
✓	accuracy	81.6%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
✓	accuracy	71.7%	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	99.6%	(/.f64 (cos.f64 x) (*.f64 x x))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	accuracy	52.3%	(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
✓	accuracy	99.8%	(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
✓	accuracy	99.8%	(.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))))))
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal -1/40320 binary64))
✓	accuracy	51.6%	(/.f64 (.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)))))))) (/.f64 x (/.f64 #s(literal 1 binary64) 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	99.7%	(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (*.f64 x x) (sin.f64 x)))
✓	accuracy	81.7%	(/.f64 (*.f64 x x) (sin.f64 x))

Results

98.0ms	75×	2	valid
64.0ms	129×	0	valid
59.0ms	16×	3	valid
28.0ms	36×	1	valid

Compiler

Compiled 271 to 35 computations (87.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 178.0ms

ival-cos: 51.0ms (28.6% of total)

ival-div: 36.0ms (20.2% of total)

ival-mult: 25.0ms (14% of total)

backward-pass: 20.0ms (11.2% of total)

...c/correct-round.rkt:119:19: 15.0ms (8.4% of total)

ival-add: 10.0ms (5.6% of total)

ival-tan: 8.0ms (4.5% of total)

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

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

const: 1.0ms (0.6% of total)

series24.0ms (0.3%)

Counts

23 → 276

Calls

Call 1

Inputs
#<alt (/ (tan (/ x 2)) (/ (* x x) (sin x)))>
#<alt (tan (/ x 2))>
#<alt (/ x 2)>
#<alt (/ (* x x) (sin x))>
#<alt (+ 1/2 (* (* x x) -1/24))>
#<alt (* (* x x) -1/24)>
#<alt (* x x)>
#<alt (/ (* (* x x) (+ 1/2 (* (* x x) (+ -1/24 (* (* x x) (+ 1/720 (* (* x x) -1/40320))))))) (/ x (/ 1 x)))>
#<alt (/ x (/ 1 x))>
#<alt (* (* x x) (+ 1/2 (* (* x x) (+ -1/24 (* (* x x) (+ 1/720 (* (* x x) -1/40320)))))))>
#<alt (- (/ 1 (* x x)) (/ (cos x) (* x x)))>
#<alt (/ 1 (* x x))>
#<alt (/ (cos x) (* x x))>
#<alt (* (/ 1 (/ 1 (/ (- 1 (cos x)) x))) (/ 1 x))>
#<alt (/ 1 (/ 1 (/ (- 1 (cos x)) x)))>
#<alt (/ 1 (/ (- 1 (cos x)) x))>
#<alt (/ (- 1 (cos x)) x)>
#<alt (sin x)>
#<alt (* (* x x) -1/40320)>
#<alt (* (* x x) (+ -1/24 (* (* x x) (+ 1/720 (* (* x x) -1/40320)))))>
#<alt (* (* x x) (+ 1/720 (* (* x x) -1/40320)))>
#<alt (cos x)>
#<alt (- 1 (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 (* 1/2 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 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt x>
#<alt (* x (+ 1 (* 1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/6 (* 7/360 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 7/360 (* 31/15120 (pow x 2))))))))>
#<alt (/ (pow x 2) (sin x))>
#<alt (/ (pow x 2) (sin x))>
#<alt (/ (pow x 2) (sin x))>
#<alt (/ (pow x 2) (sin x))>
#<alt (/ (pow x 2) (sin x))>
#<alt (/ (pow x 2) (sin x))>
#<alt (/ (pow x 2) (sin x))>
#<alt (/ (pow x 2) (sin 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 (* -1/40320 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* -1/40320 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<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 (* -1/40320 (pow x 8))>
#<alt (* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 8) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* -1/40320 (pow x 8))>
#<alt (* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 8) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<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 (pow x 2))>
#<alt (/ (+ 1 (* -1/2 (pow x 2))) (pow x 2))>
#<alt (/ (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) (pow x 2))>
#<alt (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) (pow x 2))>
#<alt (/ (cos x) (pow x 2))>
#<alt (/ (cos x) (pow x 2))>
#<alt (/ (cos x) (pow x 2))>
#<alt (/ (cos x) (pow x 2))>
#<alt (/ (cos x) (pow x 2))>
#<alt (/ (cos x) (pow x 2))>
#<alt (/ (cos x) (pow x 2))>
#<alt (/ (cos x) (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 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 (/ 2 x)>
#<alt (/ (+ 2 (* 1/6 (pow x 2))) x)>
#<alt (/ (+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))) x)>
#<alt (/ (+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2))))))) x)>
#<alt (/ x (- 1 (cos x)))>
#<alt (/ x (- 1 (cos x)))>
#<alt (/ x (- 1 (cos x)))>
#<alt (/ x (- 1 (cos x)))>
#<alt (/ x (- 1 (cos x)))>
#<alt (/ x (- 1 (cos x)))>
#<alt (/ x (- 1 (cos x)))>
#<alt (/ x (- 1 (cos x)))>
#<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 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 (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))>
#<alt (* -1/40320 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* -1/40320 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* 1/720 (pow x 2))>
#<alt (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))>
#<alt (* -1/40320 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* -1/40320 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<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 (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))>

Calls

69 calls:

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

rewrite451.0ms (4.7%)

Algorithm

1×	batch-egg-rewrite

Rules

4888×	`-lowering-.f32`
4888×	`-lowering-.f64`
2986×	`/-lowering-/.f32`
2986×	`/-lowering-/.f64`
2034×	`--lowering--.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	179
1	261	166
2	2423	160
0	9389	160

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 825

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x)))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) (sin.f64 x)))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 (*.f64 x x) (sin.f64 x))))
(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (*.f64 x x) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) (.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x))) #s(literal 1 binary64)))
(/.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 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 x x) (.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) (sin.f64 x))))
(/.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
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(*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 (pow.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 (pow.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(.f64 (pow.f64 (/.f64 x (-.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 x (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(sin.f64 x)
(.f64 x (.f64 x #s(literal -1/40320 binary64)))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(.f64 #s(literal -1/40320 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal -1/40320 binary64)) x)
(+.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) (.f64 (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))) (.f64 x (.f64 x (.f64 x x)))))
(+.f64 (.f64 (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
(fma.f64 x (.f64 x #s(literal -1/24 binary64)) (.f64 (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 x (.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))))) (.f64 (*.f64 x x) #s(literal -1/24 binary64)))
(fma.f64 x (.f64 (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))) (.f64 x x)) (.f64 (*.f64 x x) #s(literal -1/24 binary64)))
(fma.f64 (.f64 x x) #s(literal -1/24 binary64) (.f64 (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 (*.f64 x x) #s(literal -1/24 binary64)))
(fma.f64 #s(literal -1/24 binary64) (.f64 x x) (.f64 (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))) (.f64 x (.f64 x (.f64 x x))) (.f64 (*.f64 x x) #s(literal -1/24 binary64)))
(fma.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 x x) (.f64 (*.f64 x x) #s(literal -1/24 binary64)))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))) (.f64 (*.f64 x x) #s(literal -1/24 binary64)))
(fma.f64 (.f64 x #s(literal -1/24 binary64)) x (.f64 (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))) (.f64 (*.f64 x x) #s(literal -1/24 binary64)))
(fma.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) x) x (.f64 (*.f64 x x) #s(literal -1/24 binary64)))
(/.f64 (+.f64 (.f64 #s(literal -1/13824 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/576 binary64)) (-.f64 (.f64 (.f64 (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) (.f64 (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))) (.f64 x (.f64 x (.f64 x x))))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/576 binary64)) (.f64 (.f64 (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))) (.f64 x (.f64 x (.f64 x x)))))) (-.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) (.f64 (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/13824 binary64) (.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))))))) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (-.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (*.f64 x x) #s(literal -1/40320 binary64))))) #s(literal -1/24 binary64)))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))) (-.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)))))))
(/.f64 (.f64 (+.f64 #s(literal -1/13824 binary64) (.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))) (.f64 x x)) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (-.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (*.f64 x x) #s(literal -1/40320 binary64))))) #s(literal -1/24 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))))) (.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)))))))
(.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))))))))
(.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)))))))
(.f64 (+.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)))))) (.f64 x x))
(.f64 (.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))))))) x)
(+.f64 (.f64 x (.f64 x #s(literal 1/720 binary64))) (.f64 #s(literal -1/40320 binary64) (.f64 x (.f64 x (.f64 x x)))))
(+.f64 (.f64 #s(literal -1/40320 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x #s(literal 1/720 binary64))))
(fma.f64 x (.f64 x #s(literal 1/720 binary64)) (.f64 #s(literal -1/40320 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1/40320 binary64))) (.f64 x (*.f64 x #s(literal 1/720 binary64))))
(fma.f64 x (.f64 (.f64 x #s(literal -1/40320 binary64)) (.f64 x x)) (.f64 x (*.f64 x #s(literal 1/720 binary64))))
(fma.f64 (.f64 x x) #s(literal 1/720 binary64) (.f64 #s(literal -1/40320 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -1/40320 binary64)) (.f64 x (*.f64 x #s(literal 1/720 binary64))))
(fma.f64 #s(literal 1/720 binary64) (.f64 x x) (.f64 #s(literal -1/40320 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 #s(literal -1/40320 binary64) (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x #s(literal 1/720 binary64))))
(fma.f64 (.f64 (.f64 x x) #s(literal -1/40320 binary64)) (.f64 x x) (.f64 x (*.f64 x #s(literal 1/720 binary64))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/40320 binary64) (.f64 x (*.f64 x #s(literal 1/720 binary64))))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal -1/40320 binary64)) (.f64 x (*.f64 x #s(literal 1/720 binary64))))
(fma.f64 (.f64 #s(literal 1/720 binary64) x) x (.f64 #s(literal -1/40320 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/40320 binary64)) x) x (.f64 x (*.f64 x #s(literal 1/720 binary64))))
(/.f64 (+.f64 (.f64 #s(literal 1/373248000 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/65548320768000 binary64))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 (.f64 (.f64 x (.f64 x #s(literal 1/720 binary64))) (.f64 x (.f64 x #s(literal 1/720 binary64)))) (-.f64 (.f64 (.f64 #s(literal -1/40320 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal -1/40320 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x #s(literal 1/720 binary64))) (.f64 #s(literal -1/40320 binary64) (.f64 x (.f64 x (*.f64 x x))))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/720 binary64))) (.f64 x (.f64 x #s(literal 1/720 binary64)))) (.f64 (.f64 #s(literal -1/40320 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal -1/40320 binary64) (.f64 x (.f64 x (.f64 x x)))))) (-.f64 (.f64 x (.f64 x #s(literal 1/720 binary64))) (.f64 #s(literal -1/40320 binary64) (.f64 x (.f64 x (.f64 x x))))))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/373248000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/65548320768000 binary64))))) (+.f64 #s(literal 1/518400 binary64) (.f64 (.f64 (.f64 x x) #s(literal -1/40320 binary64)) (-.f64 (.f64 (*.f64 x x) #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/1625702400 binary64)))) (+.f64 #s(literal 1/720 binary64) (.f64 #s(literal 1/40320 binary64) (.f64 x x))))
(/.f64 (.f64 (+.f64 #s(literal 1/373248000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/65548320768000 binary64)))) (.f64 x x)) (+.f64 #s(literal 1/518400 binary64) (.f64 (.f64 (.f64 x x) #s(literal -1/40320 binary64)) (-.f64 (.f64 (*.f64 x x) #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/518400 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/1625702400 binary64))) (.f64 x x)) (+.f64 #s(literal 1/720 binary64) (.f64 #s(literal 1/40320 binary64) (.f64 x x))))
(.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
(.f64 (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))) (.f64 x x))
(.f64 (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))) x)
(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)))
(+.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(-.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 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (+.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))))
(fma.f64 #s(literal -1 binary64) (cos.f64 x) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.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 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 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) (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 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (+.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 #s(literal 0 binary64) (cos.f64 x))))))
(/.f64 (-.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 (-.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 #s(literal 0 binary64) (cos.f64 x))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (neg.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (-.f64 (.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) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 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) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 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) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(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 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) 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) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
(.f64 (-.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 #s(literal 1 binary64) (cos.f64 x))))

simplify254.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

4408×	`-lowering-.f32`
4408×	`-lowering-.f64`
3782×	`+-lowering-+.f64`
3782×	`+-lowering-+.f32`
1646×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	157	2096
1	447	2014
2	1306	1986
3	4077	1986
4	7115	1986
0	8340	1986

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

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))))
(* 1/2 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 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
x
(* x (+ 1 (* 1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* 7/360 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 7/360 (* 31/15120 (pow x 2))))))))
(/ (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) (sin 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)))
(* -1/40320 (pow x 6))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/40320 (pow x 6))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(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))))
(* -1/40320 (pow x 8))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 8) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/40320 (pow x 8))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 8) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
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 (pow x 2))
(/ (+ 1 (* -1/2 (pow x 2))) (pow x 2))
(/ (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) (pow x 2))
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) (pow x 2))
(/ (cos x) (pow x 2))
(/ (cos x) (pow x 2))
(/ (cos x) (pow x 2))
(/ (cos x) (pow x 2))
(/ (cos x) (pow x 2))
(/ (cos x) (pow x 2))
(/ (cos x) (pow x 2))
(/ (cos x) (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 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)
(/ 2 x)
(/ (+ 2 (* 1/6 (pow x 2))) x)
(/ (+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))) x)
(/ (+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2))))))) 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 (cos x)))
(* 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)
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)
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))
(* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))
(* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))
(* -1/40320 (pow x 6))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/40320 (pow x 6))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* 1/720 (pow x 2))
(* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))
(* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))
(* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))
(* -1/40320 (pow x 4))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* -1/40320 (pow x 4))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
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 (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))

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 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 (.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))))
(* 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 x (*.f64 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 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
x
(* x (+ 1 (* 1/6 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* 7/360 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (*.f64 x x) #s(literal 7/360 binary64))))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 7/360 (* 31/15120 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 7/360 binary64) (.f64 (*.f64 x x) #s(literal 31/15120 binary64))))))))
(/ (pow x 2) (sin x))
(*.f64 x (/.f64 x (sin.f64 x)))
(/ (pow x 2) (sin x))
(*.f64 x (/.f64 x (sin.f64 x)))
(/ (pow x 2) (sin x))
(*.f64 x (/.f64 x (sin.f64 x)))
(/ (pow x 2) (sin x))
(*.f64 x (/.f64 x (sin.f64 x)))
(/ (pow x 2) (sin x))
(*.f64 x (/.f64 x (sin.f64 x)))
(/ (pow x 2) (sin x))
(*.f64 x (/.f64 x (sin.f64 x)))
(/ (pow x 2) (sin x))
(*.f64 x (/.f64 x (sin.f64 x)))
(/ (pow x 2) (sin x))
(*.f64 x (/.f64 x (sin.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 (* -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 #s(literal -1/24 binary64) (.f64 x x))
(* -1/24 (pow x 2))
(.f64 #s(literal -1/24 binary64) (.f64 x x))
(* -1/24 (pow x 2))
(.f64 #s(literal -1/24 binary64) (.f64 x x))
(* -1/24 (pow x 2))
(.f64 #s(literal -1/24 binary64) (.f64 x x))
(* -1/24 (pow x 2))
(.f64 #s(literal -1/24 binary64) (.f64 x x))
(* -1/24 (pow x 2))
(.f64 #s(literal -1/24 binary64) (.f64 x x))
(* -1/24 (pow x 2))
(.f64 #s(literal -1/24 binary64) (.f64 x x))
(* -1/24 (pow x 2))
(.f64 #s(literal -1/24 binary64) (.f64 x x))
(* -1/24 (pow x 2))
(.f64 #s(literal -1/24 binary64) (.f64 x x))
(* -1/24 (pow x 2))
(.f64 #s(literal -1/24 binary64) (.f64 x x))
(* -1/24 (pow x 2))
(.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)
(*.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)
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(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* 1/720 (pow x 2))
(.f64 x (.f64 x #s(literal 1/720 binary64)))
(* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
(* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
(* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
(* -1/40320 (pow x 4))
(.f64 x (.f64 #s(literal -1/40320 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
(* -1/40320 (pow x 4))
(.f64 x (.f64 #s(literal -1/40320 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
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 (.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 (.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 (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 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 (.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))

eval192.0ms (2%)

Compiler: Compiled 30954 to 3079 computations (90.1% saved)

prune138.0ms (1.4%)

Pruning

26 alts after pruning (18 fresh and 8 done)

	Pruned	Kept	Total
New	1416	8	1424
Fresh	3	10	13
Picked	1	4	5
Done	0	4	4
Total	1420	26	1446

Accuracy

100.0%

Counts

1446 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
	52.2%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	31.1%	(/.f64 (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (+.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)))))) (.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)))))))))) (.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))))))))) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
▶	52.2%	(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))))
	16.4%	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (neg.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x))))) (.f64 x (.f64 x (.f64 x x))))
	45.2%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 (.f64 x (.f64 x x)) x))
✓	51.4%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
	28.1%	(/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (*.f64 x x))
✓	31.2%	(/.f64 (.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)))))))) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
✓	80.7%	(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (*.f64 x x) (sin.f64 x)))
▶	50.7%	(/.f64 #s(literal 1 binary64) (/.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 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (.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 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 x (*.f64 x #s(literal -1/40320 binary64))))))))))))
	16.5%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
▶	80.1%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))
	52.0%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
✓	51.4%	(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
✓	51.3%	(+.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 x (.f64 x #s(literal -1/40320 binary64))))))))
	51.7%	(+.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)))))
✓	51.1%	(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
✓	80.6%	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
	80.0%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))) x)) (/.f64 #s(literal 1 binary64) x))
	52.1%	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))) x))) (/.f64 #s(literal 1 binary64) x))
	52.2%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) x)) (/.f64 #s(literal 1 binary64) x))
▶	51.2%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 x (*.f64 x (cos.f64 x))))))
	52.1%	(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) x)) (/.f64 #s(literal 1 binary64) x))
	80.0%	(.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
▶	51.6%	(.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) x))
✓	51.7%	#s(literal 1/2 binary64)

Compiler

Compiled 800 to 425 computations (46.9% saved)

simplify185.0ms (1.9%)

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	cost-diff	384	(/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 x (*.f64 x (cos.f64 x)))))
✓	cost-diff	512	(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 x (*.f64 x (cos.f64 x))))))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	cost-diff	0	(/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	128	(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))))
✓	cost-diff	0	(.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))))))))
✓	cost-diff	0	(-.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)))))))))
✓	cost-diff	0	(/.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 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (.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 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 x (*.f64 x #s(literal -1/40320 binary64)))))))))))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.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 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (.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 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 x (*.f64 x #s(literal -1/40320 binary64))))))))))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	384	(.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) #s(literal 1/6 binary64))
✓	cost-diff	0	(+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))

Rules

2598×	`-lowering-.f32`
2598×	`-lowering-.f64`
2088×	`fma-lowering-fma.f32`
2088×	`fma-lowering-fma.f64`
1670×	`sum4-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	436
1	123	385
2	492	366
3	2596	358
4	6570	358
0	8482	358

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ 1 (+ 2 (* (* x x) 1/6)))
1
(+ 2 (* (* x x) 1/6))
2
(* (* x x) 1/6)
(* x x)
x
1/6
(* (* 1/2 x) (/ 1 x))
(* 1/2 x)
1/2
x
(/ 1 x)
1
(/ 1 (/ (- 1/2 (* x (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))) (- 1/4 (* (* x x) (* (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))) (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))))))
1
(/ (- 1/2 (* x (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))) (- 1/4 (* (* x x) (* (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))) (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320))))))))))
(- 1/2 (* x (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320))))))))
1/2
(* x (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))
x
(* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320))))))
(+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))
-1/24
(* (* x x) (+ 1/720 (* x (* x -1/40320))))
(* x x)
(+ 1/720 (* x (* x -1/40320)))
1/720
(* x (* x -1/40320))
(* x -1/40320)
-1/40320
(- 1/4 (* (* x x) (* (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))) (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))))
1/4
(* (* x x) (* (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))) (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320))))))))
(* (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))) (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))
(/ (/ 1 x) (/ x (- 1 (cos x))))
(/ 1 x)
1
x
(/ x (- 1 (cos x)))
(- 1 (cos x))
(cos x)
(* (/ 1 (* x x)) (/ 1 (/ x (- x (* x (cos x))))))
(/ 1 (* x x))
1
(* x x)
x
(/ 1 (/ x (- x (* x (cos x)))))
(/ x (- x (* x (cos x))))
(- x (* x (cos x)))
(* x (cos x))
(cos x)

Outputs
(/ 1 (+ 2 (* (* x x) 1/6)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))))
1
#s(literal 1 binary64)
(+ 2 (* (* x x) 1/6))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
2
#s(literal 2 binary64)
(* (* x x) 1/6)
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* x x)
(*.f64 x x)
x
1/6
#s(literal 1/6 binary64)
(* (* 1/2 x) (/ 1 x))
#s(literal 1/2 binary64)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
x
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
(/ 1 (/ (- 1/2 (* x (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))) (- 1/4 (* (* x x) (* (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))) (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x (.f64 (+.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 (+.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 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 x (*.f64 x #s(literal -1/40320 binary64)))))))))
1
#s(literal 1 binary64)
(/ (- 1/2 (* x (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))) (- 1/4 (* (* x x) (* (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))) (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320))))))))))
(/.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 x (.f64 x #s(literal -1/40320 binary64)))))))) (-.f64 #s(literal 1/4 binary64) (.f64 x (.f64 (+.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 (+.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 x)))))))
(- 1/2 (* x (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320))))))))
(+.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 x (.f64 x #s(literal -1/40320 binary64))))))))
1/2
#s(literal 1/2 binary64)
(* x (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))
(.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))))))))
x
(* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320))))))
(.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)))))))
(+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))
(+.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))))))
-1/24
#s(literal -1/24 binary64)
(* (* x x) (+ 1/720 (* x (* x -1/40320))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x #s(literal -1/40320 binary64)))))
(* x x)
(*.f64 x x)
(+ 1/720 (* x (* x -1/40320)))
(+.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x #s(literal -1/40320 binary64))))
1/720
#s(literal 1/720 binary64)
(* x (* x -1/40320))
(.f64 x (.f64 x #s(literal -1/40320 binary64)))
(* x -1/40320)
(*.f64 x #s(literal -1/40320 binary64))
-1/40320
#s(literal -1/40320 binary64)
(- 1/4 (* (* x x) (* (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))) (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))))
(-.f64 #s(literal 1/4 binary64) (.f64 x (.f64 (+.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 (+.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 x))))))
1/4
#s(literal 1/4 binary64)
(* (* x x) (* (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))) (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320))))))))
(.f64 x (.f64 (+.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 (+.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 x)))))
(* (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))) (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))
(.f64 x (.f64 (+.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 #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 x) (/ x (- 1 (cos x))))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(/ x (- 1 (cos x)))
(/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos x)
(cos.f64 x)
(* (/ 1 (* x x)) (/ 1 (/ x (- x (* x (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 (/ x (- x (* x (cos x)))))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(/ x (- x (* x (cos x))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 1 binary64))
(- x (* x (cos x)))
(*.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(* x (cos x))
(*.f64 x (cos.f64 x))
(cos x)
(cos.f64 x)

localize314.0ms (3.3%)

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	accuracy	87.1%	(/.f64 x (-.f64 x (*.f64 x (cos.f64 x))))
✓	accuracy	84.7%	(-.f64 x (*.f64 x (cos.f64 x)))
✓	accuracy	80.9%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 x (*.f64 x (cos.f64 x))))))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	99.9%	(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))))
✓	accuracy	81.5%	(/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
✓	accuracy	71.7%	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	accuracy	99.8%	(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x #s(literal -1/40320 binary64)))))
✓	accuracy	99.8%	(.f64 (.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 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 x (*.f64 x #s(literal -1/40320 binary64))))))))
✓	accuracy	99.7%	(.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)))))))
✓	accuracy	54.1%	(/.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 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (.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 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 x (*.f64 x #s(literal -1/40320 binary64)))))))))))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	accuracy	99.8%	(.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal 1/6 binary64))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))

Results

103.0ms	71×	2	valid
65.0ms	131×	0	valid
37.0ms	40×	1	valid
32.0ms	14×	3	valid

Compiler

Compiled 448 to 40 computations (91.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 155.0ms

ival-mult: 39.0ms (25.1% of total)

ival-cos: 33.0ms (21.3% of total)

ival-div: 26.0ms (16.7% of total)

...c/correct-round.rkt:119:19: 22.0ms (14.2% of total)

backward-pass: 19.0ms (12.2% of total)

ival-sub: 9.0ms (5.8% of total)

ival-add: 5.0ms (3.2% of total)

const: 1.0ms (0.6% of total)

series47.0ms (0.5%)

Counts

23 → 276

Calls

Call 1

Inputs
#<alt (/ 1 (+ 2 (* (* x x) 1/6)))>
#<alt (+ 2 (* (* x x) 1/6))>
#<alt (* (* x x) 1/6)>
#<alt (* x x)>
#<alt (* (* 1/2 x) (/ 1 x))>
#<alt (* 1/2 x)>
#<alt (/ 1 x)>
#<alt (/ 1 (/ (- 1/2 (* x (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))) (- 1/4 (* (* x x) (* (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))) (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))))))>
#<alt (/ (- 1/2 (* x (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))) (- 1/4 (* (* x x) (* (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))) (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320))))))))))>
#<alt (- 1/2 (* x (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320))))))))>
#<alt (* x (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))>
#<alt (/ (/ 1 x) (/ x (- 1 (cos x))))>
#<alt (/ x (- 1 (cos x)))>
#<alt (- 1 (cos x))>
#<alt (* (/ 1 (* x x)) (/ 1 (/ x (- x (* x (cos x))))))>
#<alt (/ 1 (/ x (- x (* x (cos x)))))>
#<alt (/ 1 (* x x))>
#<alt (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320))))))>
#<alt (* (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))) (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))>
#<alt (* (* x x) (+ 1/720 (* x (* x -1/40320))))>
#<alt (cos x)>
#<alt (- x (* x (cos x)))>
#<alt (/ x (- x (* x (cos x))))>

Outputs
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/288 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/288 (* -1/3456 (pow x 2)))) 1/24)))>
#<alt (/ 6 (pow x 2))>
#<alt (/ (- 6 (* 72 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 6 (/ 864 (pow x 4))) (* 72 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 6 (/ 864 (pow x 4))) (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6))))) (pow x 2))>
#<alt (/ 6 (pow x 2))>
#<alt (/ (- 6 (* 72 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 6 (/ 864 (pow x 4))) (* 72 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 6 (/ 864 (pow x 4))) (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6))))) (pow x 2))>
#<alt 2>
#<alt (+ 2 (* 1/6 (pow x 2)))>
#<alt (+ 2 (* 1/6 (pow x 2)))>
#<alt (+ 2 (* 1/6 (pow x 2)))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (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>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 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 (* -1/40320 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* -1/40320 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt 2>
#<alt (+ 2 (* 1/6 (pow x 2)))>
#<alt (+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2)))))>
#<alt (+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2)))))))>
#<alt (/ -40320 (pow x 6))>
#<alt (* -1 (/ (+ 40320 (* 2257920 (/ 1 (pow x 2)))) (pow x 6)))>
#<alt (/ (- (* -1 (/ (+ 2257920 (* 58705920 (/ 1 (pow x 2)))) (pow x 2))) 40320) (pow x 6))>
#<alt (/ (- (* -1 (/ (+ 58705920 (* 307077120 (/ 1 (pow x 2)))) (pow x 4))) (+ 40320 (* 2257920 (/ 1 (pow x 2))))) (pow x 6))>
#<alt (/ -40320 (pow x 6))>
#<alt (* -1 (/ (+ 40320 (* 2257920 (/ 1 (pow x 2)))) (pow x 6)))>
#<alt (/ (- (* -1 (/ (+ 2257920 (* 58705920 (/ 1 (pow x 2)))) (pow x 2))) 40320) (pow x 6))>
#<alt (/ (- (* -1 (/ (+ 58705920 (* 307077120 (/ 1 (pow x 2)))) (pow x 4))) (+ 40320 (* 2257920 (/ 1 (pow x 2))))) (pow x 6))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))>
#<alt (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))))>
#<alt (* 1/40320 (pow x 6))>
#<alt (* (pow x 6) (- 1/40320 (* 1/720 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/40320 (+ (/ 1/24 (pow x 4)) (* 1/2 (/ 1 (pow x 6))))) (* 1/720 (/ 1 (pow x 2)))))>
#<alt (* 1/40320 (pow x 6))>
#<alt (* (pow x 6) (- 1/40320 (* 1/720 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/40320 (+ (/ 1/24 (pow x 4)) (* 1/2 (/ 1 (pow x 6))))) (* 1/720 (/ 1 (pow x 2)))))>
#<alt (* -1/24 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))>
#<alt (* -1/40320 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* -1/40320 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<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 (/ 2 x)>
#<alt (/ (+ 2 (* 1/6 (pow x 2))) x)>
#<alt (/ (+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))) x)>
#<alt (/ (+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2))))))) x)>
#<alt (/ x (- 1 (cos x)))>
#<alt (/ x (- 1 (cos x)))>
#<alt (/ x (- 1 (cos x)))>
#<alt (/ x (- 1 (cos x)))>
#<alt (/ x (- 1 (cos x)))>
#<alt (/ x (- 1 (cos x)))>
#<alt (/ x (- 1 (cos x)))>
#<alt (/ x (- 1 (cos 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 1/2>
#<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 (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 (* -1/24 x)>
#<alt (* x (- (* 1/720 (pow x 2)) 1/24))>
#<alt (* x (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))>
#<alt (* x (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))>
#<alt (* -1/40320 (pow x 5))>
#<alt (* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* -1/40320 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2))))))>
#<alt (* 1/576 (pow x 2))>
#<alt (* (pow x 2) (+ 1/576 (* -1/8640 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/576 (* (pow x 2) (- (* 29/7257600 (pow x 2)) 1/8640))))>
#<alt (* (pow x 2) (+ 1/576 (* (pow x 2) (- (* (pow x 2) (+ 29/7257600 (* -1/14515200 (pow x 2)))) 1/8640))))>
#<alt (* 1/1625702400 (pow x 10))>
#<alt (* (pow x 10) (- 1/1625702400 (* 1/14515200 (/ 1 (pow x 2)))))>
#<alt (* (pow x 10) (- (+ 1/1625702400 (/ 29/7257600 (pow x 4))) (* 1/14515200 (/ 1 (pow x 2)))))>
#<alt (* (pow x 10) (- (+ 1/1625702400 (/ 29/7257600 (pow x 4))) (+ (* 1/14515200 (/ 1 (pow x 2))) (* 1/8640 (/ 1 (pow x 6))))))>
#<alt (* 1/1625702400 (pow x 10))>
#<alt (* (pow x 10) (- 1/1625702400 (* 1/14515200 (/ 1 (pow x 2)))))>
#<alt (* (pow x 10) (- (+ 1/1625702400 (/ 29/7257600 (pow x 4))) (* 1/14515200 (/ 1 (pow x 2)))))>
#<alt (* (pow x 10) (- (+ 1/1625702400 (/ 29/7257600 (pow x 4))) (+ (* 1/14515200 (/ 1 (pow x 2))) (* 1/8640 (/ 1 (pow x 6))))))>
#<alt (* 1/720 (pow x 2))>
#<alt (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))>
#<alt (* -1/40320 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* -1/40320 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<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 (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 (/ 2 (pow x 2))>
#<alt (/ (+ 2 (* 1/6 (pow x 2))) (pow x 2))>
#<alt (/ (+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))) (pow x 2))>
#<alt (/ (+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2))))))) (pow x 2))>
#<alt (/ 1 (- 1 (cos x)))>
#<alt (/ 1 (- 1 (cos x)))>
#<alt (/ 1 (- 1 (cos x)))>
#<alt (/ 1 (- 1 (cos x)))>
#<alt (/ 1 (+ 1 (* -1 (cos x))))>
#<alt (/ 1 (+ 1 (* -1 (cos x))))>
#<alt (/ 1 (+ 1 (* -1 (cos x))))>
#<alt (/ 1 (+ 1 (* -1 (cos x))))>

Calls

69 calls:

Time	Variable		Point	Expression
21.0ms	x	@	0	(* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320))))))
13.0ms	x	@	-inf	(/ 1 (/ x (- x (* x (cos x)))))
3.0ms	x	@	0	(/ 1 (+ 2 (* (* x x) 1/6)))
1.0ms	x	@	-inf	(/ x (- x (* x (cos x))))
0.0ms	x	@	0	(* (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))) (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))

rewrite476.0ms (4.9%)

Algorithm

1×	batch-egg-rewrite

Rules

4002×	`-lowering-.f32`
4002×	`-lowering-.f64`
3984×	`/-lowering-/.f32`
3984×	`/-lowering-/.f64`
1878×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	260
1	278	188
2	2372	180
0	8901	180

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 933

Calls

Call 1

Inputs
(/ 1 (+ 2 (* (* x x) 1/6)))
(+ 2 (* (* x x) 1/6))
(* (* x x) 1/6)
(* x x)
(* (* 1/2 x) (/ 1 x))
(* 1/2 x)
(/ 1 x)
(/ 1 (/ (- 1/2 (* x (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))) (- 1/4 (* (* x x) (* (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))) (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))))))
(/ (- 1/2 (* x (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))) (- 1/4 (* (* x x) (* (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))) (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320))))))))))
(- 1/2 (* x (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320))))))))
(* x (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))
(/ (/ 1 x) (/ x (- 1 (cos x))))
(/ x (- 1 (cos x)))
(- 1 (cos x))
(* (/ 1 (* x x)) (/ 1 (/ x (- x (* x (cos x))))))
(/ 1 (/ x (- x (* x (cos x)))))
(/ 1 (* x x))
(* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320))))))
(* (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))) (* x (+ -1/24 (* (* x x) (+ 1/720 (* x (* x -1/40320)))))))
(* (* x x) (+ 1/720 (* x (* x -1/40320))))
(cos x)
(- x (* x (cos x)))
(/ x (- x (* x (cos x))))

Outputs
(exp.f64 (.f64 (log.f64 (+.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64)))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))))))
(pow.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) #s(literal -1 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) (+.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64)))) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64)))) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64)))))
(.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64))) #s(literal -1/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))))) (+.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64))))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)))) (-.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64)))) #s(literal -1 binary64)))
(+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))
(+.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64))
(exp.f64 (neg.f64 (.f64 (log.f64 (+.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64)))) #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)) (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))))
(-.f64 (/.f64 (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))) #s(literal 1 binary64)) (/.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)) (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 4 binary64) (.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)) (.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 4 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64))))
(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal 2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 2 binary64))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64)))) (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)))))
(/.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64)))) (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))) #s(literal -1 binary64))
(/.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (-.f64 (.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64)))))
(/.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x)))))
(/.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64))))))
(/.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64))) (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))
(/.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64))) (.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))) #s(literal 1 binary64))
(/.f64 (neg.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))))) (neg.f64 (+.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (-.f64 (.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64))))))
(/.f64 (neg.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))))) (neg.f64 (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x))))))
(/.f64 (neg.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))))) (neg.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)))) (neg.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)))) (neg.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)) #s(literal 4 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))) (.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)))) (.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) (-.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))))) (neg.f64 (neg.f64 (+.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (-.f64 (.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64))))) (neg.f64 (neg.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)) #s(literal 4 binary64))) (neg.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64))))
(pow.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64)))) (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64))) #s(literal 1 binary64))
(.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64))))))
(.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64)))))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 1/6 binary64)) x)
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (neg.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 x x) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 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) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -1 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal -1 binary64))
(/.f64 (neg.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 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 x (pow.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))))
#s(literal 1/2 binary64)
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal -1/2 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x))))
(pow.f64 x #s(literal -1 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) #s(literal -1 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal -1 binary64))
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(.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x (.f64 x (cos.f64 x))))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (.f64 x (cos.f64 x)))) 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 (.f64 x (cos.f64 x)) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) 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 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 (.f64 x (cos.f64 x)) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x))))))
(.f64 (/.f64 x (-.f64 (.f64 x 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) (cos.f64 x)) x))
(.f64 (/.f64 x (-.f64 (.f64 x 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 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x))))
(.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x (.f64 x (cos.f64 x))))))
(.f64 (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) #s(literal 1 binary64)))) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) #s(literal 1 binary64)))) #s(literal 1/2 binary64)) #s(literal -1 binary64)))

simplify249.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

3760×	`-lowering-.f32`
3760×	`-lowering-.f64`
2776×	`+-lowering-+.f64`
2776×	`+-lowering-+.f32`
1442×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	2189
1	599	2102
2	1719	2066
3	5366	2066
0	8401	2066

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/288 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/288 (* -1/3456 (pow x 2)))) 1/24)))
(/ 6 (pow x 2))
(/ (- 6 (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 6 (/ 864 (pow x 4))) (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 6 (/ 864 (pow x 4))) (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6))))) (pow x 2))
(/ 6 (pow x 2))
(/ (- 6 (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 6 (/ 864 (pow x 4))) (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 6 (/ 864 (pow x 4))) (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6))))) (pow x 2))
2
(+ 2 (* 1/6 (pow x 2)))
(+ 2 (* 1/6 (pow x 2)))
(+ 2 (* 1/6 (pow x 2)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (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
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 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)))
(* -1/40320 (pow x 6))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/40320 (pow x 6))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
2
(+ 2 (* 1/6 (pow x 2)))
(+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2)))))))
(/ -40320 (pow x 6))
(* -1 (/ (+ 40320 (* 2257920 (/ 1 (pow x 2)))) (pow x 6)))
(/ (- (* -1 (/ (+ 2257920 (* 58705920 (/ 1 (pow x 2)))) (pow x 2))) 40320) (pow x 6))
(/ (- (* -1 (/ (+ 58705920 (* 307077120 (/ 1 (pow x 2)))) (pow x 4))) (+ 40320 (* 2257920 (/ 1 (pow x 2))))) (pow x 6))
(/ -40320 (pow x 6))
(* -1 (/ (+ 40320 (* 2257920 (/ 1 (pow x 2)))) (pow x 6)))
(/ (- (* -1 (/ (+ 2257920 (* 58705920 (/ 1 (pow x 2)))) (pow x 2))) 40320) (pow x 6))
(/ (- (* -1 (/ (+ 58705920 (* 307077120 (/ 1 (pow x 2)))) (pow x 4))) (+ 40320 (* 2257920 (/ 1 (pow x 2))))) (pow x 6))
1/2
(+ 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)))))
(* 1/40320 (pow x 6))
(* (pow x 6) (- 1/40320 (* 1/720 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/40320 (+ (/ 1/24 (pow x 4)) (* 1/2 (/ 1 (pow x 6))))) (* 1/720 (/ 1 (pow x 2)))))
(* 1/40320 (pow x 6))
(* (pow x 6) (- 1/40320 (* 1/720 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/40320 (+ (/ 1/24 (pow x 4)) (* 1/2 (/ 1 (pow x 6))))) (* 1/720 (/ 1 (pow x 2)))))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))
(* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))
(* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))
(* -1/40320 (pow x 6))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/40320 (pow x 6))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
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))
(/ 2 x)
(/ (+ 2 (* 1/6 (pow x 2))) x)
(/ (+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))) x)
(/ (+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2))))))) 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 (cos 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))
1/2
(+ 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 (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))
(* -1/24 x)
(* x (- (* 1/720 (pow x 2)) 1/24))
(* x (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))
(* x (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))
(* -1/40320 (pow x 5))
(* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/40320 (pow x 5))
(* -1 (* (pow x 5) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2))))))
(* 1/576 (pow x 2))
(* (pow x 2) (+ 1/576 (* -1/8640 (pow x 2))))
(* (pow x 2) (+ 1/576 (* (pow x 2) (- (* 29/7257600 (pow x 2)) 1/8640))))
(* (pow x 2) (+ 1/576 (* (pow x 2) (- (* (pow x 2) (+ 29/7257600 (* -1/14515200 (pow x 2)))) 1/8640))))
(* 1/1625702400 (pow x 10))
(* (pow x 10) (- 1/1625702400 (* 1/14515200 (/ 1 (pow x 2)))))
(* (pow x 10) (- (+ 1/1625702400 (/ 29/7257600 (pow x 4))) (* 1/14515200 (/ 1 (pow x 2)))))
(* (pow x 10) (- (+ 1/1625702400 (/ 29/7257600 (pow x 4))) (+ (* 1/14515200 (/ 1 (pow x 2))) (* 1/8640 (/ 1 (pow x 6))))))
(* 1/1625702400 (pow x 10))
(* (pow x 10) (- 1/1625702400 (* 1/14515200 (/ 1 (pow x 2)))))
(* (pow x 10) (- (+ 1/1625702400 (/ 29/7257600 (pow x 4))) (* 1/14515200 (/ 1 (pow x 2)))))
(* (pow x 10) (- (+ 1/1625702400 (/ 29/7257600 (pow x 4))) (+ (* 1/14515200 (/ 1 (pow x 2))) (* 1/8640 (/ 1 (pow x 6))))))
(* 1/720 (pow x 2))
(* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))
(* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))
(* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))
(* -1/40320 (pow x 4))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* -1/40320 (pow x 4))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
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 (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))))
(/ 2 (pow x 2))
(/ (+ 2 (* 1/6 (pow x 2))) (pow x 2))
(/ (+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))) (pow x 2))
(/ (+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2))))))) (pow x 2))
(/ 1 (- 1 (cos x)))
(/ 1 (- 1 (cos x)))
(/ 1 (- 1 (cos x)))
(/ 1 (- 1 (cos x)))
(/ 1 (+ 1 (* -1 (cos x))))
(/ 1 (+ 1 (* -1 (cos x))))
(/ 1 (+ 1 (* -1 (cos x))))
(/ 1 (+ 1 (* -1 (cos 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) (- (* 1/288 (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 1/288 binary64)))))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/288 (* -1/3456 (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 1/288 binary64) (.f64 (.f64 x x) #s(literal -1/3456 binary64)))))))
(/ 6 (pow x 2))
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(/ (- 6 (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 6 binary64) (/.f64 #s(literal 72 binary64) (*.f64 x x))) x) x)
(/ (- (+ 6 (/ 864 (pow x 4))) (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 (-.f64 #s(literal 6 binary64) (/.f64 #s(literal 72 binary64) (.f64 x x))) (/.f64 #s(literal 864 binary64) (.f64 x (.f64 x (.f64 x x))))) (*.f64 x x))
(/ (- (+ 6 (/ 864 (pow x 4))) (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 #s(literal 6 binary64) (+.f64 (/.f64 #s(literal 864 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (/.f64 #s(literal -72 binary64) (.f64 x x)) (/.f64 #s(literal -10368 binary64) (pow.f64 x #s(literal 6 binary64)))))) (*.f64 x x))
(/ 6 (pow x 2))
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(/ (- 6 (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 6 binary64) (/.f64 #s(literal 72 binary64) (*.f64 x x))) x) x)
(/ (- (+ 6 (/ 864 (pow x 4))) (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 (-.f64 #s(literal 6 binary64) (/.f64 #s(literal 72 binary64) (.f64 x x))) (/.f64 #s(literal 864 binary64) (.f64 x (.f64 x (.f64 x x))))) (*.f64 x x))
(/ (- (+ 6 (/ 864 (pow x 4))) (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 #s(literal 6 binary64) (+.f64 (/.f64 #s(literal 864 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (/.f64 #s(literal -72 binary64) (.f64 x x)) (/.f64 #s(literal -10368 binary64) (pow.f64 x #s(literal 6 binary64)))))) (*.f64 x x))
2
#s(literal 2 binary64)
(+ 2 (* 1/6 (pow x 2)))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(+ 2 (* 1/6 (pow x 2)))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(+ 2 (* 1/6 (pow x 2)))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 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
#s(literal 1/2 binary64)
1/2
#s(literal 1/2 binary64)
1/2
#s(literal 1/2 binary64)
1/2
#s(literal 1/2 binary64)
1/2
#s(literal 1/2 binary64)
1/2
#s(literal 1/2 binary64)
1/2
#s(literal 1/2 binary64)
1/2
#s(literal 1/2 binary64)
1/2
#s(literal 1/2 binary64)
1/2
#s(literal 1/2 binary64)
1/2
#s(literal 1/2 binary64)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
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(*.f64 #s(literal -1/24 binary64) x)
(* x (- (* 1/720 (pow x 2)) 1/24))
(.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/720 binary64))))
(* x (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))
(.f64 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))))))
(* x (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))
(.f64 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))))))
(* -1/40320 (pow x 5))
(.f64 #s(literal -1/40320 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x x))))
(* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (.f64 (.f64 x x) (.f64 x (.f64 x x))))
(* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (+.f64 #s(literal -1/40320 binary64) (+.f64 (/.f64 #s(literal 1/720 binary64) (.f64 x x)) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x x) (.f64 x (*.f64 x x))))
(* (pow x 5) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (+.f64 #s(literal -1/40320 binary64) (+.f64 (/.f64 #s(literal 1/720 binary64) (.f64 x x)) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x x) (.f64 x (*.f64 x x))))
(* -1/40320 (pow x 5))
(.f64 #s(literal -1/40320 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x x))))
(* -1 (* (pow x 5) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))))
(.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (.f64 (.f64 x x) (.f64 x (.f64 x x))))
(* -1 (* (pow x 5) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2))))))
(.f64 (+.f64 #s(literal -1/40320 binary64) (+.f64 (/.f64 #s(literal 1/720 binary64) (.f64 x x)) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x x) (.f64 x (*.f64 x x))))
(* -1 (* (pow x 5) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2))))))
(.f64 (+.f64 #s(literal -1/40320 binary64) (+.f64 (/.f64 #s(literal 1/720 binary64) (.f64 x x)) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x x) (.f64 x (*.f64 x x))))
(* 1/576 (pow x 2))
(.f64 x (.f64 x #s(literal 1/576 binary64)))
(* (pow x 2) (+ 1/576 (* -1/8640 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1/576 binary64) (.f64 x (.f64 x #s(literal -1/8640 binary64))))))
(* (pow x 2) (+ 1/576 (* (pow x 2) (- (* 29/7257600 (pow x 2)) 1/8640))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8640 binary64) (.f64 (.f64 x x) #s(literal 29/7257600 binary64))))))
(* (pow x 2) (+ 1/576 (* (pow x 2) (- (* (pow x 2) (+ 29/7257600 (* -1/14515200 (pow x 2)))) 1/8640))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8640 binary64) (.f64 x (.f64 x (+.f64 #s(literal 29/7257600 binary64) (.f64 (.f64 x x) #s(literal -1/14515200 binary64)))))))))
(* 1/1625702400 (pow x 10))
(*.f64 #s(literal 1/1625702400 binary64) (pow.f64 x #s(literal 10 binary64)))
(* (pow x 10) (- 1/1625702400 (* 1/14515200 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 10 binary64)) (+.f64 #s(literal 1/1625702400 binary64) (/.f64 #s(literal -1/14515200 binary64) (.f64 x x))))
(* (pow x 10) (- (+ 1/1625702400 (/ 29/7257600 (pow x 4))) (* 1/14515200 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 10 binary64)) (+.f64 #s(literal 1/1625702400 binary64) (+.f64 (/.f64 #s(literal 29/7257600 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/14515200 binary64) (*.f64 x x)))))
(* (pow x 10) (- (+ 1/1625702400 (/ 29/7257600 (pow x 4))) (+ (* 1/14515200 (/ 1 (pow x 2))) (* 1/8640 (/ 1 (pow x 6))))))
(.f64 (pow.f64 x #s(literal 10 binary64)) (+.f64 #s(literal 1/1625702400 binary64) (+.f64 (/.f64 #s(literal 29/7257600 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (/.f64 #s(literal -1/14515200 binary64) (*.f64 x x)) (/.f64 #s(literal -1/8640 binary64) (pow.f64 x #s(literal 6 binary64)))))))
(* 1/1625702400 (pow x 10))
(*.f64 #s(literal 1/1625702400 binary64) (pow.f64 x #s(literal 10 binary64)))
(* (pow x 10) (- 1/1625702400 (* 1/14515200 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 10 binary64)) (+.f64 #s(literal 1/1625702400 binary64) (/.f64 #s(literal -1/14515200 binary64) (.f64 x x))))
(* (pow x 10) (- (+ 1/1625702400 (/ 29/7257600 (pow x 4))) (* 1/14515200 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 10 binary64)) (+.f64 #s(literal 1/1625702400 binary64) (+.f64 (/.f64 #s(literal 29/7257600 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/14515200 binary64) (*.f64 x x)))))
(* (pow x 10) (- (+ 1/1625702400 (/ 29/7257600 (pow x 4))) (+ (* 1/14515200 (/ 1 (pow x 2))) (* 1/8640 (/ 1 (pow x 6))))))
(.f64 (pow.f64 x #s(literal 10 binary64)) (+.f64 #s(literal 1/1625702400 binary64) (+.f64 (/.f64 #s(literal 29/7257600 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (/.f64 #s(literal -1/14515200 binary64) (*.f64 x x)) (/.f64 #s(literal -1/8640 binary64) (pow.f64 x #s(literal 6 binary64)))))))
(* 1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/720 binary64))
(* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
(* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
(* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))
(* -1/40320 (pow x 4))
(.f64 x (.f64 #s(literal -1/40320 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* -1/40320 (pow x 4))
(.f64 x (.f64 #s(literal -1/40320 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x 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 (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))) #s(literal -1/2 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 (pow x 3))
(.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (*.f64 x x)))))
(* (pow x 3) (+ 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 x (*.f64 x x)))
(* (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 x (.f64 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)))
(/ 2 (pow x 2))
(/.f64 #s(literal 2 binary64) (*.f64 x x))
(/ (+ 2 (* 1/6 (pow x 2))) (pow x 2))
(.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 1 binary64)))
(/ (+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))) (pow x 2))
(/.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64))))) (*.f64 x x))
(/ (+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2))))))) (pow x 2))
(/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (.f64 x x) #s(literal 1/3024 binary64)))))))) (*.f64 x x))
(/ 1 (- 1 (cos x)))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(/ 1 (- 1 (cos x)))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(/ 1 (- 1 (cos x)))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(/ 1 (- 1 (cos x)))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(/ 1 (+ 1 (* -1 (cos x))))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(/ 1 (+ 1 (* -1 (cos x))))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(/ 1 (+ 1 (* -1 (cos x))))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(/ 1 (+ 1 (* -1 (cos x))))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))

eval282.0ms (2.9%)

Compiler: Compiled 87501 to 4681 computations (94.7% saved)

prune228.0ms (2.4%)

Pruning

37 alts after pruning (27 fresh and 10 done)

	Pruned	Kept	Total
New	1561	17	1578
Fresh	3	10	13
Picked	3	2	5
Done	0	8	8
Total	1567	37	1604

Accuracy

100.0%

Counts

1604 → 37

Alt Table

Click to see full alt table

Status	Accuracy	Program
	30.2%	(/.f64 (/.f64 (-.f64 #s(literal 6 binary64) (/.f64 #s(literal 72 binary64) (*.f64 x x))) x) x)
	52.2%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	80.1%	(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) x))
✓	52.2%	(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))))
	52.2%	(/.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
	16.4%	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (neg.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x))))) (.f64 x (.f64 x (.f64 x x))))
	45.2%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 (.f64 x (.f64 x x)) x))
✓	51.4%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
✓	31.2%	(/.f64 (.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)))))))) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
✓	80.7%	(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (*.f64 x x) (sin.f64 x)))
	32.1%	(/.f64 #s(literal 6 binary64) (*.f64 x x))
	53.2%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)) #s(literal 4 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64))))
	51.8%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))) (.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)))) (.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) (-.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64))))))
	50.9%	(/.f64 #s(literal 1 binary64) (/.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 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8640 binary64) (.f64 x (.f64 x (+.f64 #s(literal 29/7257600 binary64) (.f64 (.f64 x x) #s(literal -1/14515200 binary64)))))))))))))
	51.8%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x))))))
	51.8%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (-.f64 (.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64))))))
	16.5%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
	53.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64))))))
	80.1%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal 1/6 binary64))))
	80.1%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1/6 binary64))))
✓	80.1%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))
	52.0%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
	51.8%	(/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64)))))))
	32.1%	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
✓	51.4%	(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
✓	51.3%	(+.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 x (.f64 x #s(literal -1/40320 binary64))))))))
	51.7%	(+.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)))))
✓	51.1%	(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
✓	80.6%	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
	80.0%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))) x)) (/.f64 #s(literal 1 binary64) x))
	52.1%	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))) x))) (/.f64 #s(literal 1 binary64) x))
	53.2%	(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)))) (-.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64))))
	52.2%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) x)) (/.f64 #s(literal 1 binary64) x))
	51.2%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (-.f64 x (*.f64 x (cos.f64 x))) x))
	60.6%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 1 binary64)))))
	80.0%	(.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	51.7%	#s(literal 1/2 binary64)

Compiler

Compiled 1668 to 635 computations (61.9% saved)

regimes35.0ms (0.4%)

Counts

57 → 2

Calls

Call 1

Inputs
#s(literal 1/2 binary64)
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) x))
(+.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 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (*.f64 x x))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal 1/6 binary64))))
(/.f64 (/.f64 (-.f64 #s(literal 6 binary64) (/.f64 #s(literal 72 binary64) (*.f64 x x))) 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)))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1/6 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) x))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))) x)) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 1 binary64)))))
(+.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 x (.f64 x #s(literal -1/40320 binary64))))))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)))) (-.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)) #s(literal 4 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64))))))
(/.f64 (.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)))))))) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (-.f64 (.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))) (.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)))) (.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) (-.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64))))))
(/.f64 #s(literal 1 binary64) (/.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 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8640 binary64) (.f64 x (.f64 x (+.f64 #s(literal 29/7257600 binary64) (.f64 (.f64 x x) #s(literal -1/14515200 binary64)))))))))))))
(/.f64 #s(literal 1 binary64) (/.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 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (.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 #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 (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (+.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)))))) (.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)))))))))) (.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))))))))) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
(/.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 #s(literal -1 binary64) (.f64 x x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) (+.f64 (cos.f64 x) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 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 #s(literal 1 binary64) x) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) x)) (/.f64 #s(literal 1 binary64) x))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (.f64 x x)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 (.f64 x (.f64 x x)) x))
(/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x (*.f64 x x)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (-.f64 x (*.f64 x (cos.f64 x))) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) x)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x))) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 x (*.f64 x (cos.f64 x))))))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))) x))) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x x)) (*.f64 x x))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x))))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (neg.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x))))) (.f64 x (.f64 x (.f64 x x))))
(/.f64 (-.f64 (.f64 x x) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))) (.f64 x (.f64 x (.f64 x x))))
(/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (cos.f64 x))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)))
(.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 (*.f64 x x) (sin.f64 x)))
(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.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 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) #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 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (cos.f64 x)))

Outputs

(+.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 x (*.f64 x #s(literal -1/40320 binary64))))))))

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

Calls

2 calls:

16.0ms	x
14.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Results

Accuracy	Segments	Branch
99.8%	2	`x`
99.7%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes23.0ms (0.2%)

Counts

28 → 2

Calls

Call 1

Inputs
#s(literal 1/2 binary64)
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) x))
(+.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 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (*.f64 x x))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal 1/6 binary64))))
(/.f64 (/.f64 (-.f64 #s(literal 6 binary64) (/.f64 #s(literal 72 binary64) (*.f64 x x))) 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)))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1/6 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) x))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))) x)) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 1 binary64)))))
(+.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 x (.f64 x #s(literal -1/40320 binary64))))))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)))) (-.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)) #s(literal 4 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64))))))
(/.f64 (.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)))))))) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (-.f64 (.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))) (.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)))) (.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) (-.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64))))))
(/.f64 #s(literal 1 binary64) (/.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 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8640 binary64) (.f64 x (.f64 x (+.f64 #s(literal 29/7257600 binary64) (.f64 (.f64 x x) #s(literal -1/14515200 binary64)))))))))))))
(/.f64 #s(literal 1 binary64) (/.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 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (.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 #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 (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (+.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)))))) (.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)))))))))) (.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))))))))) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Outputs

(+.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 x (*.f64 x #s(literal -1/40320 binary64))))))))

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

Calls

2 calls:

12.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
8.0ms	x

Results

Accuracy	Segments	Branch
99.6%	3	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`
99.6%	2	`x`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes9.0ms (0.1%)

Counts

27 → 1

Calls

Call 1

Inputs
#s(literal 1/2 binary64)
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) x))
(+.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 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (*.f64 x x))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal 1/6 binary64))))
(/.f64 (/.f64 (-.f64 #s(literal 6 binary64) (/.f64 #s(literal 72 binary64) (*.f64 x x))) 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)))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1/6 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) x))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))) x)) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 1 binary64)))))
(+.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 x (.f64 x #s(literal -1/40320 binary64))))))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)))) (-.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)) #s(literal 4 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64))))))
(/.f64 (.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)))))))) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (-.f64 (.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))) (.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/36 binary64)))) (.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) (-.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64))))))
(/.f64 #s(literal 1 binary64) (/.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 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8640 binary64) (.f64 x (.f64 x (+.f64 #s(literal 29/7257600 binary64) (.f64 (.f64 x x) #s(literal -1/14515200 binary64)))))))))))))
(/.f64 #s(literal 1 binary64) (/.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 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (.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 #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 (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (+.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)))))) (.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)))))))))) (.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))))))))) (/.f64 x (/.f64 #s(literal 1 binary64) x)))

Outputs
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
80.1%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Counts

7 → 2

Calls

Call 1

Inputs
#s(literal 1/2 binary64)
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) x))
(+.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 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (*.f64 x x))

Outputs
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
(/.f64 #s(literal 6 binary64) (*.f64 x x))

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
80.1%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

3 → 2

Calls

Call 1

Inputs
#s(literal 1/2 binary64)
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) x))

Outputs
#s(literal 1/2 binary64)
(/.f64 #s(literal 6 binary64) (*.f64 x x))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
79.5%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1/2 binary64)

Outputs
#s(literal 1/2 binary64)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
51.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch11.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.019585056554983014	0.49461092339813195

Results

6.0ms

112×

valid

Compiler

Compiled 230 to 156 computations (32.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-sub: 1.0ms (27.8% of total)

ival-div: 1.0ms (27.8% of total)

ival-cos: 1.0ms (27.8% of total)

ival-mult: 1.0ms (27.8% of total)

const: 0.0ms (0% of total)

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

bsearch11.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.019585056554983014	0.49461092339813195

Results

6.0ms

112×

valid

Compiler

Compiled 230 to 156 computations (32.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-sub: 1.0ms (27.8% of total)

ival-div: 1.0ms (27.8% of total)

ival-cos: 1.0ms (27.8% of total)

ival-mult: 1.0ms (27.8% 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	0.49461092339813195	118.66005651337666

Results

8.0ms

112×

valid

Compiler

Compiled 125 to 93 computations (25.6% saved)

Precisions

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

ival-cos: 3.0ms (51.9% of total)

ival-sub: 1.0ms (17.3% of total)

ival-div: 1.0ms (17.3% of total)

ival-mult: 1.0ms (17.3% of total)

const: 0.0ms (0% of total)

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

bsearch13.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	0.49461092339813195	118.66005651337666

Results

8.0ms

112×

valid

Compiler

Compiled 83 to 65 computations (21.7% saved)

Precisions

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

ival-cos: 4.0ms (67.6% of total)

ival-sub: 1.0ms (16.9% of total)

ival-div: 1.0ms (16.9% of total)

ival-mult: 1.0ms (16.9% of total)

const: 0.0ms (0% of total)

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

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
14×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	98
1	54	98
2	58	98
3	60	98
4	61	98

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal 3242591731706757/36028797018963968 binary64)) (+.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 x (.f64 x #s(literal -1/40320 binary64)))))))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x))
(if (<=.f64 x #s(literal 3242591731706757/36028797018963968 binary64)) (+.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 x (.f64 x #s(literal -1/40320 binary64)))))))) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))
(if (<=.f64 x #s(literal 3715469692580659/1125899906842624 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x))) (/.f64 #s(literal 6 binary64) (*.f64 x x)))
(if (<=.f64 x #s(literal 7656119366529843/2251799813685248 binary64)) #s(literal 1/2 binary64) (/.f64 #s(literal 6 binary64) (*.f64 x x)))
#s(literal 1/2 binary64)

Outputs
(if (<=.f64 x #s(literal 3242591731706757/36028797018963968 binary64)) (+.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 x (.f64 x #s(literal -1/40320 binary64)))))))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x))
(if (<=.f64 x #s(literal 3242591731706757/36028797018963968 binary64)) (+.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 x (.f64 x #s(literal -1/40320 binary64)))))))) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))
(if (<=.f64 x #s(literal 3715469692580659/1125899906842624 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x))) (/.f64 #s(literal 6 binary64) (*.f64 x x)))
(if (<=.f64 x #s(literal 3715469692580659/1125899906842624 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64))) (/.f64 #s(literal 6 binary64) (*.f64 x x)))
(if (<=.f64 x #s(literal 7656119366529843/2251799813685248 binary64)) #s(literal 1/2 binary64) (/.f64 #s(literal 6 binary64) (*.f64 x x)))
#s(literal 1/2 binary64)

soundness1.3s (13.3%)

Rules

3760×	`-lowering-.f32`
3760×	`-lowering-.f64`
3684×	`+-lowering-+.f64`
3684×	`+-lowering-+.f32`
3562×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
1	36	17
2	268	17
3	2905	17
0	8648	17
0	42	278
1	113	266
2	315	266
3	818	266
4	1931	266
5	2941	266
6	3513	266
7	4835	266
0	8655	266
0	221	2189
1	599	2102
2	1719	2066
3	5366	2066
0	8401	2066
0	135	1865
1	392	1800
2	1133	1774
3	3674	1763
4	6629	1755
0	8160	1755

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

Compiler

Compiled 205 to 115 computations (43.9% saved)

preprocess37.0ms (0.4%)

Compiler: Compiled 280 to 130 computations (53.6% saved)

analyze2.0ms (0%)

sample2.1s (21.8%)

preprocess111.0ms (1.2%)

explain160.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify58.0ms (0.6%)

localize82.0ms (0.9%)

series3.0ms (0%)

rewrite324.0ms (3.4%)

simplify197.0ms (2%)

eval60.0ms (0.6%)

prune93.0ms (1%)

simplify164.0ms (1.7%)

localize292.0ms (3%)

series16.0ms (0.2%)

rewrite448.0ms (4.7%)

simplify352.0ms (3.6%)

eval211.0ms (2.2%)

prune172.0ms (1.8%)

simplify165.0ms (1.7%)

localize327.0ms (3.4%)

series24.0ms (0.3%)

rewrite451.0ms (4.7%)

simplify254.0ms (2.6%)

eval192.0ms (2%)

prune138.0ms (1.4%)

simplify185.0ms (1.9%)

localize314.0ms (3.3%)

series47.0ms (0.5%)

rewrite476.0ms (4.9%)

simplify249.0ms (2.6%)

eval282.0ms (2.9%)

prune228.0ms (2.4%)

regimes35.0ms (0.4%)

regimes23.0ms (0.2%)

regimes9.0ms (0.1%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes3.0ms (0%)

bsearch11.0ms (0.1%)

bsearch11.0ms (0.1%)

bsearch14.0ms (0.1%)

bsearch13.0ms (0.1%)

simplify14.0ms (0.1%)

soundness1.3s (13.3%)

preprocess37.0ms (0.4%)

end0.0ms (0%)

Profiling