Metrics for Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, A

analyze290.0ms (3.1%)

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
0%	0%	100%	0%	0%	0%	0%	2
25%	25%	75%	0%	0%	0%	0%	3
37.5%	37.5%	62.5%	0%	0%	0%	0%	4
43.8%	43.7%	56.2%	0%	0%	0%	0%	5
46.9%	46.9%	53.1%	0%	0%	0%	0%	6
48.4%	48.4%	51.5%	0%	0%	0%	0%	7
49.2%	49.2%	50.8%	0%	0%	0%	0%	8
49.6%	49.6%	50.4%	0%	0%	0%	0%	9
49.8%	49.8%	50.2%	0%	0%	0%	0%	10
49.9%	49.9%	50.1%	0%	0%	0%	0%	11
50%	49.9%	50%	0%	0%	0%	0%	12

Compiler

Compiled 18 to 12 computations (33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 130.0ms

ival-mult: 70.0ms (53.9% of total)

ival-div: 28.0ms (21.6% of total)

ival-sin: 27.0ms (20.8% of total)

const: 4.0ms (3.1% of total)

backward-pass: 1.0ms (0.8% of total)

sample1.3s (13.9%)

Results

1.0s

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 787.0ms

ival-sin: 419.0ms (53.2% of total)

ival-mult: 177.0ms (22.5% of total)

ival-div: 167.0ms (21.2% of total)

const: 21.0ms (2.7% of total)

backward-pass: 3.0ms (0.4% of total)

Bogosity

preprocess74.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

934×	`fnmadd-define`
792×	`fma-define`
662×	`fmsub-define`
634×	`fnmsub-define`
598×	`times-frac`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	45
1	46	31
2	114	30
3	329	30
4	1051	30
5	2218	30
6	2912	30
7	3198	30
8	3411	30
9	3475	30
10	3563	30
11	4269	30
12	4301	30
0	12	14
1	19	10
2	30	10
3	39	10
4	42	10
0	42	10

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x))

Outputs

(/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x))

(*.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) (*.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 8/3 binary64) (sin.f64 x))))

Call 2

Inputs

(/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x))

(/ (* (* (/ 8 3) (sin (* (neg x) 1/2))) (sin (* (neg x) 1/2))) (sin (neg x)))

(neg (/ (* (* (/ 8 3) (sin (* (neg x) 1/2))) (sin (* (neg x) 1/2))) (sin (neg x))))

Outputs
(/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x))
(* (square (sin (* x 1/2))) (/ 8/3 (sin x)))
(/ (* (* (/ 8 3) (sin (* (neg x) 1/2))) (sin (* (neg x) 1/2))) (sin (neg x)))
(* (square (sin (* x 1/2))) (/ -8/3 (sin x)))
(neg (/ (* (* (/ 8 3) (sin (* (neg x) 1/2))) (sin (* (neg x) 1/2))) (sin (neg x))))
(* (square (sin (* x 1/2))) (/ 8/3 (sin x)))

Symmetry

(negabs x)

explain150.0ms (1.6%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
49	0	-	3	(6.343471056047872e-159)	`(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))`
0	0	-	0	-	`x`
0	0	-	0	-	`#s(literal 1/2 binary64)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`(/.f64 #s(literal 8 binary64) #s(literal 3 binary64))`
0	0	-	0	-	`(.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64))))`
0	0	-	0	-	`(*.f64 x #s(literal 1/2 binary64))`
0	0	-	0	-	`#s(literal 3 binary64)`
0	147	(1.069620655123243e+272)	0	-	`(sin.f64 (*.f64 x #s(literal 1/2 binary64)))`
0	0	-	0	-	`#s(literal 8 binary64)`
0	0	-	0	-	`(.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64))))`

Results

98.0ms

512×

valid

Compiler

Compiled 127 to 35 computations (72.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-sin: 25.0ms (51.1% of total)

ival-mult: 14.0ms (28.6% of total)

ival-div: 9.0ms (18.4% of total)

const: 1.0ms (2% of total)

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

eval0.0ms (0%)

Compiler: Compiled 15 to 9 computations (40% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	82.0%	(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))
▶	99.2%	(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 8/3 binary64) (sin.f64 x))))

Status

Accuracy

Program

▶

82.0%

(/.f64 (*.f64 (*.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (*.f64 x #s(literal 1/2 binary64)))) (sin.f64 (*.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))

▶

99.2%

(*.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) (*.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 8/3 binary64) (sin.f64 x))))

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
✓	cost-diff	0	(.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
✓	cost-diff	0	(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))
✓	cost-diff	128	(/.f64 #s(literal 8 binary64) #s(literal 3 binary64))
✓	cost-diff	0	(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 8/3 binary64) (sin.f64 x)))
✓	cost-diff	0	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	0	(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	0	(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 8/3 binary64) (sin.f64 x))))

Rules

46×	`-lowering-.f32`
46×	`-lowering-.f64`
18×	`*-commutative`
10×	`/-lowering-/.f32`
10×	`/-lowering-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	84
1	27	72
2	37	72
3	43	72
0	43	72

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (sin (* x 1/2)) (* (sin (* x 1/2)) (/ 8/3 (sin x))))
(sin (* x 1/2))
(* x 1/2)
x
1/2
(* (sin (* x 1/2)) (/ 8/3 (sin x)))
(/ 8/3 (sin x))
8/3
(sin x)
(/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x))
(* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2)))
(* (/ 8 3) (sin (* x 1/2)))
(/ 8 3)
8
3
(sin (* x 1/2))
(* x 1/2)
x
1/2
(sin x)

Outputs
(* (sin (* x 1/2)) (* (sin (* x 1/2)) (/ 8/3 (sin x))))
(/.f64 (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 8/3 binary64))) (sin.f64 x))
(sin (* x 1/2))
(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
(* x 1/2)
(*.f64 x #s(literal 1/2 binary64))
x
1/2
#s(literal 1/2 binary64)
(* (sin (* x 1/2)) (/ 8/3 (sin x)))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 8/3 binary64) (sin.f64 x)))
(/ 8/3 (sin x))
(/.f64 #s(literal 8/3 binary64) (sin.f64 x))
8/3
#s(literal 8/3 binary64)
(sin x)
(sin.f64 x)
(/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x))
(/.f64 (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 8/3 binary64))) (sin.f64 x))
(* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2)))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 8/3 binary64)))
(* (/ 8 3) (sin (* x 1/2)))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 8/3 binary64))
(/ 8 3)
#s(literal 8/3 binary64)
8
#s(literal 8 binary64)
3
#s(literal 3 binary64)
(sin (* x 1/2))
(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
(* x 1/2)
(*.f64 x #s(literal 1/2 binary64))
x
1/2
#s(literal 1/2 binary64)
(sin x)
(sin.f64 x)

localize99.0ms (1%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	accuracy	99.6%	(.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
✓	accuracy	99.3%	(.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
✓	accuracy	82.4%	(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))
✓	accuracy	100.0%	(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	accuracy	99.5%	(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 8/3 binary64) (sin.f64 x))))
✓	accuracy	99.4%	(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 8/3 binary64) (sin.f64 x)))
✓	accuracy	99.4%	(/.f64 #s(literal 8/3 binary64) (sin.f64 x))

Results

76.0ms

256×

valid

Compiler

Compiled 94 to 16 computations (83% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-sin: 13.0ms (38.2% of total)

ival-mult: 8.0ms (23.5% of total)

...c/correct-round.rkt:119:19: 7.0ms (20.6% of total)

ival-div: 5.0ms (14.7% of total)

const: 1.0ms (2.9% of total)

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

series15.0ms (0.2%)

Counts

9 → 96

Calls

Call 1

Inputs
#<alt (* (sin (* x 1/2)) (* (sin (* x 1/2)) (/ 8/3 (sin x))))>
#<alt (sin (* x 1/2))>
#<alt (* x 1/2)>
#<alt (* (sin (* x 1/2)) (/ 8/3 (sin x)))>
#<alt (/ 8 3)>
#<alt (/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x))>
#<alt (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2)))>
#<alt (* (/ 8 3) (sin (* x 1/2)))>
#<alt (/ 8/3 (sin x))>

Outputs
#<alt (* 2/3 x)>
#<alt (* x (+ 2/3 (* 1/18 (pow x 2))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/48 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 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 4/3>
#<alt (+ 4/3 (* 1/6 (pow x 2)))>
#<alt (+ 4/3 (* (pow x 2) (+ 1/6 (* 5/288 (pow x 2)))))>
#<alt (+ 4/3 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 5/288 (* 61/34560 (pow x 2)))))))>
#<alt (* 8/3 (/ (sin (* 1/2 x)) (sin x)))>
#<alt (* 8/3 (/ (sin (* 1/2 x)) (sin x)))>
#<alt (* 8/3 (/ (sin (* 1/2 x)) (sin x)))>
#<alt (* 8/3 (/ (sin (* 1/2 x)) (sin x)))>
#<alt (* 8/3 (/ (sin (* 1/2 x)) (sin x)))>
#<alt (* 8/3 (/ (sin (* 1/2 x)) (sin x)))>
#<alt (* 8/3 (/ (sin (* 1/2 x)) (sin x)))>
#<alt (* 8/3 (/ (sin (* 1/2 x)) (sin x)))>
#<alt (* 2/3 x)>
#<alt (* x (+ 2/3 (* 1/18 (pow x 2))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 2/3 (pow x 2))>
#<alt (* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))>
#<alt (* (pow x 2) (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))>
#<alt (* (pow x 2) (+ 2/3 (* (pow x 2) (- (* (pow x 2) (+ 1/540 (* -1/30240 (pow x 2)))) 1/18))))>
#<alt (* 8/3 (pow (sin (* 1/2 x)) 2))>
#<alt (* 8/3 (pow (sin (* 1/2 x)) 2))>
#<alt (* 8/3 (pow (sin (* 1/2 x)) 2))>
#<alt (* 8/3 (pow (sin (* 1/2 x)) 2))>
#<alt (* 8/3 (pow (sin (* 1/2 x)) 2))>
#<alt (* 8/3 (pow (sin (* 1/2 x)) 2))>
#<alt (* 8/3 (pow (sin (* 1/2 x)) 2))>
#<alt (* 8/3 (pow (sin (* 1/2 x)) 2))>
#<alt (* 4/3 x)>
#<alt (* x (+ 4/3 (* -1/18 (pow x 2))))>
#<alt (* x (+ 4/3 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/18))))>
#<alt (* x (+ 4/3 (* (pow x 2) (- (* (pow x 2) (+ 1/1440 (* -1/241920 (pow x 2)))) 1/18))))>
#<alt (* 8/3 (sin (* 1/2 x)))>
#<alt (* 8/3 (sin (* 1/2 x)))>
#<alt (* 8/3 (sin (* 1/2 x)))>
#<alt (* 8/3 (sin (* 1/2 x)))>
#<alt (* 8/3 (sin (* 1/2 x)))>
#<alt (* 8/3 (sin (* 1/2 x)))>
#<alt (* 8/3 (sin (* 1/2 x)))>
#<alt (* 8/3 (sin (* 1/2 x)))>
#<alt (/ 8/3 x)>
#<alt (/ (+ 8/3 (* 4/9 (pow x 2))) x)>
#<alt (/ (+ 8/3 (* (pow x 2) (+ 4/9 (* 7/135 (pow x 2))))) x)>
#<alt (/ (+ 8/3 (* (pow x 2) (+ 4/9 (* (pow x 2) (+ 7/135 (* 31/5670 (pow x 2))))))) x)>
#<alt (/ 8/3 (sin x))>
#<alt (/ 8/3 (sin x))>
#<alt (/ 8/3 (sin x))>
#<alt (/ 8/3 (sin x))>
#<alt (/ 8/3 (sin x))>
#<alt (/ 8/3 (sin x))>
#<alt (/ 8/3 (sin x))>
#<alt (/ 8/3 (sin x))>

Calls

24 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	(* (sin (* x 1/2)) (* (sin (* x 1/2)) (/ 8/3 (sin x))))
1.0ms	x	@	0	(/ 8/3 (sin x))
1.0ms	x	@	inf	(* (sin (* x 1/2)) (* (sin (* x 1/2)) (/ 8/3 (sin x))))
1.0ms	x	@	inf	(* x 1/2)
1.0ms	x	@	-inf	(* (sin (* x 1/2)) (/ 8/3 (sin x)))

rewrite385.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3094×	`-lowering-.f32`
3094×	`-lowering-.f64`
2474×	`/-lowering-/.f32`
2474×	`/-lowering-/.f64`
1490×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	66
1	41	54
2	157	54
3	827	51
4	5954	51
0	8053	51

Stop Event

1×	iter limit
1×	node limit

Counts

9 → 866

Calls

Call 1

Inputs
(* (sin (* x 1/2)) (* (sin (* x 1/2)) (/ 8/3 (sin x))))
(sin (* x 1/2))
(* x 1/2)
(* (sin (* x 1/2)) (/ 8/3 (sin x)))
(/ 8 3)
(/ (* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2))) (sin x))
(* (* (/ 8 3) (sin (* x 1/2))) (sin (* x 1/2)))
(* (/ 8 3) (sin (* x 1/2)))
(/ 8/3 (sin x))

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

simplify220.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

3050×	`+-lowering-+.f64`
3050×	`+-lowering-+.f32`
2254×	`-lowering-.f32`
2254×	`-lowering-.f64`
1984×	`sum4-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	126	790
1	355	684
2	1041	684
3	2764	684
4	4237	684
5	7294	684
0	8029	684

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

Inputs
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 1/2 x)
(* x (+ 1/2 (* -1/48 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 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)
4/3
(+ 4/3 (* 1/6 (pow x 2)))
(+ 4/3 (* (pow x 2) (+ 1/6 (* 5/288 (pow x 2)))))
(+ 4/3 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 5/288 (* 61/34560 (pow x 2)))))))
(* 8/3 (/ (sin (* 1/2 x)) (sin x)))
(* 8/3 (/ (sin (* 1/2 x)) (sin x)))
(* 8/3 (/ (sin (* 1/2 x)) (sin x)))
(* 8/3 (/ (sin (* 1/2 x)) (sin x)))
(* 8/3 (/ (sin (* 1/2 x)) (sin x)))
(* 8/3 (/ (sin (* 1/2 x)) (sin x)))
(* 8/3 (/ (sin (* 1/2 x)) (sin x)))
(* 8/3 (/ (sin (* 1/2 x)) (sin x)))
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 2/3 (pow x 2))
(* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* (pow x 2) (+ 1/540 (* -1/30240 (pow x 2)))) 1/18))))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 4/3 x)
(* x (+ 4/3 (* -1/18 (pow x 2))))
(* x (+ 4/3 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/18))))
(* x (+ 4/3 (* (pow x 2) (- (* (pow x 2) (+ 1/1440 (* -1/241920 (pow x 2)))) 1/18))))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(/ 8/3 x)
(/ (+ 8/3 (* 4/9 (pow x 2))) x)
(/ (+ 8/3 (* (pow x 2) (+ 4/9 (* 7/135 (pow x 2))))) x)
(/ (+ 8/3 (* (pow x 2) (+ 4/9 (* (pow x 2) (+ 7/135 (* 31/5670 (pow x 2))))))) x)
(/ 8/3 (sin x))
(/ 8/3 (sin x))
(/ 8/3 (sin x))
(/ 8/3 (sin x))
(/ 8/3 (sin x))
(/ 8/3 (sin x))
(/ 8/3 (sin x))
(/ 8/3 (sin x))

Outputs
(* 2/3 x)
(*.f64 #s(literal 2/3 binary64) x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 1/18 binary64)))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/18 binary64) (.f64 (*.f64 x x) #s(literal 1/180 binary64)))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/180 binary64) (.f64 (*.f64 x x) #s(literal 17/30240 binary64)))))))))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/48 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal -1/48 binary64)))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/48 binary64) (.f64 x (*.f64 x #s(literal 1/3840 binary64)))))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3840 binary64) (.f64 (*.f64 x x) #s(literal -1/645120 binary64))))))))
(sin (* 1/2 x))
(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
(sin (* 1/2 x))
(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
(sin (* 1/2 x))
(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
(sin (* 1/2 x))
(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
(sin (* 1/2 x))
(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
(sin (* 1/2 x))
(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
(sin (* 1/2 x))
(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
(sin (* 1/2 x))
(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
4/3
#s(literal 4/3 binary64)
(+ 4/3 (* 1/6 (pow x 2)))
(+.f64 #s(literal 4/3 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(+ 4/3 (* (pow x 2) (+ 1/6 (* 5/288 (pow x 2)))))
(+.f64 #s(literal 4/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) #s(literal 5/288 binary64))))))
(+ 4/3 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 5/288 (* 61/34560 (pow x 2)))))))
(+.f64 #s(literal 4/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64)))))))
(* 8/3 (/ (sin (* 1/2 x)) (sin x)))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 8/3 binary64) (sin.f64 x)))
(* 8/3 (/ (sin (* 1/2 x)) (sin x)))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 8/3 binary64) (sin.f64 x)))
(* 8/3 (/ (sin (* 1/2 x)) (sin x)))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 8/3 binary64) (sin.f64 x)))
(* 8/3 (/ (sin (* 1/2 x)) (sin x)))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 8/3 binary64) (sin.f64 x)))
(* 8/3 (/ (sin (* 1/2 x)) (sin x)))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 8/3 binary64) (sin.f64 x)))
(* 8/3 (/ (sin (* 1/2 x)) (sin x)))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 8/3 binary64) (sin.f64 x)))
(* 8/3 (/ (sin (* 1/2 x)) (sin x)))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 8/3 binary64) (sin.f64 x)))
(* 8/3 (/ (sin (* 1/2 x)) (sin x)))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 8/3 binary64) (sin.f64 x)))
(* 2/3 x)
(*.f64 #s(literal 2/3 binary64) x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 1/18 binary64)))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/18 binary64) (.f64 (*.f64 x x) #s(literal 1/180 binary64)))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/180 binary64) (.f64 (*.f64 x x) #s(literal 17/30240 binary64)))))))))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 2/3 (pow x 2))
(.f64 #s(literal 2/3 binary64) (.f64 x x))
(* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) #s(literal -1/18 binary64)))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))
(.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/18 binary64) (.f64 x (.f64 x #s(literal 1/540 binary64))))))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* (pow x 2) (+ 1/540 (* -1/30240 (pow x 2)))) 1/18))))
(.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/18 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/540 binary64) (.f64 (.f64 x x) #s(literal -1/30240 binary64)))))))))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 4/3 x)
(*.f64 x #s(literal 4/3 binary64))
(* x (+ 4/3 (* -1/18 (pow x 2))))
(.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 (*.f64 x x) #s(literal -1/18 binary64))))
(* x (+ 4/3 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/18))))
(.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/18 binary64) (.f64 (*.f64 x x) #s(literal 1/1440 binary64))))))
(* x (+ 4/3 (* (pow x 2) (- (* (pow x 2) (+ 1/1440 (* -1/241920 (pow x 2)))) 1/18))))
(.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/18 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/1440 binary64) (.f64 (*.f64 x x) #s(literal -1/241920 binary64))))))))
(* 8/3 (sin (* 1/2 x)))
(.f64 #s(literal 8/3 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(* 8/3 (sin (* 1/2 x)))
(.f64 #s(literal 8/3 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(* 8/3 (sin (* 1/2 x)))
(.f64 #s(literal 8/3 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(* 8/3 (sin (* 1/2 x)))
(.f64 #s(literal 8/3 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(* 8/3 (sin (* 1/2 x)))
(.f64 #s(literal 8/3 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(* 8/3 (sin (* 1/2 x)))
(.f64 #s(literal 8/3 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(* 8/3 (sin (* 1/2 x)))
(.f64 #s(literal 8/3 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(* 8/3 (sin (* 1/2 x)))
(.f64 #s(literal 8/3 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64))))
(/ 8/3 x)
(/.f64 #s(literal 8/3 binary64) x)
(/ (+ 8/3 (* 4/9 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 8/3 binary64) (.f64 x (.f64 x #s(literal 4/9 binary64)))) x)
(/ (+ 8/3 (* (pow x 2) (+ 4/9 (* 7/135 (pow x 2))))) x)
(/.f64 (+.f64 #s(literal 8/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 4/9 binary64) (.f64 x (.f64 x #s(literal 7/135 binary64))))))) x)
(/ (+ 8/3 (* (pow x 2) (+ 4/9 (* (pow x 2) (+ 7/135 (* 31/5670 (pow x 2))))))) x)
(/.f64 (+.f64 #s(literal 8/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 4/9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 7/135 binary64) (.f64 (.f64 x x) #s(literal 31/5670 binary64))))))) x)
(/ 8/3 (sin x))
(/.f64 #s(literal 8/3 binary64) (sin.f64 x))
(/ 8/3 (sin x))
(/.f64 #s(literal 8/3 binary64) (sin.f64 x))
(/ 8/3 (sin x))
(/.f64 #s(literal 8/3 binary64) (sin.f64 x))
(/ 8/3 (sin x))
(/.f64 #s(literal 8/3 binary64) (sin.f64 x))
(/ 8/3 (sin x))
(/.f64 #s(literal 8/3 binary64) (sin.f64 x))
(/ 8/3 (sin x))
(/.f64 #s(literal 8/3 binary64) (sin.f64 x))
(/ 8/3 (sin x))
(/.f64 #s(literal 8/3 binary64) (sin.f64 x))
(/ 8/3 (sin x))
(/.f64 #s(literal 8/3 binary64) (sin.f64 x))

eval239.0ms (2.5%)

Compiler: Compiled 22381 to 1575 computations (93% saved)

prune238.0ms (2.5%)

Pruning

39 alts after pruning (38 fresh and 1 done)

	Pruned	Kept	Total
New	1050	38	1088
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	1051	39	1090

Accuracy

100.0%

Counts

1090 → 39

Alt Table

Click to see full alt table

Status	Accuracy	Program
	60.9%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) #s(literal 3/4 binary64))
	60.8%	(/.f64 (/.f64 #s(literal 8/3 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))) (sin.f64 x))
	60.8%	(/.f64 (/.f64 #s(literal 8/3 binary64) (sin.f64 x)) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
	60.9%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/8 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))))) (sin.f64 x))
	60.6%	(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))) (.f64 (.f64 (sin.f64 x) #s(literal 3/4 binary64)) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
	60.8%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (sin.f64 x) #s(literal 3/4 binary64)))
	60.6%	(/.f64 (+.f64 #s(literal 4/3 binary64) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) #s(literal 8/3 binary64))) (sin.f64 x))
	60.8%	(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))) #s(literal -3/4 binary64))
	60.8%	(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)) (sin.f64 x))
	82.0%	(/.f64 (.f64 (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 8/3 binary64)) (sin.f64 (*.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))
	25.0%	(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/18 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/540 binary64) (.f64 (.f64 x x) #s(literal -1/30240 binary64))))))))) (sin.f64 x))
	26.5%	(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/18 binary64) (.f64 x (.f64 x #s(literal 1/540 binary64)))))))) (sin.f64 x))
	24.7%	(/.f64 (.f64 x (.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) #s(literal -1/18 binary64))))) (sin.f64 x))
▶	82.0%	(/.f64 (.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))) (sin.f64 x))
	26.2%	(/.f64 (.f64 #s(literal 2/3 binary64) (.f64 x x)) (sin.f64 x))
	99.3%	(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (/.f64 (sin.f64 x) #s(literal 8/3 binary64)) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
	60.8%	(/.f64 #s(literal 8/3 binary64) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))))
▶	60.8%	(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 x) #s(literal 3/4 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
	60.8%	(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal -3/4 binary64)))
	60.7%	(-.f64 (/.f64 #s(literal 4/3 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (/.f64 #s(literal 4/3 binary64) (sin.f64 x))))
	60.8%	(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) #s(literal 4/3 binary64))
	60.8%	(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 3/8 binary64)) (/.f64 #s(literal 1/2 binary64) (sin.f64 x)))
▶	99.4%	(*.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/8 binary64)))
	81.9%	(*.f64 (/.f64 #s(literal 8/3 binary64) (sin.f64 x)) (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))))
	82.1%	(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/8 binary64)) (/.f64 #s(literal 1 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))))
	60.7%	(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 4/3 binary64) (sin.f64 x)))
	42.5%	(.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 8/3 binary64) (sin.f64 x))))
▶	42.8%	(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 4/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64))))))))
	42.8%	(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 4/3 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))))
	99.1%	(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (*.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x)) #s(literal 8/3 binary64)))
✓	99.2%	(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 8/3 binary64) (sin.f64 x))))
	71.0%	(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (*.f64 (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) #s(literal 3/8 binary64)))))
	47.2%	(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 4/3 binary64))
	42.9%	(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/180 binary64) (.f64 (*.f64 x x) #s(literal 17/30240 binary64)))))))))
	42.8%	(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/18 binary64) (.f64 (*.f64 x x) #s(literal 1/180 binary64)))))))
	42.8%	(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 1/18 binary64)))))
	82.0%	(.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
▶	42.8%	(*.f64 #s(literal 2/3 binary64) x)
	60.8%	(.f64 #s(literal -8/3 binary64) (pow.f64 (.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal -2 binary64)) #s(literal -1 binary64)))

Compiler

Compiled 1085 to 781 computations (28% saved)

simplify204.0ms (2.1%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	0	(pow.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))
✓	cost-diff	0	(.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 (.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))) (sin.f64 x))
✓	cost-diff	0	(sin.f64 x)
✓	cost-diff	0	(*.f64 (sin.f64 x) #s(literal 3/4 binary64))
✓	cost-diff	0	(/.f64 (*.f64 (sin.f64 x) #s(literal 3/4 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
✓	cost-diff	6656	(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 x) #s(literal 3/4 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
✓	cost-diff	0	(+.f64 #s(literal 4/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64)))))))
✓	cost-diff	0	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	0	(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	0	(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 4/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64))))))))
✓	cost-diff	0	(*.f64 #s(literal 2/3 binary64) x)
✓	cost-diff	0	(/.f64 x #s(literal 2 binary64))
✓	cost-diff	0	(sin.f64 (/.f64 x #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x))
✓	cost-diff	0	(*.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/8 binary64)))

Rules

3394×	`fma-lowering-fma.f32`
3394×	`fma-lowering-fma.f64`
3016×	`fma-define`
2078×	`sum3-define`
1594×	`-lowering-.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	212
1	90	196
2	270	192
3	759	189
4	1876	189
5	2791	189
6	3193	189
7	3708	189
8	5828	189
9	6511	189
0	8438	189

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (/ (sin (/ x 2)) (sin x)) (/ (sin (/ x 2)) 3/8))
(/ (sin (/ x 2)) (sin x))
(sin (/ x 2))
(/ x 2)
x
2
(sin x)
(/ (sin (/ x 2)) 3/8)
3/8
(* 2/3 x)
2/3
x
(* (sin (* x 1/2)) (+ 4/3 (* (* x x) (+ 1/6 (* (* x x) (+ 5/288 (* (* x x) 61/34560)))))))
(sin (* x 1/2))
(* x 1/2)
x
1/2
(+ 4/3 (* (* x x) (+ 1/6 (* (* x x) (+ 5/288 (* (* x x) 61/34560))))))
4/3
(* (* x x) (+ 1/6 (* (* x x) (+ 5/288 (* (* x x) 61/34560)))))
(* x x)
(+ 1/6 (* (* x x) (+ 5/288 (* (* x x) 61/34560))))
1/6
(* (* x x) (+ 5/288 (* (* x x) 61/34560)))
(+ 5/288 (* (* x x) 61/34560))
5/288
(* (* x x) 61/34560)
61/34560
(/ 1 (/ (* (sin x) 3/4) (- 1 (cos x))))
1
(/ (* (sin x) 3/4) (- 1 (cos x)))
(* (sin x) 3/4)
(sin x)
x
3/4
(- 1 (cos x))
(cos x)
(/ (* 8/3 (pow (sin (* x 1/2)) 2)) (sin x))
(* 8/3 (pow (sin (* x 1/2)) 2))
8/3
(pow (sin (* x 1/2)) 2)
(sin (* x 1/2))
(* x 1/2)
x
1/2
2
(sin x)

Outputs
(* (/ (sin (/ x 2)) (sin x)) (/ (sin (/ x 2)) 3/8))
(.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (.f64 (sin.f64 x) #s(literal 3/8 binary64))))
(/ (sin (/ x 2)) (sin x))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x))
(sin (/ x 2))
(sin.f64 (/.f64 x #s(literal 2 binary64)))
(/ x 2)
(/.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
(sin x)
(sin.f64 x)
(/ (sin (/ x 2)) 3/8)
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/8 binary64))
3/8
#s(literal 3/8 binary64)
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
2/3
#s(literal 2/3 binary64)
x
(* (sin (* x 1/2)) (+ 4/3 (* (* x x) (+ 1/6 (* (* x x) (+ 5/288 (* (* x x) 61/34560)))))))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 4/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64))))))))
(sin (* x 1/2))
(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
(* x 1/2)
(*.f64 x #s(literal 1/2 binary64))
x
1/2
#s(literal 1/2 binary64)
(+ 4/3 (* (* x x) (+ 1/6 (* (* x x) (+ 5/288 (* (* x x) 61/34560))))))
(+.f64 #s(literal 4/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64)))))))
4/3
#s(literal 4/3 binary64)
(* (* x x) (+ 1/6 (* (* x x) (+ 5/288 (* (* x x) 61/34560)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64))))))
(* x x)
(*.f64 x x)
(+ 1/6 (* (* x x) (+ 5/288 (* (* x x) 61/34560))))
(+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64)))))
1/6
#s(literal 1/6 binary64)
(* (* x x) (+ 5/288 (* (* x x) 61/34560)))
(.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64))))
(+ 5/288 (* (* x x) 61/34560))
(+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64)))
5/288
#s(literal 5/288 binary64)
(* (* x x) 61/34560)
(.f64 (.f64 x x) #s(literal 61/34560 binary64))
61/34560
#s(literal 61/34560 binary64)
(/ 1 (/ (* (sin x) 3/4) (- 1 (cos x))))
(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64))
1
#s(literal 1 binary64)
(/ (* (sin x) 3/4) (- 1 (cos x)))
(/.f64 (*.f64 (sin.f64 x) #s(literal 3/4 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(* (sin x) 3/4)
(*.f64 (sin.f64 x) #s(literal 3/4 binary64))
(sin x)
(sin.f64 x)
x
3/4
#s(literal 3/4 binary64)
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos x)
(cos.f64 x)
(/ (* 8/3 (pow (sin (* x 1/2)) 2)) (sin x))
(.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (pow (sin (* x 1/2)) 2))
(.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)))
8/3
#s(literal 8/3 binary64)
(pow (sin (* x 1/2)) 2)
(pow.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))
(sin (* x 1/2))
(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
(* x 1/2)
(*.f64 x #s(literal 1/2 binary64))
x
1/2
#s(literal 1/2 binary64)
2
#s(literal 2 binary64)
(sin x)
(sin.f64 x)

localize418.0ms (4.4%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	accuracy	99.5%	(pow.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))
✓	accuracy	99.5%	(.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)))
✓	accuracy	82.4%	(/.f64 (.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))) (sin.f64 x))
✓	accuracy	99.7%	(*.f64 (sin.f64 x) #s(literal 3/4 binary64))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 x) #s(literal 3/4 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
✓	accuracy	82.4%	(/.f64 (*.f64 (sin.f64 x) #s(literal 3/4 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
✓	accuracy	78.8%	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	accuracy	99.8%	(.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64))))))
✓	accuracy	99.8%	(.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64))))
✓	accuracy	99.7%	(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 4/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64))))))))
✓	accuracy	99.1%	(.f64 (.f64 x x) #s(literal 61/34560 binary64))
✓	accuracy	99.5%	(*.f64 #s(literal 2/3 binary64) x)
✓	accuracy	100.0%	(sin.f64 (/.f64 x #s(literal 2 binary64)))
✓	accuracy	99.7%	(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/8 binary64))
✓	accuracy	99.7%	(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x))
✓	accuracy	99.7%	(*.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/8 binary64)))

Results

121.0ms	153×	0	valid
110.0ms	42×	2	valid
76.0ms	54×	1	valid
17.0ms	7×	3	valid

Compiler

Compiled 231 to 38 computations (83.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 169.0ms

ival-mult: 41.0ms (24.3% of total)

...c/correct-round.rkt:119:19: 31.0ms (18.4% of total)

ival-sin: 24.0ms (14.2% of total)

ival-div: 22.0ms (13% of total)

ival-cos: 22.0ms (13% of total)

backward-pass: 16.0ms (9.5% of total)

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

ival-pow: 4.0ms (2.4% of total)

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

const: 2.0ms (1.2% of total)

series17.0ms (0.2%)

Counts

21 → 252

Calls

Call 1

Inputs
#<alt (* (/ (sin (/ x 2)) (sin x)) (/ (sin (/ x 2)) 3/8))>
#<alt (/ (sin (/ x 2)) (sin x))>
#<alt (sin (/ x 2))>
#<alt (/ x 2)>
#<alt (* 2/3 x)>
#<alt (* (sin (* x 1/2)) (+ 4/3 (* (* x x) (+ 1/6 (* (* x x) (+ 5/288 (* (* x x) 61/34560)))))))>
#<alt (sin (* x 1/2))>
#<alt (* x 1/2)>
#<alt (+ 4/3 (* (* x x) (+ 1/6 (* (* x x) (+ 5/288 (* (* x x) 61/34560))))))>
#<alt (/ 1 (/ (* (sin x) 3/4) (- 1 (cos x))))>
#<alt (/ (* (sin x) 3/4) (- 1 (cos x)))>
#<alt (* (sin x) 3/4)>
#<alt (sin x)>
#<alt (/ (* 8/3 (pow (sin (* x 1/2)) 2)) (sin x))>
#<alt (* 8/3 (pow (sin (* x 1/2)) 2))>
#<alt (pow (sin (* x 1/2)) 2)>
#<alt (/ (sin (/ x 2)) 3/8)>
#<alt (* (* x x) 61/34560)>
#<alt (* (* x x) (+ 5/288 (* (* x x) 61/34560)))>
#<alt (* (* x x) (+ 1/6 (* (* x x) (+ 5/288 (* (* x x) 61/34560)))))>
#<alt (- 1 (cos x))>

Outputs
#<alt (* 2/3 x)>
#<alt (* x (+ 2/3 (* 1/18 (pow x 2))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/16 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (+ 1/16 (* 5/768 (pow x 2)))))>
#<alt (+ 1/2 (* (pow x 2) (+ 1/16 (* (pow x 2) (+ 5/768 (* 61/92160 (pow x 2)))))))>
#<alt (/ (sin (* 1/2 x)) (sin x))>
#<alt (/ (sin (* 1/2 x)) (sin x))>
#<alt (/ (sin (* 1/2 x)) (sin x))>
#<alt (/ (sin (* 1/2 x)) (sin x))>
#<alt (/ (sin (* 1/2 x)) (sin x))>
#<alt (/ (sin (* 1/2 x)) (sin x))>
#<alt (/ (sin (* 1/2 x)) (sin x))>
#<alt (/ (sin (* 1/2 x)) (sin x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/48 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 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 (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* x (+ 2/3 (* 1/18 (pow x 2))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))>
#<alt (* 61/34560 (* (pow x 6) (sin (* 1/2 x))))>
#<alt (* (pow x 6) (+ (* 61/34560 (sin (* 1/2 x))) (* 5/288 (/ (sin (* 1/2 x)) (pow x 2)))))>
#<alt (* (pow x 6) (+ (* 61/34560 (sin (* 1/2 x))) (+ (* 5/288 (/ (sin (* 1/2 x)) (pow x 2))) (* 1/6 (/ (sin (* 1/2 x)) (pow x 4))))))>
#<alt (* (pow x 6) (+ (* 61/34560 (sin (* 1/2 x))) (+ (* 5/288 (/ (sin (* 1/2 x)) (pow x 2))) (+ (* 1/6 (/ (sin (* 1/2 x)) (pow x 4))) (* 4/3 (/ (sin (* 1/2 x)) (pow x 6)))))))>
#<alt (* 61/34560 (* (pow x 6) (sin (* 1/2 x))))>
#<alt (* (pow x 6) (+ (* 61/34560 (sin (* 1/2 x))) (* 5/288 (/ (sin (* 1/2 x)) (pow x 2)))))>
#<alt (* (pow x 6) (+ (* 61/34560 (sin (* 1/2 x))) (+ (* 5/288 (/ (sin (* 1/2 x)) (pow x 2))) (* 1/6 (/ (sin (* 1/2 x)) (pow x 4))))))>
#<alt (* (pow x 6) (+ (* 61/34560 (sin (* 1/2 x))) (+ (* 5/288 (/ (sin (* 1/2 x)) (pow x 2))) (+ (* 1/6 (/ (sin (* 1/2 x)) (pow x 4))) (* 4/3 (/ (sin (* 1/2 x)) (pow x 6)))))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/48 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 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 4/3>
#<alt (+ 4/3 (* 1/6 (pow x 2)))>
#<alt (+ 4/3 (* (pow x 2) (+ 1/6 (* 5/288 (pow x 2)))))>
#<alt (+ 4/3 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 5/288 (* 61/34560 (pow x 2)))))))>
#<alt (* 61/34560 (pow x 6))>
#<alt (* (pow x 6) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 61/34560 (+ (/ 1/6 (pow x 4)) (* 5/288 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 61/34560 (+ (/ 1/6 (pow x 4)) (+ (* 5/288 (/ 1 (pow x 2))) (* 4/3 (/ 1 (pow x 6)))))))>
#<alt (* 61/34560 (pow x 6))>
#<alt (* (pow x 6) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 61/34560 (+ (/ 1/6 (pow x 4)) (* 5/288 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 61/34560 (+ (/ 1/6 (pow x 4)) (+ (* 5/288 (/ 1 (pow x 2))) (* 4/3 (/ 1 (pow x 6)))))))>
#<alt (* 2/3 x)>
#<alt (* x (+ 2/3 (* 1/18 (pow x 2))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))>
#<alt (* 4/3 (/ (- 1 (cos x)) (sin x)))>
#<alt (* 4/3 (/ (- 1 (cos x)) (sin x)))>
#<alt (* 4/3 (/ (- 1 (cos x)) (sin x)))>
#<alt (* 4/3 (/ (- 1 (cos x)) (sin x)))>
#<alt (* 4/3 (/ (- 1 (cos x)) (sin x)))>
#<alt (* 4/3 (/ (- 1 (cos x)) (sin x)))>
#<alt (* 4/3 (/ (- 1 (cos x)) (sin x)))>
#<alt (* 4/3 (/ (- 1 (cos x)) (sin x)))>
#<alt (/ 3/2 x)>
#<alt (/ (+ 3/2 (* -1/8 (pow x 2))) x)>
#<alt (/ (+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))) x)>
#<alt (/ (+ 3/2 (* (pow x 2) (- (* (pow x 2) (- (* -1/20160 (pow x 2)) 1/480)) 1/8))) x)>
#<alt (* 3/4 (/ (sin x) (- 1 (cos x))))>
#<alt (* 3/4 (/ (sin x) (- 1 (cos x))))>
#<alt (* 3/4 (/ (sin x) (- 1 (cos x))))>
#<alt (* 3/4 (/ (sin x) (- 1 (cos x))))>
#<alt (* 3/4 (/ (sin x) (- 1 (cos x))))>
#<alt (* 3/4 (/ (sin x) (- 1 (cos x))))>
#<alt (* 3/4 (/ (sin x) (- 1 (cos x))))>
#<alt (* 3/4 (/ (sin x) (- 1 (cos x))))>
#<alt (* 3/4 x)>
#<alt (* x (+ 3/4 (* -1/8 (pow x 2))))>
#<alt (* x (+ 3/4 (* (pow x 2) (- (* 1/160 (pow x 2)) 1/8))))>
#<alt (* x (+ 3/4 (* (pow x 2) (- (* (pow x 2) (+ 1/160 (* -1/6720 (pow x 2)))) 1/8))))>
#<alt (* 3/4 (sin x))>
#<alt (* 3/4 (sin x))>
#<alt (* 3/4 (sin x))>
#<alt (* 3/4 (sin x))>
#<alt (* 3/4 (sin x))>
#<alt (* 3/4 (sin x))>
#<alt (* 3/4 (sin x))>
#<alt (* 3/4 (sin x))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (* 2/3 x)>
#<alt (* x (+ 2/3 (* 1/18 (pow x 2))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))>
#<alt (* 2/3 (pow x 2))>
#<alt (* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))>
#<alt (* (pow x 2) (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))>
#<alt (* (pow x 2) (+ 2/3 (* (pow x 2) (- (* (pow x 2) (+ 1/540 (* -1/30240 (pow x 2)))) 1/18))))>
#<alt (* 8/3 (pow (sin (* 1/2 x)) 2))>
#<alt (* 8/3 (pow (sin (* 1/2 x)) 2))>
#<alt (* 8/3 (pow (sin (* 1/2 x)) 2))>
#<alt (* 8/3 (pow (sin (* 1/2 x)) 2))>
#<alt (* 8/3 (pow (sin (* 1/2 x)) 2))>
#<alt (* 8/3 (pow (sin (* 1/2 x)) 2))>
#<alt (* 8/3 (pow (sin (* 1/2 x)) 2))>
#<alt (* 8/3 (pow (sin (* 1/2 x)) 2))>
#<alt (* 1/4 (pow x 2))>
#<alt (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))>
#<alt (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 1/1440 (* -1/80640 (pow x 2)))) 1/48))))>
#<alt (pow (sin (* 1/2 x)) 2)>
#<alt (pow (sin (* 1/2 x)) 2)>
#<alt (pow (sin (* 1/2 x)) 2)>
#<alt (pow (sin (* 1/2 x)) 2)>
#<alt (pow (sin (* 1/2 x)) 2)>
#<alt (pow (sin (* 1/2 x)) 2)>
#<alt (pow (sin (* 1/2 x)) 2)>
#<alt (pow (sin (* 1/2 x)) 2)>
#<alt (* 4/3 x)>
#<alt (* x (+ 4/3 (* -1/18 (pow x 2))))>
#<alt (* x (+ 4/3 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/18))))>
#<alt (* x (+ 4/3 (* (pow x 2) (- (* (pow x 2) (+ 1/1440 (* -1/241920 (pow x 2)))) 1/18))))>
#<alt (* 8/3 (sin (* 1/2 x)))>
#<alt (* 8/3 (sin (* 1/2 x)))>
#<alt (* 8/3 (sin (* 1/2 x)))>
#<alt (* 8/3 (sin (* 1/2 x)))>
#<alt (* 8/3 (sin (* 1/2 x)))>
#<alt (* 8/3 (sin (* 1/2 x)))>
#<alt (* 8/3 (sin (* 1/2 x)))>
#<alt (* 8/3 (sin (* 1/2 x)))>
#<alt (* 61/34560 (pow x 2))>
#<alt (* 61/34560 (pow x 2))>
#<alt (* 61/34560 (pow x 2))>
#<alt (* 61/34560 (pow x 2))>
#<alt (* 61/34560 (pow x 2))>
#<alt (* 61/34560 (pow x 2))>
#<alt (* 61/34560 (pow x 2))>
#<alt (* 61/34560 (pow x 2))>
#<alt (* 61/34560 (pow x 2))>
#<alt (* 61/34560 (pow x 2))>
#<alt (* 61/34560 (pow x 2))>
#<alt (* 61/34560 (pow x 2))>
#<alt (* 5/288 (pow x 2))>
#<alt (* (pow x 2) (+ 5/288 (* 61/34560 (pow x 2))))>
#<alt (* (pow x 2) (+ 5/288 (* 61/34560 (pow x 2))))>
#<alt (* (pow x 2) (+ 5/288 (* 61/34560 (pow x 2))))>
#<alt (* 61/34560 (pow x 4))>
#<alt (* (pow x 4) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))>
#<alt (* 61/34560 (pow x 4))>
#<alt (* (pow x 4) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 5/288 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 5/288 (* 61/34560 (pow x 2))))))>
#<alt (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 5/288 (* 61/34560 (pow x 2))))))>
#<alt (* 61/34560 (pow x 6))>
#<alt (* (pow x 6) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 61/34560 (+ (/ 1/6 (pow x 4)) (* 5/288 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 61/34560 (+ (/ 1/6 (pow x 4)) (* 5/288 (/ 1 (pow x 2))))))>
#<alt (* 61/34560 (pow x 6))>
#<alt (* (pow x 6) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 61/34560 (+ (/ 1/6 (pow x 4)) (* 5/288 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 61/34560 (+ (/ 1/6 (pow x 4)) (* 5/288 (/ 1 (pow x 2))))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>

Calls

63 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(/ (* (sin x) 3/4) (- 1 (cos x)))
3.0ms	x	@	inf	(* (sin x) 3/4)
1.0ms	x	@	-inf	(/ 1 (/ (* (sin x) 3/4) (- 1 (cos x))))
1.0ms	x	@	inf	(/ 1 (/ (* (sin x) 3/4) (- 1 (cos x))))
1.0ms	x	@	-inf	(/ (* (sin x) 3/4) (- 1 (cos x)))

rewrite416.0ms (4.4%)

Algorithm

1×	batch-egg-rewrite

Rules

3976×	`/-lowering-/.f32`
3976×	`/-lowering-/.f64`
3958×	`-lowering-.f32`
3958×	`-lowering-.f64`
1628×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	159
1	206	145
2	1467	140
0	8152	140

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 896

Calls

Call 1

Inputs
(* (/ (sin (/ x 2)) (sin x)) (/ (sin (/ x 2)) 3/8))
(/ (sin (/ x 2)) (sin x))
(sin (/ x 2))
(/ x 2)
(* 2/3 x)
(* (sin (* x 1/2)) (+ 4/3 (* (* x x) (+ 1/6 (* (* x x) (+ 5/288 (* (* x x) 61/34560)))))))
(sin (* x 1/2))
(* x 1/2)
(+ 4/3 (* (* x x) (+ 1/6 (* (* x x) (+ 5/288 (* (* x x) 61/34560))))))
(/ 1 (/ (* (sin x) 3/4) (- 1 (cos x))))
(/ (* (sin x) 3/4) (- 1 (cos x)))
(* (sin x) 3/4)
(sin x)
(/ (* 8/3 (pow (sin (* x 1/2)) 2)) (sin x))
(* 8/3 (pow (sin (* x 1/2)) 2))
(pow (sin (* x 1/2)) 2)
(/ (sin (/ x 2)) 3/8)
(* (* x x) 61/34560)
(* (* x x) (+ 5/288 (* (* x x) 61/34560)))
(* (* x x) (+ 1/6 (* (* x x) (+ 5/288 (* (* x x) 61/34560)))))
(- 1 (cos x))

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 (sin.f64 x) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))) #s(literal 3/8 binary64)))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (.f64 #s(literal -8/3 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))) (sin.f64 x))))
(-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 x) #s(literal 3/8 binary64))) (/.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64))))) (.f64 (sin.f64 x) #s(literal 3/8 binary64))))
(neg.f64 (.f64 #s(literal -8/3 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))) (sin.f64 x))))
(neg.f64 (/.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))) #s(literal -8/3 binary64)) (sin.f64 x)))
(/.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x)) (/.f64 #s(literal 3/8 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/8 binary64)) (/.f64 (sin.f64 x) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))) #s(literal 3/8 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (/.f64 (sin.f64 x) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (neg.f64 (/.f64 #s(literal 3/8 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (/.f64 #s(literal 3/8 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (neg.f64 (/.f64 (sin.f64 x) (sin.f64 (/.f64 x #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (sin.f64 x) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (/.f64 x #s(literal 2 binary64)))))) #s(literal 3/8 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 3/8 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sin.f64 x) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 x) (/.f64 #s(literal 3/8 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 3/8 binary64) (/.f64 (sin.f64 x) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 (sin.f64 x) (sin.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 3/8 binary64)) (.f64 #s(literal 1 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 #s(literal 3/8 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (sin.f64 x)) (.f64 #s(literal 1 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 (sin.f64 x) (sin.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -3/8 binary64)) (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 #s(literal 3/8 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (/.f64 #s(literal 3/8 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -3/8 binary64) (/.f64 (sin.f64 x) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 3/8 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (*.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sin.f64 x) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (*.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/8 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (*.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/8 binary64)) (-.f64 #s(literal 0 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))))))
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(/.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))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 9 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (cos.f64 x) #s(literal 6 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 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) #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 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64)) (+.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 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (+.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 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))))
(/.f64 (neg.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 (neg.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(/.f64 (+.f64 (pow.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) #s(literal 3 binary64)) #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 (-.f64 #s(literal 0 binary64) (cos.f64 x)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))) #s(literal 3 binary64))) (+.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 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))) (+.f64 (.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))) (/.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) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 3 binary64)) (pow.f64 (/.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))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (+.f64 (.f64 (/.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) (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)))))))
(pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
(.f64 (-.f64 #s(literal 1/2 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))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 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))))

simplify306.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

5298×	`+-lowering-+.f64`
5298×	`+-lowering-+.f32`
3398×	`-lowering-.f32`
3398×	`-lowering-.f64`
1884×	`distribute-lft-in`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	261	2107
1	770	1832
2	2180	1832
3	4262	1802
4	7370	1802
0	8027	1802

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 252

Calls

Call 1

Inputs
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
1/2
(+ 1/2 (* 1/16 (pow x 2)))
(+ 1/2 (* (pow x 2) (+ 1/16 (* 5/768 (pow x 2)))))
(+ 1/2 (* (pow x 2) (+ 1/16 (* (pow x 2) (+ 5/768 (* 61/92160 (pow x 2)))))))
(/ (sin (* 1/2 x)) (sin x))
(/ (sin (* 1/2 x)) (sin x))
(/ (sin (* 1/2 x)) (sin x))
(/ (sin (* 1/2 x)) (sin x))
(/ (sin (* 1/2 x)) (sin x))
(/ (sin (* 1/2 x)) (sin x))
(/ (sin (* 1/2 x)) (sin x))
(/ (sin (* 1/2 x)) (sin x))
(* 1/2 x)
(* x (+ 1/2 (* -1/48 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 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)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 61/34560 (* (pow x 6) (sin (* 1/2 x))))
(* (pow x 6) (+ (* 61/34560 (sin (* 1/2 x))) (* 5/288 (/ (sin (* 1/2 x)) (pow x 2)))))
(* (pow x 6) (+ (* 61/34560 (sin (* 1/2 x))) (+ (* 5/288 (/ (sin (* 1/2 x)) (pow x 2))) (* 1/6 (/ (sin (* 1/2 x)) (pow x 4))))))
(* (pow x 6) (+ (* 61/34560 (sin (* 1/2 x))) (+ (* 5/288 (/ (sin (* 1/2 x)) (pow x 2))) (+ (* 1/6 (/ (sin (* 1/2 x)) (pow x 4))) (* 4/3 (/ (sin (* 1/2 x)) (pow x 6)))))))
(* 61/34560 (* (pow x 6) (sin (* 1/2 x))))
(* (pow x 6) (+ (* 61/34560 (sin (* 1/2 x))) (* 5/288 (/ (sin (* 1/2 x)) (pow x 2)))))
(* (pow x 6) (+ (* 61/34560 (sin (* 1/2 x))) (+ (* 5/288 (/ (sin (* 1/2 x)) (pow x 2))) (* 1/6 (/ (sin (* 1/2 x)) (pow x 4))))))
(* (pow x 6) (+ (* 61/34560 (sin (* 1/2 x))) (+ (* 5/288 (/ (sin (* 1/2 x)) (pow x 2))) (+ (* 1/6 (/ (sin (* 1/2 x)) (pow x 4))) (* 4/3 (/ (sin (* 1/2 x)) (pow x 6)))))))
(* 1/2 x)
(* x (+ 1/2 (* -1/48 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 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)
4/3
(+ 4/3 (* 1/6 (pow x 2)))
(+ 4/3 (* (pow x 2) (+ 1/6 (* 5/288 (pow x 2)))))
(+ 4/3 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 5/288 (* 61/34560 (pow x 2)))))))
(* 61/34560 (pow x 6))
(* (pow x 6) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 61/34560 (+ (/ 1/6 (pow x 4)) (* 5/288 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 61/34560 (+ (/ 1/6 (pow x 4)) (+ (* 5/288 (/ 1 (pow x 2))) (* 4/3 (/ 1 (pow x 6)))))))
(* 61/34560 (pow x 6))
(* (pow x 6) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 61/34560 (+ (/ 1/6 (pow x 4)) (* 5/288 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 61/34560 (+ (/ 1/6 (pow x 4)) (+ (* 5/288 (/ 1 (pow x 2))) (* 4/3 (/ 1 (pow x 6)))))))
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(/ 3/2 x)
(/ (+ 3/2 (* -1/8 (pow x 2))) x)
(/ (+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))) x)
(/ (+ 3/2 (* (pow x 2) (- (* (pow x 2) (- (* -1/20160 (pow x 2)) 1/480)) 1/8))) x)
(* 3/4 (/ (sin x) (- 1 (cos x))))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(* 3/4 (/ (sin x) (- 1 (cos x))))
(* 3/4 x)
(* x (+ 3/4 (* -1/8 (pow x 2))))
(* x (+ 3/4 (* (pow x 2) (- (* 1/160 (pow x 2)) 1/8))))
(* x (+ 3/4 (* (pow x 2) (- (* (pow x 2) (+ 1/160 (* -1/6720 (pow x 2)))) 1/8))))
(* 3/4 (sin x))
(* 3/4 (sin x))
(* 3/4 (sin x))
(* 3/4 (sin x))
(* 3/4 (sin x))
(* 3/4 (sin x))
(* 3/4 (sin x))
(* 3/4 (sin x))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(* 2/3 (pow x 2))
(* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* (pow x 2) (+ 1/540 (* -1/30240 (pow x 2)))) 1/18))))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(* 1/4 (pow x 2))
(* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 1/1440 (* -1/80640 (pow x 2)))) 1/48))))
(pow (sin (* 1/2 x)) 2)
(pow (sin (* 1/2 x)) 2)
(pow (sin (* 1/2 x)) 2)
(pow (sin (* 1/2 x)) 2)
(pow (sin (* 1/2 x)) 2)
(pow (sin (* 1/2 x)) 2)
(pow (sin (* 1/2 x)) 2)
(pow (sin (* 1/2 x)) 2)
(* 4/3 x)
(* x (+ 4/3 (* -1/18 (pow x 2))))
(* x (+ 4/3 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/18))))
(* x (+ 4/3 (* (pow x 2) (- (* (pow x 2) (+ 1/1440 (* -1/241920 (pow x 2)))) 1/18))))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(* 8/3 (sin (* 1/2 x)))
(* 61/34560 (pow x 2))
(* 61/34560 (pow x 2))
(* 61/34560 (pow x 2))
(* 61/34560 (pow x 2))
(* 61/34560 (pow x 2))
(* 61/34560 (pow x 2))
(* 61/34560 (pow x 2))
(* 61/34560 (pow x 2))
(* 61/34560 (pow x 2))
(* 61/34560 (pow x 2))
(* 61/34560 (pow x 2))
(* 61/34560 (pow x 2))
(* 5/288 (pow x 2))
(* (pow x 2) (+ 5/288 (* 61/34560 (pow x 2))))
(* (pow x 2) (+ 5/288 (* 61/34560 (pow x 2))))
(* (pow x 2) (+ 5/288 (* 61/34560 (pow x 2))))
(* 61/34560 (pow x 4))
(* (pow x 4) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))
(* 61/34560 (pow x 4))
(* (pow x 4) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 5/288 (pow x 2))))
(* (pow x 2) (+ 1/6 (* (pow x 2) (+ 5/288 (* 61/34560 (pow x 2))))))
(* (pow x 2) (+ 1/6 (* (pow x 2) (+ 5/288 (* 61/34560 (pow x 2))))))
(* 61/34560 (pow x 6))
(* (pow x 6) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 61/34560 (+ (/ 1/6 (pow x 4)) (* 5/288 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 61/34560 (+ (/ 1/6 (pow x 4)) (* 5/288 (/ 1 (pow x 2))))))
(* 61/34560 (pow x 6))
(* (pow x 6) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 61/34560 (+ (/ 1/6 (pow x 4)) (* 5/288 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 61/34560 (+ (/ 1/6 (pow x 4)) (* 5/288 (/ 1 (pow x 2))))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))

Outputs
(* 2/3 x)
(*.f64 #s(literal 2/3 binary64) x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 #s(literal 1/18 binary64) (*.f64 x x))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/18 binary64) (.f64 x (*.f64 x #s(literal 1/180 binary64))))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 x (*.f64 x #s(literal 17/30240 binary64)))))))))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(*.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(*.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(*.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(*.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
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(*.f64 #s(literal 2/3 binary64) x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 #s(literal 1/18 binary64) (*.f64 x x))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/18 binary64) (.f64 x (*.f64 x #s(literal 1/180 binary64))))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 x (*.f64 x #s(literal 17/30240 binary64)))))))))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(*.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(*.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(*.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(*.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(*.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(*.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(*.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 8/3 (/ (pow (sin (* 1/2 x)) 2) (sin x)))
(*.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(* 2/3 (pow x 2))
(.f64 #s(literal 2/3 binary64) (.f64 x x))
(* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) #s(literal -1/18 binary64))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))
(.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/18 binary64) (.f64 (.f64 x x) #s(literal 1/540 binary64)))))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* (pow x 2) (+ 1/540 (* -1/30240 (pow x 2)))) 1/18))))
(.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/18 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/540 binary64) (.f64 (.f64 x x) #s(literal -1/30240 binary64))))))))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(*.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(*.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(*.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(*.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(*.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(*.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(*.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
(* 8/3 (pow (sin (* 1/2 x)) 2))
(*.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
(* 1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/4 binary64))
(* (pow x 2) (+ 1/4 (* -1/48 (pow x 2))))
(.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal -1/48 binary64))) #s(literal 1/4 binary64)))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 x x) #s(literal 1/1440 binary64))))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 1/1440 (* -1/80640 (pow x 2)))) 1/48))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/1440 binary64) (.f64 (.f64 x x) #s(literal -1/80640 binary64)))))))))
(pow (sin (* 1/2 x)) 2)
(pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(pow (sin (* 1/2 x)) 2)
(pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(pow (sin (* 1/2 x)) 2)
(pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(pow (sin (* 1/2 x)) 2)
(pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(pow (sin (* 1/2 x)) 2)
(pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(pow (sin (* 1/2 x)) 2)
(pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(pow (sin (* 1/2 x)) 2)
(pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(pow (sin (* 1/2 x)) 2)
(pow.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(* 4/3 x)
(*.f64 x #s(literal 4/3 binary64))
(* x (+ 4/3 (* -1/18 (pow x 2))))
(.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 (*.f64 x x) #s(literal -1/18 binary64))))
(* x (+ 4/3 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/18))))
(.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/18 binary64) (.f64 (*.f64 x x) #s(literal 1/1440 binary64))))))
(* x (+ 4/3 (* (pow x 2) (- (* (pow x 2) (+ 1/1440 (* -1/241920 (pow x 2)))) 1/18))))
(.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/18 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/1440 binary64) (.f64 (*.f64 x x) #s(literal -1/241920 binary64)))))))))
(* 8/3 (sin (* 1/2 x)))
(*.f64 #s(literal 8/3 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))
(* 8/3 (sin (* 1/2 x)))
(*.f64 #s(literal 8/3 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))
(* 8/3 (sin (* 1/2 x)))
(*.f64 #s(literal 8/3 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))
(* 8/3 (sin (* 1/2 x)))
(*.f64 #s(literal 8/3 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))
(* 8/3 (sin (* 1/2 x)))
(*.f64 #s(literal 8/3 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))
(* 8/3 (sin (* 1/2 x)))
(*.f64 #s(literal 8/3 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))
(* 8/3 (sin (* 1/2 x)))
(*.f64 #s(literal 8/3 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))
(* 8/3 (sin (* 1/2 x)))
(*.f64 #s(literal 8/3 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))
(* 61/34560 (pow x 2))
(.f64 (.f64 x x) #s(literal 61/34560 binary64))
(* 61/34560 (pow x 2))
(.f64 (.f64 x x) #s(literal 61/34560 binary64))
(* 61/34560 (pow x 2))
(.f64 (.f64 x x) #s(literal 61/34560 binary64))
(* 61/34560 (pow x 2))
(.f64 (.f64 x x) #s(literal 61/34560 binary64))
(* 61/34560 (pow x 2))
(.f64 (.f64 x x) #s(literal 61/34560 binary64))
(* 61/34560 (pow x 2))
(.f64 (.f64 x x) #s(literal 61/34560 binary64))
(* 61/34560 (pow x 2))
(.f64 (.f64 x x) #s(literal 61/34560 binary64))
(* 61/34560 (pow x 2))
(.f64 (.f64 x x) #s(literal 61/34560 binary64))
(* 61/34560 (pow x 2))
(.f64 (.f64 x x) #s(literal 61/34560 binary64))
(* 61/34560 (pow x 2))
(.f64 (.f64 x x) #s(literal 61/34560 binary64))
(* 61/34560 (pow x 2))
(.f64 (.f64 x x) #s(literal 61/34560 binary64))
(* 61/34560 (pow x 2))
(.f64 (.f64 x x) #s(literal 61/34560 binary64))
(* 5/288 (pow x 2))
(.f64 (.f64 x x) #s(literal 5/288 binary64))
(* (pow x 2) (+ 5/288 (* 61/34560 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64))))
(* (pow x 2) (+ 5/288 (* 61/34560 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64))))
(* (pow x 2) (+ 5/288 (* 61/34560 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64))))
(* 61/34560 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 61/34560 binary64))))
(* (pow x 4) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 61/34560 binary64) (/.f64 #s(literal 5/288 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 61/34560 binary64) (/.f64 #s(literal 5/288 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 61/34560 binary64) (/.f64 #s(literal 5/288 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* 61/34560 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 61/34560 binary64))))
(* (pow x 4) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 61/34560 binary64) (/.f64 #s(literal 5/288 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 61/34560 binary64) (/.f64 #s(literal 5/288 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 61/34560 binary64) (/.f64 #s(literal 5/288 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 5/288 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) #s(literal 5/288 binary64)))))
(* (pow x 2) (+ 1/6 (* (pow x 2) (+ 5/288 (* 61/34560 (pow x 2))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64))))))
(* (pow x 2) (+ 1/6 (* (pow x 2) (+ 5/288 (* 61/34560 (pow x 2))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64))))))
(* 61/34560 (pow x 6))
(*.f64 #s(literal 61/34560 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 61/34560 binary64) (/.f64 #s(literal 5/288 binary64) (.f64 x x))))
(* (pow x 6) (+ 61/34560 (+ (/ 1/6 (pow x 4)) (* 5/288 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 61/34560 binary64) (/.f64 #s(literal 5/288 binary64) (.f64 x x))) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (*.f64 x x)))))
(* (pow x 6) (+ 61/34560 (+ (/ 1/6 (pow x 4)) (* 5/288 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 61/34560 binary64) (/.f64 #s(literal 5/288 binary64) (.f64 x x))) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (*.f64 x x)))))
(* 61/34560 (pow x 6))
(*.f64 #s(literal 61/34560 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 61/34560 (* 5/288 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 61/34560 binary64) (/.f64 #s(literal 5/288 binary64) (.f64 x x))))
(* (pow x 6) (+ 61/34560 (+ (/ 1/6 (pow x 4)) (* 5/288 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 61/34560 binary64) (/.f64 #s(literal 5/288 binary64) (.f64 x x))) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (*.f64 x x)))))
(* (pow x 6) (+ 61/34560 (+ (/ 1/6 (pow x 4)) (* 5/288 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 61/34560 binary64) (/.f64 #s(literal 5/288 binary64) (.f64 x x))) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (*.f64 x x)))))
(* 1/2 (pow x 2))
(/.f64 (*.f64 x x) #s(literal 2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 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 x (.f64 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))

eval155.0ms (1.6%)

Compiler: Compiled 29266 to 2645 computations (91% saved)

prune169.0ms (1.8%)

Pruning

21 alts after pruning (18 fresh and 3 done)

	Pruned	Kept	Total
New	1258	12	1270
Fresh	27	6	33
Picked	3	2	5
Done	0	1	1
Total	1288	21	1309

Accuracy

100.0%

Counts

1309 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.9%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 3/4 binary64)) (sin.f64 x))
	60.8%	(/.f64 (/.f64 #s(literal 8/3 binary64) (sin.f64 x)) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
	60.8%	(/.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 3/4 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
	60.8%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (sin.f64 x) #s(literal 3/4 binary64)))
	60.6%	(/.f64 (+.f64 #s(literal 4/3 binary64) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) #s(literal 8/3 binary64))) (sin.f64 x))
✓	82.0%	(/.f64 (.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))) (sin.f64 x))
▶	99.7%	(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64))
	43.7%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/480 binary64) (.f64 (.f64 x x) #s(literal -1/20160 binary64))))))) x))
	43.7%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))) x))
▶	43.6%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64)))))) x))
▶	42.9%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/2 binary64) x))
	99.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/4 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
	99.4%	(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 3/4 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
	42.6%	(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/48 binary64))))) (+.f64 #s(literal 4/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64))))))))
✓	99.2%	(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 8/3 binary64) (sin.f64 x))))
	42.9%	(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 x (*.f64 x #s(literal 17/30240 binary64)))))))))
	42.8%	(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/18 binary64) (.f64 (*.f64 x x) #s(literal 1/180 binary64)))))))
	42.8%	(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 1/18 binary64)))))
▶	99.4%	(*.f64 #s(literal 4/3 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))
✓	42.8%	(*.f64 #s(literal 2/3 binary64) x)
	60.8%	(.f64 #s(literal -8/3 binary64) (pow.f64 (.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal -2 binary64)) #s(literal -1 binary64)))

Compiler

Compiled 515 to 380 computations (26.2% saved)

simplify122.0ms (1.3%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 3/4 binary64))
✓	cost-diff	6528	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 3/4 binary64)) (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 #s(literal 4/3 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))
✓	cost-diff	0	(.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64)))))
✓	cost-diff	0	(+.f64 #s(literal 3/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64))))))
✓	cost-diff	0	(/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64)))))) x)
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64)))))) x))
✓	cost-diff	0	(/.f64 #s(literal 3/2 binary64) x)
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/2 binary64) 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))) #s(literal 3/4 binary64))

Rules

2322×	`fma-define`
1984×	`fnmadd-define`
1510×	`sum3-define`
1080×	`fmsub-define`
942×	`fnmsub-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	27	136
1	59	127
2	124	126
3	226	126
4	377	125
5	495	125
6	646	125
7	1041	125
8	2256	125
9	3919	125
10	6241	125
11	7870	125
12	7929	125
13	7934	125
14	7945	125
15	7974	125
0	8015	125

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (tan (/ x 2)) 3/4)
(tan (/ x 2))
(/ x 2)
x
2
3/4
(/ 1 (/ 3/2 x))
1
(/ 3/2 x)
3/2
x
(/ 1 (/ (+ 3/2 (* x (* x (+ -1/8 (* (* x x) -1/480))))) x))
1
(/ (+ 3/2 (* x (* x (+ -1/8 (* (* x x) -1/480))))) x)
(+ 3/2 (* x (* x (+ -1/8 (* (* x x) -1/480)))))
3/2
(* x (* x (+ -1/8 (* (* x x) -1/480))))
x
(* x (+ -1/8 (* (* x x) -1/480)))
(+ -1/8 (* (* x x) -1/480))
-1/8
(* (* x x) -1/480)
(* x x)
-1/480
(* 4/3 (tan (/ x 2)))
4/3
(tan (/ x 2))
(/ x 2)
x
2
(/ (/ (- 1 (cos x)) 3/4) (sin x))
(/ (- 1 (cos x)) 3/4)
(- 1 (cos x))
1
(cos x)
x
3/4
(sin x)

Outputs
(/ (tan (/ x 2)) 3/4)
(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64))
(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)
3/4
#s(literal 3/4 binary64)
(/ 1 (/ 3/2 x))
(*.f64 x #s(literal 2/3 binary64))
1
#s(literal 1 binary64)
(/ 3/2 x)
(/.f64 #s(literal 3/2 binary64) x)
3/2
#s(literal 3/2 binary64)
x
(/ 1 (/ (+ 3/2 (* x (* x (+ -1/8 (* (* x x) -1/480))))) x))
(/.f64 x (+.f64 #s(literal 3/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64)))))))
1
#s(literal 1 binary64)
(/ (+ 3/2 (* x (* x (+ -1/8 (* (* x x) -1/480))))) x)
(/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64)))))) x)
(+ 3/2 (* x (* x (+ -1/8 (* (* x x) -1/480)))))
(+.f64 #s(literal 3/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64))))))
3/2
#s(literal 3/2 binary64)
(* x (* x (+ -1/8 (* (* x x) -1/480))))
(.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64)))))
x
(* x (+ -1/8 (* (* x x) -1/480)))
(.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (*.f64 x x) #s(literal -1/480 binary64))))
(+ -1/8 (* (* x x) -1/480))
(+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64)))
-1/8
#s(literal -1/8 binary64)
(* (* x x) -1/480)
(.f64 (.f64 x x) #s(literal -1/480 binary64))
(* x x)
(*.f64 x x)
-1/480
#s(literal -1/480 binary64)
(* 4/3 (tan (/ x 2)))
(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64))
4/3
#s(literal 4/3 binary64)
(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)
(/ (/ (- 1 (cos x)) 3/4) (sin x))
(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64))
(/ (- 1 (cos x)) 3/4)
(+.f64 #s(literal 4/3 binary64) (/.f64 (cos.f64 x) #s(literal -3/4 binary64)))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
1
#s(literal 1 binary64)
(cos x)
(cos.f64 x)
x
3/4
#s(literal 3/4 binary64)
(sin x)
(sin.f64 x)

localize262.0ms (2.8%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	99.8%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 3/4 binary64))
✓	accuracy	82.4%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 3/4 binary64)) (sin.f64 x))
✓	accuracy	78.8%	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	accuracy	100.0%	(/.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))
✓	accuracy	99.4%	(*.f64 #s(literal 4/3 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))
✓	accuracy	99.9%	(.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (*.f64 x x) #s(literal -1/480 binary64))))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64)))))) x))
✓	accuracy	99.5%	(.f64 (.f64 x x) #s(literal -1/480 binary64))
✓	accuracy	93.8%	(/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64)))))) x)
✓	accuracy	100.0%	(/.f64 #s(literal 3/2 binary64) x)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/2 binary64) x))
✓	accuracy	100.0%	(/.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))
✓	accuracy	99.7%	(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64))

Results

86.0ms	153×	0	valid
77.0ms	47×	2	valid
55.0ms	56×	1	valid

Compiler

Compiled 156 to 28 computations (82.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 113.0ms

ival-cos: 25.0ms (22.1% of total)

ival-div: 22.0ms (19.5% of total)

backward-pass: 17.0ms (15% of total)

...c/correct-round.rkt:119:19: 14.0ms (12.4% of total)

ival-mult: 12.0ms (10.6% of total)

ival-sin: 8.0ms (7.1% of total)

ival-tan: 7.0ms (6.2% of total)

ival-add: 5.0ms (4.4% of total)

ival-sub: 2.0ms (1.8% of total)

const: 1.0ms (0.9% of total)

series12.0ms (0.1%)

Counts

16 → 192

Calls

Call 1

Inputs
#<alt (/ (tan (/ x 2)) 3/4)>
#<alt (tan (/ x 2))>
#<alt (/ x 2)>
#<alt (/ 1 (/ 3/2 x))>
#<alt (/ 3/2 x)>
#<alt (/ 1 (/ (+ 3/2 (* x (* x (+ -1/8 (* (* x x) -1/480))))) x))>
#<alt (/ (+ 3/2 (* x (* x (+ -1/8 (* (* x x) -1/480))))) x)>
#<alt (+ 3/2 (* x (* x (+ -1/8 (* (* x x) -1/480)))))>
#<alt (* x (* x (+ -1/8 (* (* x x) -1/480))))>
#<alt (* 4/3 (tan (/ x 2)))>
#<alt (/ (/ (- 1 (cos x)) 3/4) (sin x))>
#<alt (/ (- 1 (cos x)) 3/4)>
#<alt (- 1 (cos x))>
#<alt (cos x)>
#<alt (* (* x x) -1/480)>
#<alt (* x (+ -1/8 (* (* x x) -1/480)))>

Outputs
#<alt (* 2/3 x)>
#<alt (* x (+ 2/3 (* 1/18 (pow x 2))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (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 (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (/ 3/2 x)>
#<alt (/ 3/2 x)>
#<alt (/ 3/2 x)>
#<alt (/ 3/2 x)>
#<alt (/ 3/2 x)>
#<alt (/ 3/2 x)>
#<alt (/ 3/2 x)>
#<alt (/ 3/2 x)>
#<alt (/ 3/2 x)>
#<alt (/ 3/2 x)>
#<alt (/ 3/2 x)>
#<alt (/ 3/2 x)>
#<alt (* 2/3 x)>
#<alt (* x (+ 2/3 (* 1/18 (pow x 2))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 7/12960 (pow x 2))))))))>
#<alt (/ -480 (pow x 3))>
#<alt (/ (- (* 28800 (/ 1 (pow x 2))) 480) (pow x 3))>
#<alt (/ (- (* 28800 (/ 1 (pow x 2))) (+ 480 (/ 2073600 (pow x 4)))) (pow x 3))>
#<alt (/ (- (+ (* 28800 (/ 1 (pow x 2))) (* 145152000 (/ 1 (pow x 6)))) (+ 480 (/ 2073600 (pow x 4)))) (pow x 3))>
#<alt (/ -480 (pow x 3))>
#<alt (* -1 (/ (- 480 (* 28800 (/ 1 (pow x 2)))) (pow x 3)))>
#<alt (* -1 (/ (- (+ 480 (/ 2073600 (pow x 4))) (* 28800 (/ 1 (pow x 2)))) (pow x 3)))>
#<alt (* -1 (/ (- (+ 480 (/ 2073600 (pow x 4))) (+ (* 28800 (/ 1 (pow x 2))) (* 145152000 (/ 1 (pow x 6))))) (pow x 3)))>
#<alt (/ 3/2 x)>
#<alt (/ (+ 3/2 (* -1/8 (pow x 2))) x)>
#<alt (/ (+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))) x)>
#<alt (/ (+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))) x)>
#<alt (* -1/480 (pow x 3))>
#<alt (* -1 (* (pow x 3) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* (pow x 3) (- (/ 3/2 (pow x 4)) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* (pow x 3) (- (/ 3/2 (pow x 4)) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1/480 (pow x 3))>
#<alt (* -1 (* (pow x 3) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- (+ 1/480 (* 1/8 (/ 1 (pow x 2)))) (/ 3/2 (pow x 4)))))>
#<alt (* -1 (* (pow x 3) (- (+ 1/480 (* 1/8 (/ 1 (pow x 2)))) (/ 3/2 (pow x 4)))))>
#<alt 3/2>
#<alt (+ 3/2 (* -1/8 (pow x 2)))>
#<alt (+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8)))>
#<alt (+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8)))>
#<alt (* -1/480 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (- (/ 3/2 (pow x 4)) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (- (/ 3/2 (pow x 4)) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1/480 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (- (/ 3/2 (pow x 4)) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (- (/ 3/2 (pow x 4)) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1/8 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))>
#<alt (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))>
#<alt (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))>
#<alt (* -1/480 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1/480 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* 2/3 x)>
#<alt (* x (+ 2/3 (* 1/18 (pow x 2))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 2/3 x)>
#<alt (* x (+ 2/3 (* 1/18 (pow x 2))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))>
#<alt (* 4/3 (/ (- 1 (cos x)) (sin x)))>
#<alt (* 4/3 (/ (- 1 (cos x)) (sin x)))>
#<alt (* 4/3 (/ (- 1 (cos x)) (sin x)))>
#<alt (* 4/3 (/ (- 1 (cos x)) (sin x)))>
#<alt (* 4/3 (/ (- 1 (cos x)) (sin x)))>
#<alt (* 4/3 (/ (- 1 (cos x)) (sin x)))>
#<alt (* 4/3 (/ (- 1 (cos x)) (sin x)))>
#<alt (* 4/3 (/ (- 1 (cos x)) (sin x)))>
#<alt (* 2/3 (pow x 2))>
#<alt (* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))>
#<alt (* (pow x 2) (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))>
#<alt (* (pow x 2) (+ 2/3 (* (pow x 2) (- (* (pow x 2) (+ 1/540 (* -1/30240 (pow x 2)))) 1/18))))>
#<alt (* 4/3 (- 1 (cos x)))>
#<alt (* 4/3 (- 1 (cos x)))>
#<alt (* 4/3 (- 1 (cos x)))>
#<alt (* 4/3 (- 1 (cos x)))>
#<alt (* 4/3 (- 1 (cos x)))>
#<alt (* 4/3 (- 1 (cos x)))>
#<alt (* 4/3 (- 1 (cos x)))>
#<alt (* 4/3 (- 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>
#<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 (* -1/480 (pow x 2))>
#<alt (* -1/480 (pow x 2))>
#<alt (* -1/480 (pow x 2))>
#<alt (* -1/480 (pow x 2))>
#<alt (* -1/480 (pow x 2))>
#<alt (* -1/480 (pow x 2))>
#<alt (* -1/480 (pow x 2))>
#<alt (* -1/480 (pow x 2))>
#<alt (* -1/480 (pow x 2))>
#<alt (* -1/480 (pow x 2))>
#<alt (* -1/480 (pow x 2))>
#<alt (* -1/480 (pow x 2))>
#<alt (* -1/8 x)>
#<alt (* x (- (* -1/480 (pow x 2)) 1/8))>
#<alt (* x (- (* -1/480 (pow x 2)) 1/8))>
#<alt (* x (- (* -1/480 (pow x 2)) 1/8))>
#<alt (* -1/480 (pow x 3))>
#<alt (* -1 (* (pow x 3) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1/480 (pow x 3))>
#<alt (* -1 (* (pow x 3) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))>

Calls

48 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/ (tan (/ x 2)) 3/4)
1.0ms	x	@	-inf	(/ (tan (/ x 2)) 3/4)
1.0ms	x	@	-inf	(/ 1 (/ (+ 3/2 (* x (* x (+ -1/8 (* (* x x) -1/480))))) x))
1.0ms	x	@	inf	(/ 1 (/ (+ 3/2 (* x (* x (+ -1/8 (* (* x x) -1/480))))) x))
0.0ms	x	@	inf	(* (* x x) -1/480)

rewrite352.0ms (3.7%)

Algorithm

1×	batch-egg-rewrite

Rules

4978×	`-lowering-.f32`
4978×	`-lowering-.f64`
3442×	`/-lowering-/.f32`
3442×	`/-lowering-/.f64`
1570×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	102
1	157	93
2	1018	93
0	8805	93

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 1020

Calls

Call 1

Inputs
(/ (tan (/ x 2)) 3/4)
(tan (/ x 2))
(/ x 2)
(/ 1 (/ 3/2 x))
(/ 3/2 x)
(/ 1 (/ (+ 3/2 (* x (* x (+ -1/8 (* (* x x) -1/480))))) x))
(/ (+ 3/2 (* x (* x (+ -1/8 (* (* x x) -1/480))))) x)
(+ 3/2 (* x (* x (+ -1/8 (* (* x x) -1/480)))))
(* x (* x (+ -1/8 (* (* x x) -1/480))))
(* 4/3 (tan (/ x 2)))
(/ (/ (- 1 (cos x)) 3/4) (sin x))
(/ (- 1 (cos x)) 3/4)
(- 1 (cos x))
(cos x)
(* (* x x) -1/480)
(* x (+ -1/8 (* (* x x) -1/480)))

Outputs
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 3/4 binary64) (sin.f64 x))) (neg.f64 (/.f64 (cos.f64 x) (.f64 #s(literal 3/4 binary64) (sin.f64 x)))))
(+.f64 (/.f64 #s(literal 4/3 binary64) (sin.f64 x)) (neg.f64 (/.f64 (cos.f64 x) (*.f64 #s(literal 3/4 binary64) (sin.f64 x)))))
(+.f64 (/.f64 #s(literal 4/3 binary64) (sin.f64 x)) (*.f64 (/.f64 (cos.f64 x) #s(literal -3/4 binary64)) (/.f64 #s(literal 1 binary64) (sin.f64 x))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal 4/3 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) #s(literal -3/4 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 3/4 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal -3/4 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 3/4 binary64) (sin.f64 x))) (/.f64 (cos.f64 x) (.f64 #s(literal 3/4 binary64) (sin.f64 x))))
(-.f64 (/.f64 #s(literal 4/3 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) (*.f64 #s(literal 3/4 binary64) (sin.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 #s(literal 3/4 binary64) (sin.f64 x))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))) (.f64 #s(literal 3/4 binary64) (sin.f64 x))))
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(neg.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal -3/4 binary64)))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (sin.f64 x) #s(literal -3/4 binary64))))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal -3/4 binary64))))
(neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (-.f64 #s(literal -4/3 binary64) (/.f64 (cos.f64 x) #s(literal -3/4 binary64)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 3/4 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(neg.f64 (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) (*.f64 #s(literal 3/4 binary64) (sin.f64 x))))
(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/4 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (.f64 #s(literal 3/4 binary64) (sin.f64 x))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 3/4 binary64) (+.f64 (cos.f64 x) #s(literal -1 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x))))
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(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 3/4 binary64) (.f64 #s(literal 3/4 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 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 3/4 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
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(/.f64 #s(literal 4/3 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 #s(literal 3/4 binary64) (sin.f64 x)))
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(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) #s(literal -3/4 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (neg.f64 (*.f64 (sin.f64 x) #s(literal -3/4 binary64))))
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(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 #s(literal 3/4 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/4 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal 3/4 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) (-.f64 #s(literal 0 binary64) (sin.f64 x))))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal 3/4 binary64) (+.f64 (cos.f64 x) #s(literal -1 binary64))) (sin.f64 x)))
(/.f64 (-.f64 #s(literal -4/3 binary64) (/.f64 (cos.f64 x) #s(literal -3/4 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(/.f64 (-.f64 #s(literal 0 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -3/4 binary64))
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(/.f64 (.f64 x (+.f64 (neg.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/110592000 binary64))) #s(literal 1/512 binary64))) (+.f64 (neg.f64 (.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/230400 binary64)) #s(literal 1/3840 binary64)))) #s(literal -1/64 binary64)))
(/.f64 (.f64 x (+.f64 #s(literal -1/64 binary64) (neg.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/230400 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1/8 binary64) (.f64 (*.f64 x x) #s(literal 1/480 binary64)))))
(/.f64 (.f64 x (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/230400 binary64))) #s(literal -1/64 binary64))) (+.f64 (.f64 (*.f64 x x) #s(literal -1/480 binary64)) #s(literal 1/8 binary64)))
(.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (*.f64 x x) #s(literal -1/480 binary64))))
(.f64 (+.f64 #s(literal -1/8 binary64) (.f64 (*.f64 x x) #s(literal -1/480 binary64))) x)
(.f64 (+.f64 #s(literal -1/512 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/110592000 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/230400 binary64)) #s(literal 1/3840 binary64))))) x))
(.f64 (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/230400 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 1/480 binary64)))) x))
(.f64 (+.f64 (.f64 #s(literal -1/512 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/110592000 binary64)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 1/64 binary64)) (.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/480 binary64))) (-.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/480 binary64))) (*.f64 x #s(literal -1/8 binary64)))))))
(.f64 (.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64)))) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 1/480 binary64))))) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (*.f64 x x) #s(literal 1/480 binary64))))))
(.f64 (.f64 x (+.f64 #s(literal -1/512 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/110592000 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/230400 binary64)) #s(literal 1/3840 binary64))))))
(.f64 (.f64 x (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/230400 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 1/480 binary64)))))
(.f64 (.f64 (+.f64 #s(literal -1/512 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/110592000 binary64))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/230400 binary64)) #s(literal 1/3840 binary64))))))
(.f64 (.f64 (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/230400 binary64))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal 1/480 binary64)))))

simplify234.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

3476×	`-lowering-.f32`
3476×	`-lowering-.f64`
1894×	`+-lowering-+.f64`
1894×	`+-lowering-+.f32`
1840×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	180	1572
1	530	1406
2	1723	1373
3	5451	1332
0	8201	1332

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

Inputs
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (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)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(/ 3/2 x)
(/ 3/2 x)
(/ 3/2 x)
(/ 3/2 x)
(/ 3/2 x)
(/ 3/2 x)
(/ 3/2 x)
(/ 3/2 x)
(/ 3/2 x)
(/ 3/2 x)
(/ 3/2 x)
(/ 3/2 x)
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 7/12960 (pow x 2))))))))
(/ -480 (pow x 3))
(/ (- (* 28800 (/ 1 (pow x 2))) 480) (pow x 3))
(/ (- (* 28800 (/ 1 (pow x 2))) (+ 480 (/ 2073600 (pow x 4)))) (pow x 3))
(/ (- (+ (* 28800 (/ 1 (pow x 2))) (* 145152000 (/ 1 (pow x 6)))) (+ 480 (/ 2073600 (pow x 4)))) (pow x 3))
(/ -480 (pow x 3))
(* -1 (/ (- 480 (* 28800 (/ 1 (pow x 2)))) (pow x 3)))
(* -1 (/ (- (+ 480 (/ 2073600 (pow x 4))) (* 28800 (/ 1 (pow x 2)))) (pow x 3)))
(* -1 (/ (- (+ 480 (/ 2073600 (pow x 4))) (+ (* 28800 (/ 1 (pow x 2))) (* 145152000 (/ 1 (pow x 6))))) (pow x 3)))
(/ 3/2 x)
(/ (+ 3/2 (* -1/8 (pow x 2))) x)
(/ (+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))) x)
(/ (+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))) x)
(* -1/480 (pow x 3))
(* -1 (* (pow x 3) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* (pow x 3) (- (/ 3/2 (pow x 4)) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* (pow x 3) (- (/ 3/2 (pow x 4)) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* -1/480 (pow x 3))
(* -1 (* (pow x 3) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- (+ 1/480 (* 1/8 (/ 1 (pow x 2)))) (/ 3/2 (pow x 4)))))
(* -1 (* (pow x 3) (- (+ 1/480 (* 1/8 (/ 1 (pow x 2)))) (/ 3/2 (pow x 4)))))
3/2
(+ 3/2 (* -1/8 (pow x 2)))
(+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8)))
(+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8)))
(* -1/480 (pow x 4))
(* -1 (* (pow x 4) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 3/2 (pow x 4)) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 3/2 (pow x 4)) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* -1/480 (pow x 4))
(* -1 (* (pow x 4) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 3/2 (pow x 4)) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 3/2 (pow x 4)) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))
(* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))
(* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))
(* -1/480 (pow x 4))
(* -1 (* (pow x 4) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* -1/480 (pow x 4))
(* -1 (* (pow x 4) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 4/3 (/ (- 1 (cos x)) (sin x)))
(* 2/3 (pow x 2))
(* (pow x 2) (+ 2/3 (* -1/18 (pow x 2))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* 1/540 (pow x 2)) 1/18))))
(* (pow x 2) (+ 2/3 (* (pow x 2) (- (* (pow x 2) (+ 1/540 (* -1/30240 (pow x 2)))) 1/18))))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 1 (cos x)))
(* 4/3 (- 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
(+ 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)
(* -1/480 (pow x 2))
(* -1/480 (pow x 2))
(* -1/480 (pow x 2))
(* -1/480 (pow x 2))
(* -1/480 (pow x 2))
(* -1/480 (pow x 2))
(* -1/480 (pow x 2))
(* -1/480 (pow x 2))
(* -1/480 (pow x 2))
(* -1/480 (pow x 2))
(* -1/480 (pow x 2))
(* -1/480 (pow x 2))
(* -1/8 x)
(* x (- (* -1/480 (pow x 2)) 1/8))
(* x (- (* -1/480 (pow x 2)) 1/8))
(* x (- (* -1/480 (pow x 2)) 1/8))
(* -1/480 (pow x 3))
(* -1 (* (pow x 3) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* -1/480 (pow x 3))
(* -1 (* (pow x 3) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))

Outputs
(* 2/3 x)
(*.f64 #s(literal 2/3 binary64) x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 1/18 binary64)))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 x (*.f64 x #s(literal 1/180 binary64)))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 x (*.f64 x #s(literal 17/30240 binary64)))))))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(/.f64 (.f64 #s(literal 4/3 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (cos.f64 (*.f64 x #s(literal 1/2 binary64))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(/.f64 (.f64 #s(literal 4/3 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (cos.f64 (*.f64 x #s(literal 1/2 binary64))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(/.f64 (.f64 #s(literal 4/3 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (cos.f64 (*.f64 x #s(literal 1/2 binary64))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(/.f64 (.f64 #s(literal 4/3 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (cos.f64 (*.f64 x #s(literal 1/2 binary64))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(/.f64 (.f64 #s(literal 4/3 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (cos.f64 (*.f64 x #s(literal 1/2 binary64))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(/.f64 (.f64 #s(literal 4/3 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (cos.f64 (*.f64 x #s(literal 1/2 binary64))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(/.f64 (.f64 #s(literal 4/3 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (cos.f64 (*.f64 x #s(literal 1/2 binary64))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(/.f64 (.f64 #s(literal 4/3 binary64) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (cos.f64 (*.f64 x #s(literal 1/2 binary64))))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 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 x (.f64 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 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 2/3 x)
(*.f64 #s(literal 2/3 binary64) x)
(* 2/3 x)
(*.f64 #s(literal 2/3 binary64) x)
(* 2/3 x)
(*.f64 #s(literal 2/3 binary64) x)
(* 2/3 x)
(*.f64 #s(literal 2/3 binary64) x)
(* 2/3 x)
(*.f64 #s(literal 2/3 binary64) x)
(* 2/3 x)
(*.f64 #s(literal 2/3 binary64) x)
(* 2/3 x)
(*.f64 #s(literal 2/3 binary64) x)
(* 2/3 x)
(*.f64 #s(literal 2/3 binary64) x)
(* 2/3 x)
(*.f64 #s(literal 2/3 binary64) x)
(* 2/3 x)
(*.f64 #s(literal 2/3 binary64) x)
(* 2/3 x)
(*.f64 #s(literal 2/3 binary64) x)
(* 2/3 x)
(*.f64 #s(literal 2/3 binary64) x)
(/ 3/2 x)
(/.f64 #s(literal 3/2 binary64) x)
(/ 3/2 x)
(/.f64 #s(literal 3/2 binary64) x)
(/ 3/2 x)
(/.f64 #s(literal 3/2 binary64) x)
(/ 3/2 x)
(/.f64 #s(literal 3/2 binary64) x)
(/ 3/2 x)
(/.f64 #s(literal 3/2 binary64) x)
(/ 3/2 x)
(/.f64 #s(literal 3/2 binary64) x)
(/ 3/2 x)
(/.f64 #s(literal 3/2 binary64) x)
(/ 3/2 x)
(/.f64 #s(literal 3/2 binary64) x)
(/ 3/2 x)
(/.f64 #s(literal 3/2 binary64) x)
(/ 3/2 x)
(/.f64 #s(literal 3/2 binary64) x)
(/ 3/2 x)
(/.f64 #s(literal 3/2 binary64) x)
(/ 3/2 x)
(/.f64 #s(literal 3/2 binary64) x)
(* 2/3 x)
(*.f64 #s(literal 2/3 binary64) x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 1/18 binary64)))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
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(.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (*.f64 x x) #s(literal -1/480 binary64))))
(* -1 (* (pow x 3) (+ 1/480 (* 1/8 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (*.f64 x x) #s(literal -1/480 binary64))))

eval186.0ms (2%)

Compiler: Compiled 29424 to 2562 computations (91.3% saved)

prune120.0ms (1.3%)

Pruning

26 alts after pruning (21 fresh and 5 done)

	Pruned	Kept	Total
New	1276	13	1289
Fresh	5	8	13
Picked	1	4	5
Done	2	1	3
Total	1284	26	1310

Accuracy

100.0%

Counts

1310 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	60.9%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 3/4 binary64)) (sin.f64 x))
	60.8%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (sin.f64 x) #s(literal 3/4 binary64)))
	60.6%	(/.f64 (+.f64 #s(literal 4/3 binary64) (*.f64 #s(literal -4/3 binary64) (cos.f64 x))) (sin.f64 x))
▶	99.6%	(/.f64 (*.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal 3/4 binary64))
	99.3%	(/.f64 (*.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 4/3 binary64)) (cos.f64 (/.f64 x #s(literal 2 binary64))))
	43.0%	(/.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))) #s(literal 3/4 binary64))
✓	99.7%	(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64))
	43.8%	(/.f64 x (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64))))))
▶	43.0%	(/.f64 x #s(literal 3/2 binary64))
	99.4%	(/.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
	42.8%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2/3 binary64)))
	43.7%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/480 binary64) (.f64 (.f64 x x) #s(literal -1/20160 binary64))))))) x))
	43.7%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))) x))
✓	42.9%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/2 binary64) x))
	99.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/4 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
▶	2.4%	(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/480 binary64)))
▶	99.4%	(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 3/4 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
	42.8%	(/.f64 #s(literal 2/3 binary64) (/.f64 #s(literal 1 binary64) x))
	2.4%	(/.f64 #s(literal -480 binary64) (.f64 x (.f64 x x)))
	43.6%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (*.f64 x x) #s(literal -1/480 binary64)))))) x)
	42.6%	(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/48 binary64))))) (+.f64 #s(literal 4/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64))))))))
	99.4%	(.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 3/4 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))))
▶	42.9%	(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 x (*.f64 x #s(literal 17/30240 binary64)))))))))
	42.8%	(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 1/18 binary64)))))
✓	99.4%	(*.f64 #s(literal 4/3 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))
✓	42.8%	(*.f64 #s(literal 2/3 binary64) x)

Compiler

Compiled 572 to 408 computations (28.7% saved)

simplify69.0ms (0.7%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(tan.f64 (/.f64 x #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))
✓	cost-diff	128	(*.f64 #s(literal 3/4 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 3/4 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 x (.f64 x #s(literal 17/30240 binary64)))))))
✓	cost-diff	0	(+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 x (.f64 x #s(literal 17/30240 binary64))))))))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 x (*.f64 x #s(literal 17/30240 binary64)))))))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 x (.f64 x x))
✓	cost-diff	0	(.f64 (.f64 x (*.f64 x x)) #s(literal -1/480 binary64))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/480 binary64)))
✓	cost-diff	0	(/.f64 x #s(literal 3/2 binary64))
✓	cost-diff	0	(/.f64 x #s(literal 2 binary64))
✓	cost-diff	0	(sin.f64 (/.f64 x #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 (*.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal 3/4 binary64))
✓	cost-diff	128	(*.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))))

Rules

1572×	`fma-define`
1312×	`fma-lowering-fma.f32`
1312×	`fma-lowering-fma.f64`
502×	`-lowering-.f32`
502×	`-lowering-.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	183
1	90	167
2	250	167
3	644	167
4	1260	167
5	1795	167
6	2032	167
7	2034	167
0	2034	167

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ (* (sin (/ x 2)) (/ 1 (cos (/ x 2)))) 3/4)
(* (sin (/ x 2)) (/ 1 (cos (/ x 2))))
(sin (/ x 2))
(/ x 2)
x
2
(/ 1 (cos (/ x 2)))
1
(cos (/ x 2))
3/4
(/ x 3/2)
x
3/2
(/ 1 (* (* x (* x x)) -1/480))
1
(* (* x (* x x)) -1/480)
(* x (* x x))
x
(* x x)
-1/480
(* x (+ 2/3 (* (* x x) (+ 1/18 (* (* x x) (+ 1/180 (* x (* x 17/30240))))))))
x
(+ 2/3 (* (* x x) (+ 1/18 (* (* x x) (+ 1/180 (* x (* x 17/30240)))))))
2/3
(* (* x x) (+ 1/18 (* (* x x) (+ 1/180 (* x (* x 17/30240))))))
(* x x)
(+ 1/18 (* (* x x) (+ 1/180 (* x (* x 17/30240)))))
1/18
(* (* x x) (+ 1/180 (* x (* x 17/30240))))
(+ 1/180 (* x (* x 17/30240)))
1/180
(* x (* x 17/30240))
(* x 17/30240)
17/30240
(/ 1 (* 3/4 (/ 1 (tan (/ x 2)))))
1
(* 3/4 (/ 1 (tan (/ x 2))))
3/4
(/ 1 (tan (/ x 2)))
(tan (/ x 2))
(/ x 2)
x
2

Outputs
(/ (* (sin (/ x 2)) (/ 1 (cos (/ x 2)))) 3/4)
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64)))
(* (sin (/ x 2)) (/ 1 (cos (/ x 2))))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(sin (/ x 2))
(sin.f64 (/.f64 x #s(literal 2 binary64)))
(/ x 2)
(/.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
(/ 1 (cos (/ x 2)))
(/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))
1
#s(literal 1 binary64)
(cos (/ x 2))
(cos.f64 (/.f64 x #s(literal 2 binary64)))
3/4
#s(literal 3/4 binary64)
(/ x 3/2)
(/.f64 x #s(literal 3/2 binary64))
x
3/2
#s(literal 3/2 binary64)
(/ 1 (* (* x (* x x)) -1/480))
(/.f64 #s(literal -480 binary64) (.f64 x (.f64 x x)))
1
#s(literal 1 binary64)
(* (* x (* x x)) -1/480)
(.f64 x (.f64 (*.f64 x x) #s(literal -1/480 binary64)))
(* x (* x x))
(.f64 x (.f64 x x))
x
(* x x)
(*.f64 x x)
-1/480
#s(literal -1/480 binary64)
(* x (+ 2/3 (* (* x x) (+ 1/18 (* (* x x) (+ 1/180 (* x (* x 17/30240))))))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 (*.f64 x x) #s(literal 17/30240 binary64))))))))
x
(+ 2/3 (* (* x x) (+ 1/18 (* (* x x) (+ 1/180 (* x (* x 17/30240)))))))
(+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 (.f64 x x) #s(literal 17/30240 binary64)))))))
2/3
#s(literal 2/3 binary64)
(* (* x x) (+ 1/18 (* (* x x) (+ 1/180 (* x (* x 17/30240))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 (.f64 x x) #s(literal 17/30240 binary64))))))
(* x x)
(*.f64 x x)
(+ 1/18 (* (* x x) (+ 1/180 (* x (* x 17/30240)))))
(+.f64 #s(literal 1/18 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 (.f64 x x) #s(literal 17/30240 binary64)))))
1/18
#s(literal 1/18 binary64)
(* (* x x) (+ 1/180 (* x (* x 17/30240))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 (.f64 x x) #s(literal 17/30240 binary64))))
(+ 1/180 (* x (* x 17/30240)))
(+.f64 #s(literal 1/180 binary64) (.f64 (.f64 x x) #s(literal 17/30240 binary64)))
1/180
#s(literal 1/180 binary64)
(* x (* x 17/30240))
(.f64 (.f64 x x) #s(literal 17/30240 binary64))
(* x 17/30240)
(*.f64 x #s(literal 17/30240 binary64))
17/30240
#s(literal 17/30240 binary64)
(/ 1 (* 3/4 (/ 1 (tan (/ x 2)))))
(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64))
1
#s(literal 1 binary64)
(* 3/4 (/ 1 (tan (/ x 2))))
(/.f64 #s(literal 3/4 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))
3/4
#s(literal 3/4 binary64)
(/ 1 (tan (/ x 2)))
(/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(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)

localize255.0ms (2.7%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 3/4 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
✓	accuracy	99.5%	(*.f64 #s(literal 3/4 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
✓	accuracy	99.8%	(.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 x (.f64 x #s(literal 17/30240 binary64)))))))
✓	accuracy	99.8%	(.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 x (.f64 x #s(literal 17/30240 binary64)))))
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal 17/30240 binary64)))
✓	accuracy	99.7%	(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 x (*.f64 x #s(literal 17/30240 binary64)))))))))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.8%	(.f64 x (.f64 x x))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/480 binary64)))
✓	accuracy	99.5%	(.f64 (.f64 x (*.f64 x x)) #s(literal -1/480 binary64))
✓	accuracy	100.0%	(/.f64 x #s(literal 3/2 binary64))
✓	accuracy	100.0%	(sin.f64 (/.f64 x #s(literal 2 binary64)))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))
✓	accuracy	99.7%	(/.f64 (*.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal 3/4 binary64))
✓	accuracy	99.7%	(*.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))))

Results

190.0ms

256×

valid

Compiler

Compiled 218 to 34 computations (84.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 83.0ms

ival-sin: 18.0ms (21.6% of total)

...c/correct-round.rkt:119:19: 17.0ms (20.4% of total)

ival-div: 16.0ms (19.2% of total)

ival-mult: 16.0ms (19.2% of total)

ival-tan: 6.0ms (7.2% of total)

ival-cos: 6.0ms (7.2% of total)

ival-add: 3.0ms (3.6% of total)

const: 1.0ms (1.2% of total)

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

series11.0ms (0.1%)

Counts

19 → 228

Calls

Call 1

Inputs
#<alt (* (sin (/ x 2)) (/ 1 (cos (/ x 2))))>
#<alt (/ (* (sin (/ x 2)) (/ 1 (cos (/ x 2)))) 3/4)>
#<alt (sin (/ x 2))>
#<alt (/ x 2)>
#<alt (/ x 3/2)>
#<alt (/ 1 (* (* x (* x x)) -1/480))>
#<alt (* (* x (* x x)) -1/480)>
#<alt (* x (* x x))>
#<alt (* x x)>
#<alt (* x (+ 2/3 (* (* x x) (+ 1/18 (* (* x x) (+ 1/180 (* x (* x 17/30240))))))))>
#<alt (+ 2/3 (* (* x x) (+ 1/18 (* (* x x) (+ 1/180 (* x (* x 17/30240)))))))>
#<alt (* (* x x) (+ 1/18 (* (* x x) (+ 1/180 (* x (* x 17/30240))))))>
#<alt (/ 1 (* 3/4 (/ 1 (tan (/ x 2)))))>
#<alt (* 3/4 (/ 1 (tan (/ x 2))))>
#<alt (/ 1 (tan (/ x 2)))>
#<alt (tan (/ x 2))>
#<alt (/ 1 (cos (/ x 2)))>
#<alt (* x (* x 17/30240))>
#<alt (* (* x x) (+ 1/180 (* x (* x 17/30240))))>

Outputs
#<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 (* 2/3 x)>
#<alt (* x (+ 2/3 (* 1/18 (pow x 2))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/48 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 1/2 x))>
#<alt (sin (* 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 (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (/ -480 (pow x 3))>
#<alt (/ -480 (pow x 3))>
#<alt (/ -480 (pow x 3))>
#<alt (/ -480 (pow x 3))>
#<alt (/ -480 (pow x 3))>
#<alt (/ -480 (pow x 3))>
#<alt (/ -480 (pow x 3))>
#<alt (/ -480 (pow x 3))>
#<alt (/ -480 (pow x 3))>
#<alt (/ -480 (pow x 3))>
#<alt (/ -480 (pow x 3))>
#<alt (/ -480 (pow x 3))>
#<alt (* -1/480 (pow x 3))>
#<alt (* -1/480 (pow x 3))>
#<alt (* -1/480 (pow x 3))>
#<alt (* -1/480 (pow x 3))>
#<alt (* -1/480 (pow x 3))>
#<alt (* -1/480 (pow x 3))>
#<alt (* -1/480 (pow x 3))>
#<alt (* -1/480 (pow x 3))>
#<alt (* -1/480 (pow x 3))>
#<alt (* -1/480 (pow x 3))>
#<alt (* -1/480 (pow x 3))>
#<alt (* -1/480 (pow x 3))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<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 (* 2/3 x)>
#<alt (* x (+ 2/3 (* 1/18 (pow x 2))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))>
#<alt (* 17/30240 (pow x 7))>
#<alt (* (pow x 7) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))>
#<alt (* (pow x 7) (+ 17/30240 (+ (/ 1/18 (pow x 4)) (* 1/180 (/ 1 (pow x 2))))))>
#<alt (* (pow x 7) (+ 17/30240 (+ (/ 1/18 (pow x 4)) (+ (* 1/180 (/ 1 (pow x 2))) (* 2/3 (/ 1 (pow x 6)))))))>
#<alt (* 17/30240 (pow x 7))>
#<alt (* (pow x 7) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/180 (* 1/18 (/ 1 (pow x 2)))) (pow x 2))) 17/30240)))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/18 (* 2/3 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))))>
#<alt 2/3>
#<alt (+ 2/3 (* 1/18 (pow x 2)))>
#<alt (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2)))))>
#<alt (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2)))))))>
#<alt (* 17/30240 (pow x 6))>
#<alt (* (pow x 6) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 17/30240 (+ (/ 1/18 (pow x 4)) (* 1/180 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 17/30240 (+ (/ 1/18 (pow x 4)) (+ (* 1/180 (/ 1 (pow x 2))) (* 2/3 (/ 1 (pow x 6)))))))>
#<alt (* 17/30240 (pow x 6))>
#<alt (* (pow x 6) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 17/30240 (+ (/ 1/18 (pow x 4)) (* 1/180 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 17/30240 (+ (/ 1/18 (pow x 4)) (+ (* 1/180 (/ 1 (pow x 2))) (* 2/3 (/ 1 (pow x 6)))))))>
#<alt (* 1/18 (pow x 2))>
#<alt (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))>
#<alt (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))>
#<alt (* 17/30240 (pow x 6))>
#<alt (* (pow x 6) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 17/30240 (+ (/ 1/18 (pow x 4)) (* 1/180 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 17/30240 (+ (/ 1/18 (pow x 4)) (* 1/180 (/ 1 (pow x 2))))))>
#<alt (* 17/30240 (pow x 6))>
#<alt (* (pow x 6) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 17/30240 (+ (/ 1/18 (pow x 4)) (* 1/180 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 17/30240 (+ (/ 1/18 (pow x 4)) (* 1/180 (/ 1 (pow x 2))))))>
#<alt (* 2/3 x)>
#<alt (* x (+ 2/3 (* 1/18 (pow x 2))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))>
#<alt (* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))>
#<alt (/ 3/2 x)>
#<alt (/ (+ 3/2 (* -1/8 (pow x 2))) x)>
#<alt (/ (+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))) x)>
#<alt (/ (+ 3/2 (* (pow x 2) (- (* (pow x 2) (- (* -1/20160 (pow x 2)) 1/480)) 1/8))) x)>
#<alt (* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))>
#<alt (* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))>
#<alt (* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))>
#<alt (* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))>
#<alt (* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))>
#<alt (* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))>
#<alt (* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))>
#<alt (* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))>
#<alt (/ 2 x)>
#<alt (/ (+ 2 (* -1/6 (pow x 2))) x)>
#<alt (/ (+ 2 (* (pow x 2) (- (* -1/360 (pow x 2)) 1/6))) x)>
#<alt (/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/15120 (pow x 2)) 1/360)) 1/6))) x)>
#<alt (/ (cos (* 1/2 x)) (sin (* 1/2 x)))>
#<alt (/ (cos (* 1/2 x)) (sin (* 1/2 x)))>
#<alt (/ (cos (* 1/2 x)) (sin (* 1/2 x)))>
#<alt (/ (cos (* 1/2 x)) (sin (* 1/2 x)))>
#<alt (/ (cos (* 1/2 x)) (sin (* 1/2 x)))>
#<alt (/ (cos (* 1/2 x)) (sin (* 1/2 x)))>
#<alt (/ (cos (* 1/2 x)) (sin (* 1/2 x)))>
#<alt (/ (cos (* 1/2 x)) (sin (* 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>
#<alt (+ 1 (* 1/8 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (+ 1/8 (* 5/384 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 5/384 (* 61/46080 (pow x 2)))))))>
#<alt (/ 1 (cos (* 1/2 x)))>
#<alt (/ 1 (cos (* 1/2 x)))>
#<alt (/ 1 (cos (* 1/2 x)))>
#<alt (/ 1 (cos (* 1/2 x)))>
#<alt (/ 1 (cos (* 1/2 x)))>
#<alt (/ 1 (cos (* 1/2 x)))>
#<alt (/ 1 (cos (* 1/2 x)))>
#<alt (/ 1 (cos (* 1/2 x)))>
#<alt (* 17/30240 (pow x 2))>
#<alt (* 17/30240 (pow x 2))>
#<alt (* 17/30240 (pow x 2))>
#<alt (* 17/30240 (pow x 2))>
#<alt (* 17/30240 (pow x 2))>
#<alt (* 17/30240 (pow x 2))>
#<alt (* 17/30240 (pow x 2))>
#<alt (* 17/30240 (pow x 2))>
#<alt (* 17/30240 (pow x 2))>
#<alt (* 17/30240 (pow x 2))>
#<alt (* 17/30240 (pow x 2))>
#<alt (* 17/30240 (pow x 2))>
#<alt (* 1/180 (pow x 2))>
#<alt (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))>
#<alt (* 17/30240 (pow x 4))>
#<alt (* (pow x 4) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))>
#<alt (* 17/30240 (pow x 4))>
#<alt (* (pow x 4) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))>

Calls

57 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/ 1 (* (* x (* x x)) -1/480))
1.0ms	x	@	inf	(* 3/4 (/ 1 (tan (/ x 2))))
1.0ms	x	@	-inf	(* 3/4 (/ 1 (tan (/ x 2))))
0.0ms	x	@	inf	(/ 1 (tan (/ x 2)))
0.0ms	x	@	-inf	(/ 1 (tan (/ x 2)))

rewrite369.0ms (3.9%)

Algorithm

1×	batch-egg-rewrite

Rules

4494×	`-lowering-.f32`
4494×	`-lowering-.f64`
3114×	`/-lowering-/.f32`
3114×	`/-lowering-/.f64`
2002×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	123
1	185	113
2	1233	113
0	8388	113

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 528

Calls

Call 1

Inputs
(* (sin (/ x 2)) (/ 1 (cos (/ x 2))))
(/ (* (sin (/ x 2)) (/ 1 (cos (/ x 2)))) 3/4)
(sin (/ x 2))
(/ x 2)
(/ x 3/2)
(/ 1 (* (* x (* x x)) -1/480))
(* (* x (* x x)) -1/480)
(* x (* x x))
(* x x)
(* x (+ 2/3 (* (* x x) (+ 1/18 (* (* x x) (+ 1/180 (* x (* x 17/30240))))))))
(+ 2/3 (* (* x x) (+ 1/18 (* (* x x) (+ 1/180 (* x (* x 17/30240)))))))
(* (* x x) (+ 1/18 (* (* x x) (+ 1/180 (* x (* x 17/30240))))))
(/ 1 (* 3/4 (/ 1 (tan (/ x 2)))))
(* 3/4 (/ 1 (tan (/ x 2))))
(/ 1 (tan (/ x 2)))
(tan (/ x 2))
(/ 1 (cos (/ x 2)))
(* x (* x 17/30240))
(* (* x x) (+ 1/180 (* x (* x 17/30240))))

Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (log.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(neg.f64 (-.f64 #s(literal 0 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(neg.f64 (tan.f64 (/.f64 x #s(literal -2 binary64))))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64))
(*.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(*.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (sin.f64 (/.f64 x #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))))
(*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(*.f64 #s(literal -1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(*.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 3/4 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal -3/4 binary64)))
(neg.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal -3/4 binary64)))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64))))
(neg.f64 (*.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal -3/4 binary64)) #s(literal 1 binary64)))
(neg.f64 (*.f64 #s(literal -4/3 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(neg.f64 (/.f64 #s(literal 4/3 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(neg.f64 (/.f64 #s(literal -4/3 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 #s(literal 3/4 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/4 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64))))
(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/4 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -3/4 binary64))
(/.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal -4/3 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (neg.f64 (*.f64 #s(literal 3/4 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 3/4 binary64)))
(/.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64)) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (neg.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64))) (-.f64 #s(literal 0 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(pow.f64 (/.f64 #s(literal 3/4 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 #s(literal 3/4 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 3/4 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 3/4 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 #s(literal 3/4 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))) #s(literal -1 binary64))
(.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 3/4 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))))
(*.f64 #s(literal 1 binary64) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64)))
(*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 4/3 binary64))
(*.f64 (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal -3/4 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -4/3 binary64))
(*.f64 #s(literal 4/3 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 3/4 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))) (sin.f64 (/.f64 x #s(literal 2 binary64))))
(*.f64 #s(literal -4/3 binary64) (-.f64 #s(literal 0 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 (/.f64 #s(literal 3/4 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 3/4 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(*.f64 (pow.f64 (/.f64 #s(literal 3/4 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(sin.f64 (/.f64 x #s(literal 2 binary64)))
(neg.f64 (sin.f64 (/.f64 x #s(literal -2 binary64))))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64))
(*.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 x #s(literal -2 binary64)))
(neg.f64 (/.f64 x #s(literal -2 binary64)))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 x #s(literal -2 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) x)))
(/.f64 x #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 x #s(literal 2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 x #s(literal -2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
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(/.f64 (neg.f64 (+.f64 (.f64 #s(literal 1/5832000 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/27653197824000 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (neg.f64 (+.f64 (.f64 #s(literal 1/32400 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 289/914457600 binary64))) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 (.f64 x x) #s(literal 1/180 binary64)) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 17/30240 binary64)))))))))
(/.f64 (neg.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/180 binary64) (.f64 (.f64 x x) #s(literal 17/30240 binary64))))) (-.f64 (.f64 (.f64 x x) #s(literal 1/180 binary64)) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 17/30240 binary64))))))) (neg.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/180 binary64)) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 17/30240 binary64)))))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/5832000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/27653197824000 binary64)))))) (+.f64 (neg.f64 (.f64 (.f64 (.f64 x x) #s(literal 17/30240 binary64)) (+.f64 (.f64 (*.f64 x x) #s(literal 17/30240 binary64)) #s(literal -1/180 binary64)))) #s(literal -1/32400 binary64)))
(/.f64 (neg.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/32400 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -289/914457600 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/180 binary64) (.f64 (.f64 x x) #s(literal 17/30240 binary64)))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/5832000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/27653197824000 binary64)))) (.f64 x x))) (+.f64 (neg.f64 (.f64 (.f64 (.f64 x x) #s(literal 17/30240 binary64)) (+.f64 (.f64 (*.f64 x x) #s(literal 17/30240 binary64)) #s(literal -1/180 binary64)))) #s(literal -1/32400 binary64)))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/32400 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -289/914457600 binary64))) (.f64 x x))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/180 binary64) (.f64 (.f64 x x) #s(literal 17/30240 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/27653197824000 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 #s(literal 1/5832000 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 289/914457600 binary64))) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 #s(literal 1/32400 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 17/30240 binary64)))) (.f64 (*.f64 x x) #s(literal 1/180 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 289/914457600 binary64))) (.f64 (.f64 x x) (.f64 x x))) (.f64 #s(literal 1/32400 binary64) (.f64 (.f64 x x) (.f64 x x)))) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 17/30240 binary64)))) (.f64 (.f64 x x) #s(literal 1/180 binary64))))
(.f64 x (.f64 x (+.f64 #s(literal 1/180 binary64) (.f64 (.f64 x x) #s(literal 17/30240 binary64)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 (.f64 x x) #s(literal 17/30240 binary64))))
(.f64 (+.f64 #s(literal 1/180 binary64) (.f64 (.f64 x x) #s(literal 17/30240 binary64))) (.f64 x x))
(.f64 (.f64 x (+.f64 #s(literal 1/180 binary64) (.f64 (.f64 x x) #s(literal 17/30240 binary64)))) x)
(.f64 (+.f64 (.f64 #s(literal 1/5832000 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/27653197824000 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/32400 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 289/914457600 binary64))) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 (.f64 x x) #s(literal 1/180 binary64)) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 17/30240 binary64)))))))))
(.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/180 binary64) (.f64 (.f64 x x) #s(literal 17/30240 binary64))))) (-.f64 (.f64 (.f64 x x) #s(literal 1/180 binary64)) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 17/30240 binary64)))))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/180 binary64)) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 17/30240 binary64)))))))
(.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/5832000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/27653197824000 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/32400 binary64) (.f64 (.f64 (.f64 x x) #s(literal 17/30240 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 17/30240 binary64)) #s(literal -1/180 binary64))))))
(.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/32400 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -289/914457600 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/180 binary64) (.f64 (*.f64 x x) #s(literal 17/30240 binary64)))))
(.f64 (.f64 (+.f64 #s(literal 1/5832000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 4913/27653197824000 binary64)))) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/32400 binary64) (.f64 (.f64 (.f64 x x) #s(literal 17/30240 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 17/30240 binary64)) #s(literal -1/180 binary64))))))
(.f64 (.f64 (+.f64 #s(literal 1/32400 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -289/914457600 binary64))) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/180 binary64) (.f64 (*.f64 x x) #s(literal 17/30240 binary64)))))

simplify363.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

3006×	`-lowering-.f32`
3006×	`-lowering-.f64`
2816×	`+-lowering-+.f64`
2816×	`+-lowering-+.f32`
1826×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	176	1824
1	487	1625
2	1409	1622
3	3906	1614
4	6556	1614
0	8420	1614

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

Calls

Call 1

Inputs
(* 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)))
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 1/2 x)
(* x (+ 1/2 (* -1/48 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 1/2 x))
(sin (* 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)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(/ -480 (pow x 3))
(/ -480 (pow x 3))
(/ -480 (pow x 3))
(/ -480 (pow x 3))
(/ -480 (pow x 3))
(/ -480 (pow x 3))
(/ -480 (pow x 3))
(/ -480 (pow x 3))
(/ -480 (pow x 3))
(/ -480 (pow x 3))
(/ -480 (pow x 3))
(/ -480 (pow x 3))
(* -1/480 (pow x 3))
(* -1/480 (pow x 3))
(* -1/480 (pow x 3))
(* -1/480 (pow x 3))
(* -1/480 (pow x 3))
(* -1/480 (pow x 3))
(* -1/480 (pow x 3))
(* -1/480 (pow x 3))
(* -1/480 (pow x 3))
(* -1/480 (pow x 3))
(* -1/480 (pow x 3))
(* -1/480 (pow x 3))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(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)
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 17/30240 (pow x 7))
(* (pow x 7) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 17/30240 (+ (/ 1/18 (pow x 4)) (* 1/180 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 17/30240 (+ (/ 1/18 (pow x 4)) (+ (* 1/180 (/ 1 (pow x 2))) (* 2/3 (/ 1 (pow x 6)))))))
(* 17/30240 (pow x 7))
(* (pow x 7) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/180 (* 1/18 (/ 1 (pow x 2)))) (pow x 2))) 17/30240)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/18 (* 2/3 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))))
2/3
(+ 2/3 (* 1/18 (pow x 2)))
(+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2)))))
(+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2)))))))
(* 17/30240 (pow x 6))
(* (pow x 6) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/30240 (+ (/ 1/18 (pow x 4)) (* 1/180 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 17/30240 (+ (/ 1/18 (pow x 4)) (+ (* 1/180 (/ 1 (pow x 2))) (* 2/3 (/ 1 (pow x 6)))))))
(* 17/30240 (pow x 6))
(* (pow x 6) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/30240 (+ (/ 1/18 (pow x 4)) (* 1/180 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 17/30240 (+ (/ 1/18 (pow x 4)) (+ (* 1/180 (/ 1 (pow x 2))) (* 2/3 (/ 1 (pow x 6)))))))
(* 1/18 (pow x 2))
(* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))
(* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))
(* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))
(* 17/30240 (pow x 6))
(* (pow x 6) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/30240 (+ (/ 1/18 (pow x 4)) (* 1/180 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 17/30240 (+ (/ 1/18 (pow x 4)) (* 1/180 (/ 1 (pow x 2))))))
(* 17/30240 (pow x 6))
(* (pow x 6) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/30240 (+ (/ 1/18 (pow x 4)) (* 1/180 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 17/30240 (+ (/ 1/18 (pow x 4)) (* 1/180 (/ 1 (pow x 2))))))
(* 2/3 x)
(* x (+ 2/3 (* 1/18 (pow x 2))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
(/ 3/2 x)
(/ (+ 3/2 (* -1/8 (pow x 2))) x)
(/ (+ 3/2 (* (pow x 2) (- (* -1/480 (pow x 2)) 1/8))) x)
(/ (+ 3/2 (* (pow x 2) (- (* (pow x 2) (- (* -1/20160 (pow x 2)) 1/480)) 1/8))) x)
(* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(/ 2 x)
(/ (+ 2 (* -1/6 (pow x 2))) x)
(/ (+ 2 (* (pow x 2) (- (* -1/360 (pow x 2)) 1/6))) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/15120 (pow x 2)) 1/360)) 1/6))) 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)) (sin (* 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
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/8 (* 5/384 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 5/384 (* 61/46080 (pow x 2)))))))
(/ 1 (cos (* 1/2 x)))
(/ 1 (cos (* 1/2 x)))
(/ 1 (cos (* 1/2 x)))
(/ 1 (cos (* 1/2 x)))
(/ 1 (cos (* 1/2 x)))
(/ 1 (cos (* 1/2 x)))
(/ 1 (cos (* 1/2 x)))
(/ 1 (cos (* 1/2 x)))
(* 17/30240 (pow x 2))
(* 17/30240 (pow x 2))
(* 17/30240 (pow x 2))
(* 17/30240 (pow x 2))
(* 17/30240 (pow x 2))
(* 17/30240 (pow x 2))
(* 17/30240 (pow x 2))
(* 17/30240 (pow x 2))
(* 17/30240 (pow x 2))
(* 17/30240 (pow x 2))
(* 17/30240 (pow x 2))
(* 17/30240 (pow x 2))
(* 1/180 (pow x 2))
(* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))
(* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))
(* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))
(* 17/30240 (pow x 4))
(* (pow x 4) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))
(* 17/30240 (pow x 4))
(* (pow x 4) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))

Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/240 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)))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* 1/18 (pow x 2))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (*.f64 x x) #s(literal 1/18 binary64))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* 1/180 (pow x 2))))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 (*.f64 x x) #s(literal 1/180 binary64))))))
(* x (+ 2/3 (* (pow x 2) (+ 1/18 (* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 (*.f64 x x) #s(literal 17/30240 binary64))))))))
(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
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(* 4/3 (/ (sin (* 1/2 x)) (cos (* 1/2 x))))
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(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 3/4 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) x))))
(* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 3/4 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) x))))
(* 3/4 (/ (cos (* 1/2 x)) (sin (* 1/2 x))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 3/4 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) x))))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* -1/6 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64)))) x)
(/ (+ 2 (* (pow x 2) (- (* -1/360 (pow x 2)) 1/6))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal -1/360 binary64)))))) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/15120 (pow x 2)) 1/360)) 1/6))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/360 binary64) (.f64 (.f64 x x) #s(literal -1/15120 binary64))))))) x)
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (cos (* 1/2 x)) (sin (* 1/2 x)))
(/.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.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 #s(literal 1/24 binary64) (*.f64 x x))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/240 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
#s(literal 1 binary64)
(+ 1 (* 1/8 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/8 binary64))))
(+ 1 (* (pow x 2) (+ 1/8 (* 5/384 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal 5/384 binary64))))))
(+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 5/384 (* 61/46080 (pow x 2)))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (+.f64 #s(literal 5/384 binary64) (.f64 (.f64 x x) #s(literal 61/46080 binary64))))))))
(/ 1 (cos (* 1/2 x)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) x)))
(/ 1 (cos (* 1/2 x)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) x)))
(/ 1 (cos (* 1/2 x)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) x)))
(/ 1 (cos (* 1/2 x)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) x)))
(/ 1 (cos (* 1/2 x)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) x)))
(/ 1 (cos (* 1/2 x)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) x)))
(/ 1 (cos (* 1/2 x)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) x)))
(/ 1 (cos (* 1/2 x)))
(/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) x)))
(* 17/30240 (pow x 2))
(.f64 (.f64 x x) #s(literal 17/30240 binary64))
(* 17/30240 (pow x 2))
(.f64 (.f64 x x) #s(literal 17/30240 binary64))
(* 17/30240 (pow x 2))
(.f64 (.f64 x x) #s(literal 17/30240 binary64))
(* 17/30240 (pow x 2))
(.f64 (.f64 x x) #s(literal 17/30240 binary64))
(* 17/30240 (pow x 2))
(.f64 (.f64 x x) #s(literal 17/30240 binary64))
(* 17/30240 (pow x 2))
(.f64 (.f64 x x) #s(literal 17/30240 binary64))
(* 17/30240 (pow x 2))
(.f64 (.f64 x x) #s(literal 17/30240 binary64))
(* 17/30240 (pow x 2))
(.f64 (.f64 x x) #s(literal 17/30240 binary64))
(* 17/30240 (pow x 2))
(.f64 (.f64 x x) #s(literal 17/30240 binary64))
(* 17/30240 (pow x 2))
(.f64 (.f64 x x) #s(literal 17/30240 binary64))
(* 17/30240 (pow x 2))
(.f64 (.f64 x x) #s(literal 17/30240 binary64))
(* 17/30240 (pow x 2))
(.f64 (.f64 x x) #s(literal 17/30240 binary64))
(* 1/180 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/180 binary64))
(* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 (.f64 x x) #s(literal 17/30240 binary64))))
(* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 (.f64 x x) #s(literal 17/30240 binary64))))
(* (pow x 2) (+ 1/180 (* 17/30240 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 (.f64 x x) #s(literal 17/30240 binary64))))
(* 17/30240 (pow x 4))
(.f64 x (.f64 #s(literal 17/30240 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 17/30240 binary64) (/.f64 #s(literal 1/180 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* (pow x 4) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 17/30240 binary64) (/.f64 #s(literal 1/180 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* (pow x 4) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 17/30240 binary64) (/.f64 #s(literal 1/180 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* 17/30240 (pow x 4))
(.f64 x (.f64 #s(literal 17/30240 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 17/30240 binary64) (/.f64 #s(literal 1/180 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* (pow x 4) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 17/30240 binary64) (/.f64 #s(literal 1/180 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(* (pow x 4) (+ 17/30240 (* 1/180 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 17/30240 binary64) (/.f64 #s(literal 1/180 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))

eval119.0ms (1.3%)

Compiler: Compiled 20184 to 1995 computations (90.1% saved)

prune126.0ms (1.3%)

Pruning

34 alts after pruning (25 fresh and 9 done)

	Pruned	Kept	Total
New	839	11	850
Fresh	2	14	16
Picked	1	4	5
Done	0	5	5
Total	842	34	876

Accuracy

100.0%

Counts

876 → 34

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	60.9%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 3/4 binary64)) (sin.f64 x))
	99.7%	(/.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64)) (cos.f64 (/.f64 x #s(literal 2 binary64))))
	2.4%	(/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal -1/480 binary64))
	2.4%	(/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x #s(literal -1/480 binary64))))
	60.8%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (sin.f64 x) #s(literal 3/4 binary64)))
	60.6%	(/.f64 (+.f64 #s(literal 4/3 binary64) (*.f64 #s(literal -4/3 binary64) (cos.f64 x))) (sin.f64 x))
	99.3%	(/.f64 (*.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 4/3 binary64)) (cos.f64 (/.f64 x #s(literal 2 binary64))))
	43.0%	(/.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))) #s(literal 3/4 binary64))
✓	99.7%	(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64))
	2.4%	(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x x) #s(literal 1/480 binary64)))
	43.8%	(/.f64 x (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64))))))
✓	43.0%	(/.f64 x #s(literal 3/2 binary64))
	99.4%	(/.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
	99.3%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 4/3 binary64)))
	42.8%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2/3 binary64)))
	43.7%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/480 binary64) (.f64 (.f64 x x) #s(literal -1/20160 binary64))))))) x))
	43.7%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))) x))
✓	42.9%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/2 binary64) x))
	99.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/4 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
✓	2.4%	(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/480 binary64)))
	2.4%	(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x #s(literal -1/480 binary64))) x))
	2.4%	(/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x #s(literal -1/480 binary64))))
	43.6%	(/.f64 #s(literal 1 binary64) (.f64 #s(literal 3/4 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal -1/360 binary64)))))) x)))
	43.6%	(/.f64 #s(literal 1 binary64) (.f64 #s(literal 3/4 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))) x)))
✓	99.4%	(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 3/4 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
	42.8%	(/.f64 #s(literal 2/3 binary64) (/.f64 #s(literal 1 binary64) x))
	2.4%	(/.f64 #s(literal -480 binary64) (.f64 x (.f64 x x)))
	43.6%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (*.f64 x x) #s(literal -1/480 binary64)))))) x)
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 3/4 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))) (sin.f64 (/.f64 x #s(literal 2 binary64))))
	42.6%	(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/48 binary64))))) (+.f64 #s(literal 4/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64))))))))
✓	42.9%	(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 x (*.f64 x #s(literal 17/30240 binary64)))))))))
	42.8%	(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (*.f64 x x) #s(literal 1/18 binary64))))
✓	99.4%	(*.f64 #s(literal 4/3 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))
✓	42.8%	(*.f64 #s(literal 2/3 binary64) x)

Compiler

Compiled 1330 to 580 computations (56.4% saved)

regimes105.0ms (1.1%)

Counts

76 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 2/3 binary64) x)
(/.f64 x #s(literal 3/2 binary64))
(/.f64 #s(literal 2/3 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/2 binary64) x))
(/.f64 #s(literal -480 binary64) (.f64 x (.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2/3 binary64)))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 1/18 binary64)))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (*.f64 x x) #s(literal 1/18 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x #s(literal -1/480 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x #s(literal -1/480 binary64))) x))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/480 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x #s(literal -1/480 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal -1/480 binary64))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x x) #s(literal 1/480 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))) x))
(/.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))) #s(literal 3/4 binary64))
(/.f64 #s(literal 1 binary64) (.f64 #s(literal 3/4 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))) x)))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/18 binary64) (.f64 (*.f64 x x) #s(literal 1/180 binary64)))))))
(/.f64 x (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (*.f64 x x) #s(literal -1/480 binary64)))))) x)
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64)))))) x))
(/.f64 #s(literal 1 binary64) (.f64 #s(literal 3/4 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal -1/360 binary64)))))) x)))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/180 binary64) (.f64 (*.f64 x x) #s(literal 17/30240 binary64)))))))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 x (*.f64 x #s(literal 17/30240 binary64)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/480 binary64) (.f64 (.f64 x x) #s(literal -1/20160 binary64))))))) x))
(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/48 binary64))))) (+.f64 #s(literal 4/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64))))))))
(*.f64 #s(literal 4/3 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 4/3 binary64))
(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/4 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 #s(literal 2/3 binary64) (.f64 x x)) (sin.f64 x))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 3/4 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 4/3 binary64)))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 4/3 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(/.f64 (.f64 x (.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) #s(literal -1/18 binary64))))) (sin.f64 x))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/18 binary64) (.f64 x (.f64 x #s(literal 1/540 binary64)))))))) (sin.f64 x))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 4/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64))))))))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/18 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/540 binary64) (.f64 (.f64 x x) #s(literal -1/30240 binary64))))))))) (sin.f64 x))
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 4/3 binary64) (sin.f64 x)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) #s(literal 4/3 binary64))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 4/3 binary64)) (sin.f64 x))
(/.f64 (+.f64 #s(literal 4/3 binary64) (*.f64 #s(literal -4/3 binary64) (cos.f64 x))) (sin.f64 x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (sin.f64 x) #s(literal 3/4 binary64)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 3/4 binary64)) (sin.f64 x))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x)) #s(literal 3/4 binary64))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 3/8 binary64)) (/.f64 #s(literal 1/2 binary64) (sin.f64 x)))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal -3/4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 x) #s(literal 3/4 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 #s(literal 8/3 binary64) (/.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))))
(/.f64 (*.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 4/3 binary64)) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (+.f64 #s(literal 4/3 binary64) (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) #s(literal 8/3 binary64))) (sin.f64 x))
(/.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 3/4 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (/.f64 #s(literal 8/3 binary64) (sin.f64 x)) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (/.f64 #s(literal 8/3 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))) (sin.f64 x))
(/.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64)) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 3/4 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))))
(.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 8/3 binary64) (sin.f64 x))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 3/4 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))) (sin.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (*.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal 3/4 binary64))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))) #s(literal -3/4 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/8 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))))) (sin.f64 x))
(.f64 #s(literal 8/3 binary64) (/.f64 (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sin.f64 x)))
(/.f64 (.f64 #s(literal 8/3 binary64) (pow.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))) (sin.f64 x))
(-.f64 (/.f64 #s(literal 4/3 binary64) (sin.f64 x)) (*.f64 (cos.f64 x) (/.f64 #s(literal 4/3 binary64) (sin.f64 x))))
(.f64 #s(literal -8/3 binary64) (pow.f64 (.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal -2 binary64)) #s(literal -1 binary64)))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 8/3 binary64) (sin.f64 x))))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (*.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x)) #s(literal 8/3 binary64)))
(*.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x)) (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/8 binary64)))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (/.f64 (sin.f64 x) #s(literal 8/3 binary64)) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 8/3 binary64)) (sin.f64 (*.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))
(*.f64 (/.f64 #s(literal 8/3 binary64) (sin.f64 x)) (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))
(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/8 binary64)) (/.f64 #s(literal 1 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))))) (.f64 (.f64 (sin.f64 x) #s(literal 3/4 binary64)) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (*.f64 (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal -1/2 binary64)) #s(literal 3/8 binary64)))))

Outputs
(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64))

Calls

2 calls:

53.0ms	x
48.0ms	(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`(/.f64 (.f64 (.f64 (/.f64 #s(literal 8 binary64) #s(literal 3 binary64)) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))) (sin.f64 x))`

Compiler

Compiled 19 to 12 computations (36.8% saved)

regimes11.0ms (0.1%)

Counts

28 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 2/3 binary64) x)
(/.f64 x #s(literal 3/2 binary64))
(/.f64 #s(literal 2/3 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/2 binary64) x))
(/.f64 #s(literal -480 binary64) (.f64 x (.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2/3 binary64)))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 1/18 binary64)))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (*.f64 x x) #s(literal 1/18 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x #s(literal -1/480 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x #s(literal -1/480 binary64))) x))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/480 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x #s(literal -1/480 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal -1/480 binary64))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x x) #s(literal 1/480 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))) x))
(/.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))) #s(literal 3/4 binary64))
(/.f64 #s(literal 1 binary64) (.f64 #s(literal 3/4 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))) x)))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/18 binary64) (.f64 (*.f64 x x) #s(literal 1/180 binary64)))))))
(/.f64 x (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (*.f64 x x) #s(literal -1/480 binary64)))))) x)
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64)))))) x))
(/.f64 #s(literal 1 binary64) (.f64 #s(literal 3/4 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal -1/360 binary64)))))) x)))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/180 binary64) (.f64 (*.f64 x x) #s(literal 17/30240 binary64)))))))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 x (*.f64 x #s(literal 17/30240 binary64)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/480 binary64) (.f64 (.f64 x x) #s(literal -1/20160 binary64))))))) x))
(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/48 binary64))))) (+.f64 #s(literal 4/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64))))))))
(*.f64 #s(literal 4/3 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 4/3 binary64))

Outputs
(*.f64 #s(literal 4/3 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))

Calls

1 calls:

9.0ms

Results

Accuracy	Segments	Branch
99.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes10.0ms (0.1%)

Counts

26 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 2/3 binary64) x)
(/.f64 x #s(literal 3/2 binary64))
(/.f64 #s(literal 2/3 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/2 binary64) x))
(/.f64 #s(literal -480 binary64) (.f64 x (.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2/3 binary64)))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 1/18 binary64)))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (*.f64 x x) #s(literal 1/18 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x #s(literal -1/480 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x #s(literal -1/480 binary64))) x))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/480 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x #s(literal -1/480 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal -1/480 binary64))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x x) #s(literal 1/480 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))) x))
(/.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))) #s(literal 3/4 binary64))
(/.f64 #s(literal 1 binary64) (.f64 #s(literal 3/4 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))) x)))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/18 binary64) (.f64 (*.f64 x x) #s(literal 1/180 binary64)))))))
(/.f64 x (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (*.f64 x x) #s(literal -1/480 binary64)))))) x)
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64)))))) x))
(/.f64 #s(literal 1 binary64) (.f64 #s(literal 3/4 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 x x) #s(literal -1/360 binary64)))))) x)))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/180 binary64) (.f64 (*.f64 x x) #s(literal 17/30240 binary64)))))))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/18 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/180 binary64) (.f64 x (*.f64 x #s(literal 17/30240 binary64)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/480 binary64) (.f64 (.f64 x x) #s(literal -1/20160 binary64))))))) x))
(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/48 binary64))))) (+.f64 #s(literal 4/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 5/288 binary64) (.f64 (.f64 x x) #s(literal 61/34560 binary64))))))))

Outputs
(/.f64 x (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64))))))

Calls

1 calls:

8.0ms

Results

Accuracy	Segments	Branch
43.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes25.0ms (0.3%)

Counts

18 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 2/3 binary64) x)
(/.f64 x #s(literal 3/2 binary64))
(/.f64 #s(literal 2/3 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/2 binary64) x))
(/.f64 #s(literal -480 binary64) (.f64 x (.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2/3 binary64)))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 1/18 binary64)))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (*.f64 x x) #s(literal 1/18 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x #s(literal -1/480 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x #s(literal -1/480 binary64))) x))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/480 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x #s(literal -1/480 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal -1/480 binary64))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x x) #s(literal 1/480 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))) x))
(/.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))) #s(literal 3/4 binary64))
(/.f64 #s(literal 1 binary64) (.f64 #s(literal 3/4 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))) x)))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/18 binary64) (.f64 (*.f64 x x) #s(literal 1/180 binary64)))))))

Outputs
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))) x))

Calls

1 calls:

24.0ms

Results

Accuracy	Segments	Branch
43.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0.1%)

Counts

14 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 2/3 binary64) x)
(/.f64 x #s(literal 3/2 binary64))
(/.f64 #s(literal 2/3 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/2 binary64) x))
(/.f64 #s(literal -480 binary64) (.f64 x (.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2/3 binary64)))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 1/18 binary64)))))
(.f64 x (+.f64 #s(literal 2/3 binary64) (.f64 (*.f64 x x) #s(literal 1/18 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x #s(literal -1/480 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x #s(literal -1/480 binary64))) x))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/480 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x #s(literal -1/480 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal -1/480 binary64))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x x) #s(literal 1/480 binary64)))

Outputs
(/.f64 x #s(literal 3/2 binary64))

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
43.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 2/3 binary64) x)

Outputs
(*.f64 #s(literal 2/3 binary64) x)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
42.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
6×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	44
1	36	44

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64))
(*.f64 #s(literal 4/3 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 x (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))) x))
(/.f64 x #s(literal 3/2 binary64))
(*.f64 #s(literal 2/3 binary64) x)

Outputs
(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 3/4 binary64))
(*.f64 #s(literal 4/3 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 4/3 binary64))
(/.f64 x (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) #s(literal -1/480 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64))) x))
(/.f64 x #s(literal 3/2 binary64))
(*.f64 #s(literal 2/3 binary64) x)
(*.f64 x #s(literal 2/3 binary64))

soundness1.9s (20.3%)

Rules

5298×	`+-lowering-+.f64`
5298×	`+-lowering-+.f32`
4978×	`-lowering-.f32`
4978×	`-lowering-.f64`
3976×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	66
1	41	54
2	157	54
3	827	51
4	5954	51
0	8053	51
0	27	102
1	157	93
2	1018	93
0	8805	93
0	37	159
1	206	145
2	1467	140
0	8152	140
0	126	790
1	355	684
2	1041	684
3	2764	684
4	4237	684
5	7294	684
0	8029	684
0	261	2107
1	770	1832
2	2180	1832
3	4262	1802
4	7370	1802
0	8027	1802
0	12	14
1	19	10
2	30	10
3	39	10
4	42	10
0	42	10

Stop Event

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

Compiler

Compiled 214 to 139 computations (35% saved)

preprocess72.0ms (0.8%)

Remove: (negabs x)
Compiler: Compiled 200 to 130 computations (35% saved)

analyze290.0ms (3.1%)

sample1.3s (13.9%)

preprocess74.0ms (0.8%)

explain150.0ms (1.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

localize99.0ms (1%)

series15.0ms (0.2%)

rewrite385.0ms (4.1%)

simplify220.0ms (2.3%)

eval239.0ms (2.5%)

prune238.0ms (2.5%)

simplify204.0ms (2.1%)

localize418.0ms (4.4%)

series17.0ms (0.2%)

rewrite416.0ms (4.4%)

simplify306.0ms (3.2%)

eval155.0ms (1.6%)

prune169.0ms (1.8%)

simplify122.0ms (1.3%)

localize262.0ms (2.8%)

series12.0ms (0.1%)

rewrite352.0ms (3.7%)

simplify234.0ms (2.5%)

eval186.0ms (2%)

prune120.0ms (1.3%)

simplify69.0ms (0.7%)

localize255.0ms (2.7%)

series11.0ms (0.1%)

rewrite369.0ms (3.9%)

simplify363.0ms (3.8%)

eval119.0ms (1.3%)

prune126.0ms (1.3%)

regimes105.0ms (1.1%)

regimes11.0ms (0.1%)

regimes10.0ms (0.1%)

regimes25.0ms (0.3%)

regimes5.0ms (0.1%)

regimes2.0ms (0%)

simplify9.0ms (0.1%)

soundness1.9s (20.3%)

preprocess72.0ms (0.8%)

end0.0ms (0%)

Profiling