Metrics for arccos

analyze8.0ms (0.1%)

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
0%	0%	100%	0%	0%	0%	0%	3
33.3%	25%	50%	0%	0%	25%	0%	4
60%	37.5%	25%	0%	0%	37.5%	0%	5
77.8%	43.7%	12.5%	0%	0%	43.7%	0%	6
88.2%	46.9%	6.2%	0%	0%	46.9%	0%	7
93.9%	48.4%	3.1%	0%	0%	48.4%	0%	8
96.9%	49.2%	1.6%	0%	0%	49.2%	0%	9
98.4%	49.6%	0.8%	0%	0%	49.6%	0%	10
99.2%	49.8%	0.4%	0%	0%	49.8%	0%	11
99.6%	49.9%	0.2%	0%	0%	49.9%	0%	12

Compiler

Compiled 13 to 10 computations (23.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-sub: 1.0ms (31.6% of total)

ival-div: 1.0ms (31.6% of total)

ival-sqrt: 1.0ms (31.6% of total)

ival-atan: 1.0ms (31.6% of total)

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

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

const: 0.0ms (0% of total)

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

sample933.0ms (16.1%)

Results

666.0ms	8256×	0	valid
19.0ms	23×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 450.0ms

ival-sqrt: 107.0ms (23.8% of total)

ival-atan: 85.0ms (18.9% of total)

ival-sub: 67.0ms (14.9% of total)

ival-mult: 61.0ms (13.6% of total)

ival-div: 60.0ms (13.3% of total)

ival-add: 54.0ms (12% of total)

const: 13.0ms (2.9% of total)

backward-pass: 3.0ms (0.7% of total)

Bogosity

preprocess67.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

1016×	`fnmadd-define`
792×	`sum3-define`
642×	`fma-define`
532×	`fmsub-define`
516×	`fnmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	35
1	42	33
2	74	33
3	151	33
4	321	33
5	757	33
6	2069	33
7	3086	33
8	3409	33
0	9	11
1	18	11
2	25	11
3	37	11
4	63	11
5	109	11
6	181	11
7	289	11
8	660	11
9	1213	11
10	1696	11
11	1716	11
0	1716	11

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))

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

Call 2

Inputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 (neg x)) (+ 1 (neg x))))))
(neg (* 2 (atan (sqrt (/ (- 1 (neg x)) (+ 1 (neg x)))))))

Outputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 (neg x)) (+ 1 (neg x))))))
(* 2 (atan (sqrt (/ (+ 1 x) (- 1 x)))))
(neg (* 2 (atan (sqrt (/ (- 1 (neg x)) (+ 1 (neg x)))))))
(* (atan (sqrt (/ (+ 1 x) (- 1 x)))) -2)

explain103.0ms (1.8%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(+.f64 #s(literal 1 binary64) x)`
-	-	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
-	-	`#s(literal 2 binary64)`
-	-	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`
-	-	`#s(literal 1 binary64)`
-	-	`(-.f64 #s(literal 1 binary64) x)`
-	-	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
-	-	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`

Results

69.0ms

512×

valid

Compiler

Compiled 104 to 29 computations (72.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-atan: 5.0ms (20.8% of total)

ival-sub: 4.0ms (16.7% of total)

ival-div: 4.0ms (16.7% of total)

ival-mult: 4.0ms (16.7% of total)

ival-sqrt: 4.0ms (16.7% of total)

ival-add: 3.0ms (12.5% of total)

const: 1.0ms (4.2% of total)

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

eval0.0ms (0%)

Compiler: Compiled 12 to 9 computations (25% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))

Compiler

Compiled 12 to 9 computations (25% saved)

simplify31.0ms (0.5%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
✓	cost-diff	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
✓	cost-diff	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
✓	cost-diff	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))

Rules

446×	`fnmadd-define`
400×	`sum3-define`
324×	`fma-define`
294×	`fmsub-define`
282×	`fnmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	44
1	18	44
2	25	44
3	37	44
4	63	44
5	109	44
6	181	44
7	289	44
8	660	44
9	1213	44
10	1696	44
11	1716	44
0	1716	44

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
2
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(sqrt (/ (- 1 x) (+ 1 x)))
(/ (- 1 x) (+ 1 x))
(- 1 x)
1
x
(+ 1 x)

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

localize47.0ms (0.8%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
✓	accuracy	100.0%	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
✓	accuracy	100.0%	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
✓	accuracy	100.0%	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))

Results

32.0ms

256×

valid

Compiler

Compiled 46 to 10 computations (78.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-sub: 3.0ms (20.3% of total)

ival-div: 3.0ms (20.3% of total)

ival-mult: 3.0ms (20.3% of total)

ival-sqrt: 2.0ms (13.6% of total)

ival-atan: 2.0ms (13.6% of total)

ival-add: 1.0ms (6.8% of total)

const: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (sqrt (/ (- 1 x) (+ 1 x)))>
#<alt (/ (- 1 x) (+ 1 x))>

Outputs
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))>
#<alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))>
#<alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))>
#<alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))>
#<alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))>
#<alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))>
#<alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))>
#<alt (sqrt -1)>
#<alt (+ (sqrt -1) (/ 1 (* x (sqrt -1))))>
#<alt (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))>
#<alt (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))>
#<alt (sqrt -1)>
#<alt (+ (sqrt -1) (/ 1 (* x (sqrt -1))))>
#<alt (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))>
#<alt (+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))>
#<alt 1>
#<alt (+ 1 (* -2 x))>
#<alt (+ 1 (* x (- (* 2 x) 2)))>
#<alt (+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))>
#<alt -1>
#<alt (- (* 2 (/ 1 x)) 1)>
#<alt (- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))>
#<alt (- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))>
#<alt -1>
#<alt (- (* 2 (/ 1 x)) 1)>
#<alt (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)>
#<alt (- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)>

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(sqrt (/ (- 1 x) (+ 1 x)))
1.0ms	x	@	-inf	(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
0.0ms	x	@	inf	(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
0.0ms	x	@	0	(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
0.0ms	x	@	-inf	(sqrt (/ (- 1 x) (+ 1 x)))

rewrite136.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

888×	`-lowering-.f32`
888×	`-lowering-.f64`
778×	`/-lowering-/.f32`
778×	`/-lowering-/.f64`
364×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	35
1	29	35
2	105	35
3	533	35
0	2544	35

Stop Event

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

Counts

4 → 194

Calls

Call 1

Inputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(sqrt (/ (- 1 x) (+ 1 x)))
(/ (- 1 x) (+ 1 x))

Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(neg.f64 (atan.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)))
(exp.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/2 binary64) (log1p.f64 x))))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(neg.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(neg.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))))
(neg.f64 (/.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))) (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 #s(literal -1 binary64) x))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (+.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) x) (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))) (-.f64 #s(literal -1 binary64) x))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))) (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (*.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (/.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) #s(literal -1 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
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(/.f64 (+.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) x)) (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x)))
(/.f64 (+.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (-.f64 #s(literal -1 binary64) x) x)) (/.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) x) x)) (-.f64 #s(literal -1 binary64) x)) (/.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) x)) (.f64 (-.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) x)) (.f64 (-.f64 #s(literal -1 binary64) x) (+.f64 x #s(literal -1 binary64)))) (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x)))
(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (.f64 x (+.f64 #s(literal 1 binary64) x)))) (.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))) (-.f64 #s(literal -1 binary64) x)) (.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))))
(/.f64 (neg.f64 (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 #s(literal -1 binary64) x))) (/.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (+.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) x) (+.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal -1 binary64) x))
(/.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal -1 binary64) x))
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) x) (+.f64 #s(literal 1 binary64) x))) (/.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))) (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x)))
(/.f64 (.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 #s(literal -1 binary64) x)) #s(literal 1 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (*.f64 (+.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 #s(literal -1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) x))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) x))
(/.f64 (/.f64 (+.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) x))
(/.f64 (/.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))
(pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(*.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(*.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (exp.f64 (log.f64 (-.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x)))
(.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))
(.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (+.f64 x #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x)) #s(literal -1 binary64))
(*.f64 (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x)))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(*.f64 (exp.f64 (log.f64 (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(*.f64 (exp.f64 (log.f64 (+.f64 x #s(literal -1 binary64)))) (exp.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))))

simplify205.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

2544×	`-lowering-.f32`
2544×	`-lowering-.f64`
1990×	`+-lowering-+.f64`
1990×	`+-lowering-+.f32`
1986×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	107	519
1	313	442
2	910	432
3	2498	428
0	8482	428

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
1
(+ 1 (* -2 x))
(+ 1 (* x (- (* 2 x) 2)))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
-1
(- (* 2 (/ 1 x)) 1)
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
-1
(- (* 2 (/ 1 x)) 1)
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)

Outputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x) (.f64 x x))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))) x)) x))
1
#s(literal 1 binary64)
(+ 1 (* -2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -2 binary64)))
(+ 1 (* x (- (* 2 x) 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -2 binary64) (.f64 #s(literal 2 binary64) x))))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (-.f64 #s(literal -2 binary64) (.f64 x (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) x))))))
-1
#s(literal -1 binary64)
(- (* 2 (/ 1 x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) x))
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(-.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) x))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) x)) x))
-1
#s(literal -1 binary64)
(- (* 2 (/ 1 x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) x))
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) x))
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) x)) x))

eval32.0ms (0.6%)

Compiler: Compiled 4262 to 982 computations (77% saved)

prune27.0ms (0.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	236	6	242
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	236	7	243

Accuracy

100.0%

Counts

243 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))
▶	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))))
▶	99.3%	(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
▶	99.8%	(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/2 binary64)))))))))
▶	99.7%	(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
✓	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
▶	97.8%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))

Compiler

Compiled 150 to 119 computations (20.7% saved)

simplify187.0ms (3.2%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64))))))
✓	cost-diff	0	(atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64))))))))
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/2 binary64)))))))))
✓	cost-diff	128	(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal -1 binary64) (.f64 x #s(literal 1/2 binary64))))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x #s(literal 1/2 binary64)))))
✓	cost-diff	0	(atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x #s(literal 1/2 binary64))))))
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(atan.f64 (-.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(atan.f64 #s(literal 1 binary64))
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
✓	cost-diff	0	(sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))
✓	cost-diff	0	(atan.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))))

Rules

2686×	`sum5-define`
2120×	`sum3-define`
1872×	`sum4-define`
1590×	`fma-define`
1128×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	29	210
1	64	194
2	141	187
3	251	185
4	689	182
5	2189	182
6	4942	182
7	5404	182
8	5584	182
9	5782	182
10	5881	182
11	7867	182
0	8155	182

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* 2 (atan (/ 1 (sqrt (/ (+ 1 x) (- 1 x))))))
2
(atan (/ 1 (sqrt (/ (+ 1 x) (- 1 x)))))
(/ 1 (sqrt (/ (+ 1 x) (- 1 x))))
1
(sqrt (/ (+ 1 x) (- 1 x)))
(/ (+ 1 x) (- 1 x))
(+ 1 x)
x
(- 1 x)
(* 2 (atan 1))
2
(atan 1)
1
(* 2 (atan (- 1 x)))
2
(atan (- 1 x))
(- 1 x)
1
x
(* 2 (atan (+ 1 (* x (+ -1 (* x 1/2))))))
2
(atan (+ 1 (* x (+ -1 (* x 1/2)))))
(+ 1 (* x (+ -1 (* x 1/2))))
1
(* x (+ -1 (* x 1/2)))
x
(+ -1 (* x 1/2))
-1
(* x 1/2)
1/2
(* 2 (atan (+ 1 (* x (+ -1 (* x (- 1/2 (* x 1/2))))))))
2
(atan (+ 1 (* x (+ -1 (* x (- 1/2 (* x 1/2)))))))
(+ 1 (* x (+ -1 (* x (- 1/2 (* x 1/2))))))
1
(* x (+ -1 (* x (- 1/2 (* x 1/2)))))
x
(+ -1 (* x (- 1/2 (* x 1/2))))
-1
(* x (- 1/2 (* x 1/2)))
(- 1/2 (* x 1/2))
1/2
(* x 1/2)

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

localize432.0ms (7.4%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/2 binary64)))))))))
✓	accuracy	100.0%	(atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64))))))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64))))))
✓	accuracy	100.0%	(.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
✓	accuracy	100.0%	(atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x #s(literal 1/2 binary64))))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal -1 binary64) (.f64 x #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
✓	accuracy	100.0%	(atan.f64 (-.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
✓	accuracy	100.0%	(atan.f64 #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))
✓	accuracy	100.0%	(atan.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))
✓	accuracy	100.0%	(/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))

Results

384.0ms

256×

valid

Compiler

Compiled 218 to 30 computations (86.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 297.0ms

ival-mult: 269.0ms (90.6% of total)

ival-atan: 10.0ms (3.4% of total)

ival-add: 9.0ms (3% of total)

ival-div: 4.0ms (1.3% of total)

ival-sub: 3.0ms (1% of total)

ival-sqrt: 2.0ms (0.7% of total)

const: 1.0ms (0.3% of total)

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

series18.0ms (0.3%)

Counts

20 → 216

Calls

Call 1

Inputs
#<alt (* 2 (atan (/ 1 (sqrt (/ (+ 1 x) (- 1 x))))))>
#<alt (atan (/ 1 (sqrt (/ (+ 1 x) (- 1 x)))))>
#<alt (/ 1 (sqrt (/ (+ 1 x) (- 1 x))))>
#<alt (sqrt (/ (+ 1 x) (- 1 x)))>
#<alt (* 2 (atan 1))>
#<alt (atan 1)>
#<alt (* 2 (atan (- 1 x)))>
#<alt (atan (- 1 x))>
#<alt (- 1 x)>
#<alt (* 2 (atan (+ 1 (* x (+ -1 (* x 1/2))))))>
#<alt (atan (+ 1 (* x (+ -1 (* x 1/2)))))>
#<alt (+ 1 (* x (+ -1 (* x 1/2))))>
#<alt (* x (+ -1 (* x 1/2)))>
#<alt (+ 1 (* x (+ -1 (* x (- 1/2 (* x 1/2))))))>
#<alt (* 2 (atan (+ 1 (* x (+ -1 (* x (- 1/2 (* x 1/2))))))))>
#<alt (atan (+ 1 (* x (+ -1 (* x (- 1/2 (* x 1/2)))))))>
#<alt (* x (+ -1 (* x (- 1/2 (* x 1/2)))))>
#<alt (/ (+ 1 x) (- 1 x))>
#<alt (* x 1/2)>
#<alt (* x (- 1/2 (* x 1/2)))>

Outputs
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))>
#<alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))>
#<alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))>
#<alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))>
#<alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))>
#<alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))>
#<alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))>
#<alt (sqrt -1)>
#<alt (+ (sqrt -1) (/ 1 (* x (sqrt -1))))>
#<alt (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))>
#<alt (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))>
#<alt (sqrt -1)>
#<alt (+ (sqrt -1) (/ 1 (* x (sqrt -1))))>
#<alt (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))>
#<alt (+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/2 x))))))>
#<alt (sqrt -1)>
#<alt (- (sqrt -1) (/ 1 (* x (sqrt -1))))>
#<alt (- (+ (sqrt -1) (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1))))) (/ 1 (* x (sqrt -1))))>
#<alt (- (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* (pow x 3) (sqrt -1)))) (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))))) (/ 1 (* x (sqrt -1))))>
#<alt (sqrt -1)>
#<alt (- (sqrt -1) (/ 1 (* x (sqrt -1))))>
#<alt (+ (sqrt -1) (* -1 (/ (+ (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))>
#<alt (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* -1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (+ 1 (* -1 x))))>
#<alt (* 2 (atan (+ 1 (* -1 x))))>
#<alt (* 2 (atan (+ 1 (* -1 x))))>
#<alt (* 2 (atan (+ 1 (* -1 x))))>
#<alt (atan (- 1 x))>
#<alt (atan (- 1 x))>
#<alt (atan (- 1 x))>
#<alt (atan (- 1 x))>
#<alt (atan (- 1 x))>
#<alt (atan (- 1 x))>
#<alt (atan (- 1 x))>
#<alt (atan (- 1 x))>
#<alt (atan (+ 1 (* -1 x)))>
#<alt (atan (+ 1 (* -1 x)))>
#<alt (atan (+ 1 (* -1 x)))>
#<alt (atan (+ 1 (* -1 x)))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))>
#<alt (* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))>
#<alt (* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))>
#<alt (* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))>
#<alt (* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))>
#<alt (atan (+ 1 (* x (- (* 1/2 x) 1))))>
#<alt (atan (+ 1 (* x (- (* 1/2 x) 1))))>
#<alt (atan (+ 1 (* x (- (* 1/2 x) 1))))>
#<alt (atan (+ 1 (* x (- (* 1/2 x) 1))))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) x))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) x))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) x))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) x))>
#<alt (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))>
#<alt (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))>
#<alt (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))>
#<alt (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))>
#<alt (* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))>
#<alt (* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))>
#<alt (* -1 x)>
#<alt (* x (- (* 1/2 x) 1))>
#<alt (* x (- (* 1/2 x) 1))>
#<alt (* x (- (* 1/2 x) 1))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))>
#<alt (* -1/2 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* x (- 1/2 (* 1/2 x))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* x (- 1/2 (* 1/2 x))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* x (- 1/2 (* 1/2 x))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* x (- 1/2 (* 1/2 x))) 1)))))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3))))))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3))))))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3))))))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3))))))>
#<alt (* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))>
#<alt (atan (+ 1 (* x (- (* x (- 1/2 (* 1/2 x))) 1))))>
#<alt (atan (+ 1 (* x (- (* x (- 1/2 (* 1/2 x))) 1))))>
#<alt (atan (+ 1 (* x (- (* x (- 1/2 (* 1/2 x))) 1))))>
#<alt (atan (+ 1 (* x (- (* x (- 1/2 (* 1/2 x))) 1))))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3)))))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3)))))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3)))))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3)))))>
#<alt (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))>
#<alt (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))>
#<alt (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))>
#<alt (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))>
#<alt (* -1 x)>
#<alt (* x (- (* 1/2 x) 1))>
#<alt (* x (- (* x (+ 1/2 (* -1/2 x))) 1))>
#<alt (* x (- (* x (+ 1/2 (* -1/2 x))) 1))>
#<alt (* -1/2 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))>
#<alt 1>
#<alt (+ 1 (* 2 x))>
#<alt (+ 1 (* x (+ 2 (* 2 x))))>
#<alt (+ 1 (* x (+ 2 (* x (+ 2 (* 2 x))))))>
#<alt -1>
#<alt (* -1 (+ 1 (* 2 (/ 1 x))))>
#<alt (- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 1)>
#<alt (- (* -1 (/ (+ 2 (* 2 (/ 1 x))) (pow x 2))) (+ 1 (* 2 (/ 1 x))))>
#<alt -1>
#<alt (* -1 (+ 1 (* 2 (/ 1 x))))>
#<alt (- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 1)>
#<alt (- (* -1 (/ (+ 2 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))) x)) 1)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/2 x)))>
#<alt (* x (+ 1/2 (* -1/2 x)))>
#<alt (* x (+ 1/2 (* -1/2 x)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))>

Calls

54 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(+ 1 (* x (+ -1 (* x (- 1/2 (* x 1/2))))))
1.0ms	x	@	-inf	(* 2 (atan (- 1 x)))
1.0ms	x	@	-inf	(* 2 (atan (+ 1 (* x (+ -1 (* x 1/2))))))
0.0ms	x	@	-inf	(* 2 (atan (+ 1 (* x (+ -1 (* x (- 1/2 (* x 1/2))))))))
0.0ms	x	@	inf	(* 2 (atan (+ 1 (* x (+ -1 (* x (- 1/2 (* x 1/2))))))))

rewrite282.0ms (4.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1916×	`-lowering-.f32`
1916×	`-lowering-.f64`
1792×	`fma-lowering-fma.f32`
1792×	`fma-lowering-fma.f64`
1372×	`fma-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	164
1	82	150
2	258	145
3	818	140
4	3236	140
0	8057	140

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 773

Calls

Call 1

Inputs
(* 2 (atan (/ 1 (sqrt (/ (+ 1 x) (- 1 x))))))
(atan (/ 1 (sqrt (/ (+ 1 x) (- 1 x)))))
(/ 1 (sqrt (/ (+ 1 x) (- 1 x))))
(sqrt (/ (+ 1 x) (- 1 x)))
(* 2 (atan 1))
(atan 1)
(* 2 (atan (- 1 x)))
(atan (- 1 x))
(- 1 x)
(* 2 (atan (+ 1 (* x (+ -1 (* x 1/2))))))
(atan (+ 1 (* x (+ -1 (* x 1/2)))))
(+ 1 (* x (+ -1 (* x 1/2))))
(* x (+ -1 (* x 1/2)))
(+ 1 (* x (+ -1 (* x (- 1/2 (* x 1/2))))))
(* 2 (atan (+ 1 (* x (+ -1 (* x (- 1/2 (* x 1/2))))))))
(atan (+ 1 (* x (+ -1 (* x (- 1/2 (* x 1/2)))))))
(* x (+ -1 (* x (- 1/2 (* x 1/2)))))
(/ (+ 1 x) (- 1 x))
(* x 1/2)
(* x (- 1/2 (* x 1/2)))

Outputs
(neg.f64 (*.f64 (atan.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)))
(neg.f64 (*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64))
(-.f64 #s(literal 0 binary64) (atan.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(neg.f64 (atan.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))))
(*.f64 #s(literal -1 binary64) (atan.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))))
(+.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 #s(literal 1 binary64) x))) (.f64 (log1p.f64 x) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 #s(literal 1 binary64) x))) (.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x)) #s(literal -1 binary64))))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log.f64 (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) (*.f64 (log1p.f64 x) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log.f64 (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (log1p.f64 x)) #s(literal -1 binary64))))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log.f64 (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) (log1p.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1/2 binary64)) (.f64 (log1p.f64 x) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1/2 binary64)) (.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x)) #s(literal -1 binary64))))
(exp.f64 (+.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (log1p.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal -1/2 binary64)) (.f64 (log.f64 (-.f64 #s(literal -1 binary64) x)) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (.f64 (log.f64 (+.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64)) (.f64 (log.f64 (-.f64 #s(literal -1 binary64) x)) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (.f64 (log1p.f64 x) #s(literal -1/2 binary64)) (.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 #s(literal 1 binary64) x)))))
(exp.f64 (+.f64 (.f64 (log1p.f64 x) #s(literal -1/2 binary64)) (.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))))
(exp.f64 (+.f64 (.f64 (log1p.f64 x) #s(literal -1/2 binary64)) (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log1p.f64 x)) #s(literal -1 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 #s(literal 1 binary64) x)))))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log1p.f64 x)) #s(literal -1 binary64)) (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (log1p.f64 x)) (.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))))
(exp.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (log1p.f64 x)) (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (.f64 (log.f64 (-.f64 #s(literal -1 binary64) x)) #s(literal -1/2 binary64)) (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (.f64 (log.f64 (-.f64 #s(literal -1 binary64) x)) #s(literal -1/2 binary64)) (.f64 (log.f64 (+.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64))))
(exp.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log.f64 (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) (*.f64 #s(literal 1/2 binary64) (log1p.f64 x))))
(exp.f64 (-.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1/2 binary64)) (.f64 #s(literal 1/2 binary64) (log1p.f64 x))))
(exp.f64 (-.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal -1/2 binary64)) (.f64 (log.f64 (-.f64 #s(literal -1 binary64) x)) #s(literal 1/2 binary64))))
(exp.f64 (-.f64 (.f64 (log.f64 (+.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64)) (.f64 (log.f64 (-.f64 #s(literal -1 binary64) x)) #s(literal 1/2 binary64))))
(exp.f64 (-.f64 (.f64 (log1p.f64 x) #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (log.f64 (-.f64 #s(literal 1 binary64) x)))))
(exp.f64 (-.f64 (.f64 (log1p.f64 x) #s(literal -1/2 binary64)) (.f64 (log.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))
(exp.f64 (-.f64 (.f64 (log1p.f64 x) #s(literal -1/2 binary64)) (.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))))
(exp.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log1p.f64 x)) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) (log.f64 (-.f64 #s(literal 1 binary64) x)))))
(exp.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log1p.f64 x)) #s(literal -1 binary64)) (*.f64 (log.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))
(exp.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log1p.f64 x)) #s(literal -1 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))))
(exp.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (log1p.f64 x)) (.f64 (log.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))
(exp.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (log1p.f64 x)) (.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))))
(exp.f64 (-.f64 (.f64 (log.f64 (-.f64 #s(literal -1 binary64) x)) #s(literal -1/2 binary64)) (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x))) (sqrt.f64 #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(/.f64 (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64)) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x)) #s(literal -1/2 binary64)))
(/.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) (/.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (exp.f64 (log.f64 #s(literal -1 binary64)))))
(/.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 x #s(literal -1 binary64))))) (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 #s(literal -1 binary64) x)))))
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(-.f64 #s(literal 0 binary64) (.f64 x (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
(-.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1/2 binary64) (*.f64 x x))) x)
(-.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(-.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(-.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))) (-.f64 #s(literal 0 binary64) x)))
(fma.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x #s(literal 1/2 binary64)))) (.f64 x (.f64 #s(literal -1/2 binary64) (*.f64 x x))))
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(fma.f64 x (.f64 x #s(literal 1/2 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))))
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(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (-.f64 (.f64 x (.f64 #s(literal -1/2 binary64) (.f64 x x))) x))
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(fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))))
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(fma.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x #s(literal -1/2 binary64)) (-.f64 (.f64 x (.f64 #s(literal -1/2 binary64) (.f64 x x))) x))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x #s(literal 1/2 binary64)))))
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(fma.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x x)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) x) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) x (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x #s(literal 1/2 binary64)))))
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(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 (+.f64 #s(literal -1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x))) x))
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(fma.f64 (.f64 x (.f64 x (-.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) x))
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(.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/2 binary64))))) #s(literal 1 binary64)) x)
(.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/2 binary64))))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
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(+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 x (-.f64 #s(literal 1 binary64) x)))
(+.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
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(exp.f64 (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))
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(.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)))
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(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
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(neg.f64 (*.f64 x #s(literal -1/2 binary64)))
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(*.f64 x #s(literal 1/2 binary64))
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(.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
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(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (*.f64 x #s(literal 1/2 binary64)))
(-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (*.f64 x #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 x #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 x (.f64 x #s(literal -1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1 binary64) (.f64 x #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x (-.f64 #s(literal 0 binary64) x)) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) x) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) x (.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
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(fma.f64 (.f64 x x) #s(literal -1/2 binary64) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x (-.f64 #s(literal 0 binary64) x)) #s(literal 1/2 binary64) (.f64 x #s(literal 1/2 binary64)))
(neg.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/2 binary64)))))
(neg.f64 (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 x #s(literal 1/2 binary64))))
(neg.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(/.f64 (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/2 binary64))))
(.f64 (-.f64 #s(literal 1 binary64) x) (.f64 x #s(literal 1/2 binary64)))
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(.f64 #s(literal -1 binary64) (.f64 (+.f64 x #s(literal -1 binary64)) (*.f64 x #s(literal 1/2 binary64))))
(.f64 #s(literal 1/2 binary64) (.f64 x (-.f64 #s(literal 1 binary64) x)))
(.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) x))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/2 binary64))) x)
(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))))
(.f64 (.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) x)) #s(literal -1 binary64))
(.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))

simplify257.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

3528×	`-lowering-.f32`
3528×	`-lowering-.f64`
2580×	`fma-lowering-fma.f32`
2580×	`fma-lowering-fma.f64`
1734×	`fmm-def`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	200	1968
1	588	1687
2	1906	1646
3	6411	1645
0	8729	1645

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

Inputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/2 x))))))
(sqrt -1)
(- (sqrt -1) (/ 1 (* x (sqrt -1))))
(- (+ (sqrt -1) (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1))))) (/ 1 (* x (sqrt -1))))
(- (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* (pow x 3) (sqrt -1)))) (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))))) (/ 1 (* x (sqrt -1))))
(sqrt -1)
(- (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (* -1 (/ (+ (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* -1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(* 2 (atan (- 1 x)))
(* 2 (atan (- 1 x)))
(* 2 (atan (- 1 x)))
(* 2 (atan (- 1 x)))
(* 2 (atan (- 1 x)))
(* 2 (atan (- 1 x)))
(* 2 (atan (- 1 x)))
(* 2 (atan (- 1 x)))
(* 2 (atan (+ 1 (* -1 x))))
(* 2 (atan (+ 1 (* -1 x))))
(* 2 (atan (+ 1 (* -1 x))))
(* 2 (atan (+ 1 (* -1 x))))
(atan (- 1 x))
(atan (- 1 x))
(atan (- 1 x))
(atan (- 1 x))
(atan (- 1 x))
(atan (- 1 x))
(atan (- 1 x))
(atan (- 1 x))
(atan (+ 1 (* -1 x)))
(atan (+ 1 (* -1 x)))
(atan (+ 1 (* -1 x)))
(atan (+ 1 (* -1 x)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))
(* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))
(* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))
(* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))
(* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))
(* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))
(* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))
(atan (+ 1 (* x (- (* 1/2 x) 1))))
(atan (+ 1 (* x (- (* 1/2 x) 1))))
(atan (+ 1 (* x (- (* 1/2 x) 1))))
(atan (+ 1 (* x (- (* 1/2 x) 1))))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))
(atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))
(atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))
(atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* 1/2 x) 1)))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(* -1 x)
(* x (- (* 1/2 x) 1))
(* x (- (* 1/2 x) 1))
(* x (- (* 1/2 x) 1))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- 1/2 (/ 1 x)))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(* -1/2 (pow x 3))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(* 2 (atan (+ 1 (* x (- (* x (- 1/2 (* 1/2 x))) 1)))))
(* 2 (atan (+ 1 (* x (- (* x (- 1/2 (* 1/2 x))) 1)))))
(* 2 (atan (+ 1 (* x (- (* x (- 1/2 (* 1/2 x))) 1)))))
(* 2 (atan (+ 1 (* x (- (* x (- 1/2 (* 1/2 x))) 1)))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3))))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3))))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3))))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3))))))
(* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
(* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
(* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
(* 2 (atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
(atan (+ 1 (* x (- (* x (- 1/2 (* 1/2 x))) 1))))
(atan (+ 1 (* x (- (* x (- 1/2 (* 1/2 x))) 1))))
(atan (+ 1 (* x (- (* x (- 1/2 (* 1/2 x))) 1))))
(atan (+ 1 (* x (- (* x (- 1/2 (* 1/2 x))) 1))))
(atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3)))))
(atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3)))))
(atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3)))))
(atan (- (+ 1 (* 1/2 (pow x 2))) (+ x (* 1/2 (pow x 3)))))
(atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))
(atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))
(atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))
(atan (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))))
(* -1 x)
(* x (- (* 1/2 x) 1))
(* x (- (* x (+ 1/2 (* -1/2 x))) 1))
(* x (- (* x (+ 1/2 (* -1/2 x))) 1))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* -1/2 (pow x 3))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
1
(+ 1 (* 2 x))
(+ 1 (* x (+ 2 (* 2 x))))
(+ 1 (* x (+ 2 (* x (+ 2 (* 2 x))))))
-1
(* -1 (+ 1 (* 2 (/ 1 x))))
(- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 1)
(- (* -1 (/ (+ 2 (* 2 (/ 1 x))) (pow x 2))) (+ 1 (* 2 (/ 1 x))))
-1
(* -1 (+ 1 (* 2 (/ 1 x))))
(- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 1)
(- (* -1 (/ (+ 2 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))) x)) 1)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* x (+ 1/2 (* -1/2 x)))
(* x (+ 1/2 (* -1/2 x)))
(* x (+ 1/2 (* -1/2 x)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))

Outputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x x))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x x)))))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))) x))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))) x)) x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/2 x))))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(- (sqrt -1) (/ 1 (* x (sqrt -1))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 #s(literal -1 binary64))))
(- (+ (sqrt -1) (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1))))) (/ 1 (* x (sqrt -1))))
(+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x x)) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))))
(- (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* (pow x 3) (sqrt -1)))) (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))))) (/ 1 (* x (sqrt -1))))
(+.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (.f64 x (.f64 x x))))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(- (sqrt -1) (/ 1 (* x (sqrt -1))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 #s(literal -1 binary64))))
(+ (sqrt -1) (* -1 (/ (+ (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x))
(+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* -1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x))
(* 2 (atan (- 1 x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(* 2 (atan (- 1 x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(* 2 (atan (- 1 x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(* 2 (atan (- 1 x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(* 2 (atan (- 1 x)))
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#s(literal 1 binary64)
(+ 1 (* 2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) x))
(+ 1 (* x (+ 2 (* 2 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) x))))
(+ 1 (* x (+ 2 (* x (+ 2 (* 2 x))))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x))))))
-1
#s(literal -1 binary64)
(* -1 (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) x))
(- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) x)) x))
(- (* -1 (/ (+ 2 (* 2 (/ 1 x))) (pow x 2))) (+ 1 (* 2 (/ 1 x))))
(+.f64 (/.f64 (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) x) x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) x)))
-1
#s(literal -1 binary64)
(* -1 (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) x))
(- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) x)) x))
(- (* -1 (/ (+ 2 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 (-.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) (/.f64 (/.f64 #s(literal -2 binary64) x) x)) x))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 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))
(* x (+ 1/2 (* -1/2 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/2 binary64))))
(* x (+ 1/2 (* -1/2 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/2 binary64))))
(* x (+ 1/2 (* -1/2 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/2 binary64))))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))

eval127.0ms (2.2%)

Compiler: Compiled 17172 to 3730 computations (78.3% saved)

prune111.0ms (1.9%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	1047	2	1049
Fresh	0	1	1
Picked	2	3	5
Done	0	1	1
Total	1049	7	1056

Accuracy

100.0%

Counts

1056 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(.f64 (atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x))))) #s(literal 2 binary64))
▶	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))
▶	99.3%	(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
✓	99.3%	(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
✓	99.7%	(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
✓	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
✓	97.8%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))

Compiler

Compiled 74 to 59 computations (20.3% saved)

simplify151.0ms (2.6%)

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Program
✓	cost-diff	(-.f64 #s(literal 1 binary64) x)
✓	cost-diff	(.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))
✓	cost-diff	(atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
✓	cost-diff	(.f64 (atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x))))) #s(literal 2 binary64))
✓	cost-diff	(/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))
✓	cost-diff	(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
✓	cost-diff	(atan.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
✓	cost-diff	(*.f64 #s(literal 2 binary64) (atan.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) x)
✓	cost-diff	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))
✓	cost-diff	(atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
✓	cost-diff	(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))

Rules

2412×	`sum4-define`
2256×	`sum3-define`
1884×	`fnmsub-define`
1768×	`fma-define`
1364×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	121
1	42	117
2	88	117
3	270	117
4	842	117
5	2193	117
6	5618	117
0	8036	117

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* 2 (atan (/ 1 (+ 1 x))))
2
(atan (/ 1 (+ 1 x)))
(/ 1 (+ 1 x))
1
(+ 1 x)
x
(* 2 (atan (pow (/ (+ 1 x) (- 1 x)) -1/2)))
2
(atan (pow (/ (+ 1 x) (- 1 x)) -1/2))
(pow (/ (+ 1 x) (- 1 x)) -1/2)
(/ (+ 1 x) (- 1 x))
(+ 1 x)
1
x
(- 1 x)
-1/2
(* (atan (* (- 1 x) (+ 1 (* 1/2 (* x x))))) 2)
(atan (* (- 1 x) (+ 1 (* 1/2 (* x x)))))
(* (- 1 x) (+ 1 (* 1/2 (* x x))))
(- 1 x)
1
x
(+ 1 (* 1/2 (* x x)))
(* 1/2 (* x x))
1/2
(* x x)
2

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

localize228.0ms (3.9%)

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
✓	accuracy	100.0%	(atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
✓	accuracy	100.0%	(.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))
✓	accuracy	100.0%	(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(atan.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))

Results

189.0ms

256×

valid

Compiler

Compiled 134 to 21 computations (84.3% saved)

Precisions

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

ival-mult: 10.0ms (29.5% of total)

ival-atan: 8.0ms (23.6% of total)

ival-pow: 6.0ms (17.7% of total)

ival-div: 4.0ms (11.8% of total)

ival-add: 3.0ms (8.8% of total)

ival-sub: 2.0ms (5.9% of total)

const: 1.0ms (2.9% of total)

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

series8.0ms (0.1%)

Counts

14 → 168

Calls

Call 1

Inputs
#<alt (* 2 (atan (/ 1 (+ 1 x))))>
#<alt (atan (/ 1 (+ 1 x)))>
#<alt (/ 1 (+ 1 x))>
#<alt (+ 1 x)>
#<alt (* 2 (atan (pow (/ (+ 1 x) (- 1 x)) -1/2)))>
#<alt (atan (pow (/ (+ 1 x) (- 1 x)) -1/2))>
#<alt (pow (/ (+ 1 x) (- 1 x)) -1/2)>
#<alt (/ (+ 1 x) (- 1 x))>
#<alt (* (atan (* (- 1 x) (+ 1 (* 1/2 (* x x))))) 2)>
#<alt (atan (* (- 1 x) (+ 1 (* 1/2 (* x x)))))>
#<alt (* (- 1 x) (+ 1 (* 1/2 (* x x))))>
#<alt (- 1 x)>
#<alt (* 1/2 (* x x))>
#<alt (* x x)>

Outputs
#<alt (* 2 (atan (/ 1 (+ 1 x))))>
#<alt (* 2 (atan (/ 1 (+ 1 x))))>
#<alt (* 2 (atan (/ 1 (+ 1 x))))>
#<alt (* 2 (atan (/ 1 (+ 1 x))))>
#<alt (* 2 (atan (/ 1 (+ 1 x))))>
#<alt (* 2 (atan (/ 1 (+ 1 x))))>
#<alt (* 2 (atan (/ 1 (+ 1 x))))>
#<alt (* 2 (atan (/ 1 (+ 1 x))))>
#<alt (* 2 (atan (/ 1 (- 1 (* -1 x)))))>
#<alt (* 2 (atan (/ 1 (- 1 (* -1 x)))))>
#<alt (* 2 (atan (/ 1 (- 1 (* -1 x)))))>
#<alt (* 2 (atan (/ 1 (- 1 (* -1 x)))))>
#<alt (atan (/ 1 (+ 1 x)))>
#<alt (atan (/ 1 (+ 1 x)))>
#<alt (atan (/ 1 (+ 1 x)))>
#<alt (atan (/ 1 (+ 1 x)))>
#<alt (atan (/ 1 (+ 1 x)))>
#<alt (atan (/ 1 (+ 1 x)))>
#<alt (atan (/ 1 (+ 1 x)))>
#<alt (atan (/ 1 (+ 1 x)))>
#<alt (atan (/ 1 (- 1 (* -1 x))))>
#<alt (atan (/ 1 (- 1 (* -1 x))))>
#<alt (atan (/ 1 (- 1 (* -1 x))))>
#<alt (atan (/ 1 (- 1 (* -1 x))))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* x (- x 1)))>
#<alt (+ 1 (* x (- (* x (+ 1 (* -1 x))) 1)))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (/ 1 x)) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 2))) (+ (/ 1 x) (/ 1 (pow x 3)))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (/ 1 x) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) 1) x))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))>
#<alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))>
#<alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))>
#<alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))>
#<alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))>
#<alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))>
#<alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))>
#<alt (sqrt -1)>
#<alt (+ (sqrt -1) (/ 1 (* x (sqrt -1))))>
#<alt (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))>
#<alt (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))>
#<alt (sqrt -1)>
#<alt (+ (sqrt -1) (/ 1 (* x (sqrt -1))))>
#<alt (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))>
#<alt (+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))>
#<alt 1>
#<alt (+ 1 (* 2 x))>
#<alt (+ 1 (* x (+ 2 (* 2 x))))>
#<alt (+ 1 (* x (+ 2 (* x (+ 2 (* 2 x))))))>
#<alt -1>
#<alt (* -1 (+ 1 (* 2 (/ 1 x))))>
#<alt (- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 1)>
#<alt (- (* -1 (/ (+ 2 (* 2 (/ 1 x))) (pow x 2))) (+ 1 (* 2 (/ 1 x))))>
#<alt -1>
#<alt (* -1 (+ 1 (* 2 (/ 1 x))))>
#<alt (- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 1)>
#<alt (- (* -1 (/ (+ 2 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))) x)) 1)>
#<alt (* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))>
#<alt (* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))>
#<alt (* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))>
#<alt (* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))>
#<alt (* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))>
#<alt (* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))>
#<alt (* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))>
#<alt (* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))>
#<alt (* 2 (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2))))))>
#<alt (* 2 (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2))))))>
#<alt (* 2 (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2))))))>
#<alt (* 2 (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2))))))>
#<alt (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))>
#<alt (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))>
#<alt (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))>
#<alt (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))>
#<alt (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))>
#<alt (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))>
#<alt (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))>
#<alt (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))>
#<alt (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2)))))>
#<alt (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2)))))>
#<alt (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2)))))>
#<alt (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2)))))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))>
#<alt (* -1/2 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

42 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(* (atan (* (- 1 x) (+ 1 (* 1/2 (* x x))))) 2)
0.0ms	x	@	-inf	(* 2 (atan (/ 1 (+ 1 x))))
0.0ms	x	@	inf	(* (atan (* (- 1 x) (+ 1 (* 1/2 (* x x))))) 2)
0.0ms	x	@	0	(* (atan (* (- 1 x) (+ 1 (* 1/2 (* x x))))) 2)
0.0ms	x	@	0	(* 2 (atan (/ 1 (+ 1 x))))

rewrite228.0ms (3.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1864×	`-lowering-.f32`
1864×	`-lowering-.f64`
1808×	`/-lowering-/.f32`
1808×	`/-lowering-/.f64`
1586×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	98
1	60	95
2	183	95
3	705	92
4	2655	92
0	8156	92

Stop Event

1×	iter limit
1×	node limit

Counts

14 → 545

Calls

Call 1

Inputs
(* 2 (atan (/ 1 (+ 1 x))))
(atan (/ 1 (+ 1 x)))
(/ 1 (+ 1 x))
(+ 1 x)
(* 2 (atan (pow (/ (+ 1 x) (- 1 x)) -1/2)))
(atan (pow (/ (+ 1 x) (- 1 x)) -1/2))
(pow (/ (+ 1 x) (- 1 x)) -1/2)
(/ (+ 1 x) (- 1 x))
(* (atan (* (- 1 x) (+ 1 (* 1/2 (* x x))))) 2)
(atan (* (- 1 x) (+ 1 (* 1/2 (* x x)))))
(* (- 1 x) (+ 1 (* 1/2 (* x x))))
(- 1 x)
(* 1/2 (* x x))
(* x x)

Outputs
(neg.f64 (*.f64 (atan.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))) #s(literal 2 binary64)))
(neg.f64 (*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(*.f64 (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))
(-.f64 #s(literal 0 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(neg.f64 (atan.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(*.f64 #s(literal -1 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(+.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(exp.f64 (-.f64 #s(literal 0 binary64) (log1p.f64 x)))
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log1p.f64 x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (log1p.f64 x)))
(exp.f64 (-.f64 (log1p.f64 x) (*.f64 #s(literal 2 binary64) (log1p.f64 x))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (/.f64 x (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (/.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x))) (/.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x))))
(-.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal -1 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(-.f64 (/.f64 x (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal -1 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (/.f64 (-.f64 #s(literal -1 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))
(/.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x))
(/.f64 (-.f64 #s(literal -1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x)))
(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) #s(literal -1 binary64))
(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal -1 binary64))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))))
(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 #s(literal -1 binary64) x))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal -1 binary64))))
(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 #s(literal -1 binary64) x))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (+.f64 (log.f64 #s(literal -1 binary64)) #s(literal 0 binary64))))
(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 #s(literal -1 binary64) x))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (-.f64 (log.f64 #s(literal -1 binary64)) #s(literal 0 binary64))))
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log1p.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (log1p.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (log1p.f64 x)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 #s(literal -1 binary64) x) (-.f64 #s(literal -1 binary64) x)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))
(.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x))))
(.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) #s(literal -1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (/.f64 (-.f64 #s(literal -1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal -1 binary64) x))
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal -1 binary64))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 #s(literal -1 binary64) x))))
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 #s(literal -1 binary64) x))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal -1 binary64))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x))) #s(literal -1 binary64))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))
(*.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) (-.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))
(+.f64 #s(literal 1 binary64) x)
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) x))
(exp.f64 (log1p.f64 x))
(-.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))
(-.f64 x #s(literal -1 binary64))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) x))
(fma.f64 #s(literal 1 binary64) x #s(literal 1 binary64))
(fma.f64 x #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64) #s(literal 1 binary64))
(neg.f64 (-.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))
(/.f64 (-.f64 #s(literal -1 binary64) x) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal -1 binary64) x) (exp.f64 (+.f64 (log.f64 #s(literal -1 binary64)) #s(literal 0 binary64))))
(/.f64 (-.f64 #s(literal -1 binary64) x) (exp.f64 (-.f64 (log.f64 #s(literal -1 binary64)) #s(literal 0 binary64))))
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (log1p.f64 x)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log1p.f64 x))
(*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))
(*.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x))
(*.f64 (-.f64 #s(literal -1 binary64) x) #s(literal -1 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 1/2 binary64))) (log.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(exp.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (log1p.f64 x)) (.f64 (log.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))
(exp.f64 (+.f64 (.f64 (log.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (.f64 #s(literal -1/2 binary64) (log1p.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal -1/2 binary64)) (.f64 (log.f64 (-.f64 #s(literal -1 binary64) x)) #s(literal -1/2 binary64))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (log1p.f64 x))))
(/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log1p.f64 x)))
(/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(/.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal -1 binary64) x)))
(/.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (log.f64 (-.f64 #s(literal -1 binary64) x)))) (exp.f64 (.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 x #s(literal -1 binary64))))))
(/.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (log.f64 #s(literal -1 binary64)))) (exp.f64 (.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x))))))
(/.f64 (exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (-.f64 #s(literal -1 binary64) x))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x))) (sqrt.f64 #s(literal -1 binary64)))
(/.f64 (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (+.f64 #s(literal 0 binary64) (log.f64 #s(literal -1 binary64)))) (exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x))))))
(/.f64 (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))))) (exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 #s(literal -1 binary64)))))
(/.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(literal -1 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))))))
(/.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x)))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(literal -1 binary64))))
(/.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))))
(/.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) (log1p.f64 x))))
(/.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 (-.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 1 binary64) x)))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x)))))
(/.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x))))
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(fma.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64))))))
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(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) (+.f64 x #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/2 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (+.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(/.f64 (+.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 x #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(/.f64 (+.f64 (+.f64 x #s(literal -1 binary64)) (.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x))))) #s(literal -1 binary64))
(/.f64 (+.f64 (+.f64 x #s(literal -1 binary64)) (.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 x #s(literal -1 binary64))))) #s(literal -1 binary64))
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (.f64 #s(literal 1/2 binary64) (.f64 x x)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(/.f64 (+.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/2 binary64))))))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 x #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (+.f64 (.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) (.f64 x (*.f64 x #s(literal -1/2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(/.f64 (+.f64 (+.f64 x #s(literal -1 binary64)) (.f64 #s(literal -1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/2 binary64))))))) #s(literal -1 binary64))
(/.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (.f64 #s(literal -1 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 x #s(literal -1 binary64))))) #s(literal 1 binary64))
(/.f64 (+.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (+.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(/.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (+.f64 x #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/2 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/2 binary64))))) #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))
(/.f64 (+.f64 (.f64 (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(/.f64 (+.f64 (.f64 (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))
(/.f64 (+.f64 (.f64 (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (+.f64 (.f64 (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(/.f64 (+.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))
(/.f64 (+.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (+.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(/.f64 (-.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (+.f64 x #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/2 binary64))))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/2 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 (.f64 (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 (.f64 (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))
(/.f64 (-.f64 (.f64 (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (+.f64 x #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))
(/.f64 (-.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
(.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 1 binary64)))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) x))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
(.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal -1 binary64)))
(.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal -1 binary64))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))
(+.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) x))
(+.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64))
(exp.f64 (log.f64 (-.f64 #s(literal 1 binary64) x)))
(exp.f64 (*.f64 (log.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) x)
(-.f64 #s(literal 0 binary64) (+.f64 x #s(literal -1 binary64)))
(-.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64))
(fma.f64 x #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) x))
(fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64) #s(literal 1 binary64))
(neg.f64 (+.f64 x #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(/.f64 (+.f64 x #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))
(*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64)))
(*.f64 (+.f64 x #s(literal -1 binary64)) #s(literal -1 binary64))
(neg.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(.f64 (.f64 x #s(literal 1/2 binary64)) x)
(.f64 (.f64 x #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) x))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (log.f64 (*.f64 x x)))
(exp.f64 (*.f64 (log.f64 (-.f64 #s(literal 0 binary64) x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 x)))
(neg.f64 (*.f64 x (-.f64 #s(literal 0 binary64) x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 x x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal 0 binary64) x)))
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x))
(*.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 #s(literal -1 binary64))) (pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (-.f64 #s(literal 0 binary64) x))))

simplify237.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

3144×	`-lowering-.f32`
3144×	`-lowering-.f64`
1616×	`fma-lowering-fma.f32`
1616×	`fma-lowering-fma.f64`
1392×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	173	1316
1	520	1147
2	1608	1134
3	5427	1133
0	8443	1133

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

Calls

Call 1

Inputs
(* 2 (atan (/ 1 (+ 1 x))))
(* 2 (atan (/ 1 (+ 1 x))))
(* 2 (atan (/ 1 (+ 1 x))))
(* 2 (atan (/ 1 (+ 1 x))))
(* 2 (atan (/ 1 (+ 1 x))))
(* 2 (atan (/ 1 (+ 1 x))))
(* 2 (atan (/ 1 (+ 1 x))))
(* 2 (atan (/ 1 (+ 1 x))))
(* 2 (atan (/ 1 (- 1 (* -1 x)))))
(* 2 (atan (/ 1 (- 1 (* -1 x)))))
(* 2 (atan (/ 1 (- 1 (* -1 x)))))
(* 2 (atan (/ 1 (- 1 (* -1 x)))))
(atan (/ 1 (+ 1 x)))
(atan (/ 1 (+ 1 x)))
(atan (/ 1 (+ 1 x)))
(atan (/ 1 (+ 1 x)))
(atan (/ 1 (+ 1 x)))
(atan (/ 1 (+ 1 x)))
(atan (/ 1 (+ 1 x)))
(atan (/ 1 (+ 1 x)))
(atan (/ 1 (- 1 (* -1 x))))
(atan (/ 1 (- 1 (* -1 x))))
(atan (/ 1 (- 1 (* -1 x))))
(atan (/ 1 (- 1 (* -1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- x 1)))
(+ 1 (* x (- (* x (+ 1 (* -1 x))) 1)))
(/ 1 x)
(/ (- 1 (/ 1 x)) x)
(/ (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)) x)
(/ (- (+ 1 (/ 1 (pow x 2))) (+ (/ 1 x) (/ 1 (pow x 3)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 x) 1) x))
(* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) 1) x))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
1
(+ 1 (* 2 x))
(+ 1 (* x (+ 2 (* 2 x))))
(+ 1 (* x (+ 2 (* x (+ 2 (* 2 x))))))
-1
(* -1 (+ 1 (* 2 (/ 1 x))))
(- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 1)
(- (* -1 (/ (+ 2 (* 2 (/ 1 x))) (pow x 2))) (+ 1 (* 2 (/ 1 x))))
-1
(* -1 (+ 1 (* 2 (/ 1 x))))
(- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 1)
(- (* -1 (/ (+ 2 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))) x)) 1)
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(* 2 (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2))))))
(* 2 (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2))))))
(* 2 (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2))))))
(* 2 (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2))))))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2)))))
(atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2)))))
(atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2)))))
(atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2)))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(* -1/2 (pow x 3))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
(* 2 (atan (/ 1 (+ 1 x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(* 2 (atan (/ 1 (+ 1 x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(* 2 (atan (/ 1 (+ 1 x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(* 2 (atan (/ 1 (+ 1 x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(* 2 (atan (/ 1 (+ 1 x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(* 2 (atan (/ 1 (+ 1 x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(* 2 (atan (/ 1 (+ 1 x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(* 2 (atan (/ 1 (+ 1 x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(* 2 (atan (/ 1 (- 1 (* -1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(* 2 (atan (/ 1 (- 1 (* -1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(* 2 (atan (/ 1 (- 1 (* -1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(* 2 (atan (/ 1 (- 1 (* -1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(atan (/ 1 (+ 1 x)))
(atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(atan (/ 1 (+ 1 x)))
(atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(atan (/ 1 (+ 1 x)))
(atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(atan (/ 1 (+ 1 x)))
(atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(atan (/ 1 (+ 1 x)))
(atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(atan (/ 1 (+ 1 x)))
(atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(atan (/ 1 (+ 1 x)))
(atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(atan (/ 1 (+ 1 x)))
(atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(atan (/ 1 (- 1 (* -1 x))))
(atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(atan (/ 1 (- 1 (* -1 x))))
(atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(atan (/ 1 (- 1 (* -1 x))))
(atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(atan (/ 1 (- 1 (* -1 x))))
(atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- x 1)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))
(+ 1 (* x (- (* x (+ 1 (* -1 x))) 1)))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal 1 binary64) x)))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 x)) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) x)
(/ (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)
(/ (- (+ 1 (/ 1 (pow x 2))) (+ (/ 1 x) (/ 1 (pow x 3)))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 x) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) x)
(* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) 1) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)) x)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64)))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 x x))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(+.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x x))))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))) x))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))) x)) x))
1
#s(literal 1 binary64)
(+ 1 (* 2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) x))
(+ 1 (* x (+ 2 (* 2 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) x))))
(+ 1 (* x (+ 2 (* x (+ 2 (* 2 x))))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x))))))
-1
#s(literal -1 binary64)
(* -1 (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) x))
(- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 #s(literal -2 binary64) x) #s(literal -2 binary64)) x))
(- (* -1 (/ (+ 2 (* 2 (/ 1 x))) (pow x 2))) (+ 1 (* 2 (/ 1 x))))
(+.f64 (/.f64 (+.f64 (/.f64 #s(literal -2 binary64) x) #s(literal -2 binary64)) (*.f64 x x)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) x)))
-1
#s(literal -1 binary64)
(* -1 (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) x))
(- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 #s(literal -2 binary64) x) #s(literal -2 binary64)) x))
(- (* -1 (/ (+ 2 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -2 binary64) x) #s(literal -2 binary64)) x) #s(literal -2 binary64)) x))
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))))))
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))))))
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))))))
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))))))
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))))))
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))))))
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))))))
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))))))
(* 2 (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2))))))
(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))))))
(* 2 (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2))))))
(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))))))
(* 2 (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2))))))
(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))))))
(* 2 (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2))))))
(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))))))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64))))))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64))))))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64))))))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64))))))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64))))))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64))))))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64))))))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64))))))
(atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2)))))
(atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64))))))
(atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2)))))
(atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64))))))
(atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2)))))
(atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64))))))
(atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2)))))
(atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64)))))
(* -1/2 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(.f64 x (.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x x)) (-.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) (.f64 x x)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* -1/2 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(.f64 x (.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) x)))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval104.0ms (1.8%)

Compiler: Compiled 12960 to 2627 computations (79.7% saved)

prune79.0ms (1.4%)

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	788	1	789
Fresh	0	0	0
Picked	0	3	3
Done	0	4	4
Total	788	8	796

Accuracy

100.0%

Counts

796 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(.f64 (atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x))))) #s(literal 2 binary64))
✓	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))
✓	99.3%	(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
✓	99.3%	(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
▶	99.3%	(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
✓	99.7%	(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
✓	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
✓	97.8%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))

Compiler

Compiled 85 to 68 computations (20% saved)

simplify39.0ms (0.7%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x (+.f64 x #s(literal -1 binary64)))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))
✓	cost-diff	(atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
✓	cost-diff	(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))

Rules

736×	`sum5-define`
562×	`sum3-define`
520×	`fnmadd-define`
376×	`sum4-define`
340×	`fmsub-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	37
1	20	34
2	37	33
3	53	33
4	74	33
5	118	33
6	230	33
7	476	33
8	1070	33
9	1966	33
10	2068	33
11	2072	33
0	2072	33

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* 2 (atan (+ 1 (* x (+ x -1)))))
2
(atan (+ 1 (* x (+ x -1))))
(+ 1 (* x (+ x -1)))
1
(* x (+ x -1))
x
(+ x -1)
-1

Outputs
(* 2 (atan (+ 1 (* x (+ x -1)))))
(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
2
#s(literal 2 binary64)
(atan (+ 1 (* x (+ x -1))))
(atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(+ 1 (* x (+ x -1)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))
1
#s(literal 1 binary64)
(* x (+ x -1))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
x
(+ x -1)
(+.f64 x #s(literal -1 binary64))
-1
#s(literal -1 binary64)

localize46.0ms (0.8%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
✓	accuracy	100.0%	(atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
✓	accuracy	100.0%	(*.f64 x (+.f64 x #s(literal -1 binary64)))

Results

35.0ms

256×

valid

Compiler

Compiled 39 to 10 computations (74.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 4.0ms (39.7% of total)

ival-add: 3.0ms (29.8% of total)

ival-atan: 3.0ms (29.8% of total)

const: 1.0ms (9.9% of total)

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

series36.0ms (0.6%)

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (* 2 (atan (+ 1 (* x (+ x -1)))))>
#<alt (atan (+ 1 (* x (+ x -1))))>
#<alt (+ 1 (* x (+ x -1)))>
#<alt (* x (+ x -1))>

Outputs
#<alt (* 2 (atan (+ 1 (* x (- x 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- x 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- x 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- x 1)))))>
#<alt (* 2 (atan (- (+ 1 (pow x 2)) x)))>
#<alt (* 2 (atan (- (+ 1 (pow x 2)) x)))>
#<alt (* 2 (atan (- (+ 1 (pow x 2)) x)))>
#<alt (* 2 (atan (- (+ 1 (pow x 2)) x)))>
#<alt (* 2 (atan (+ 1 (+ (* -1 x) (pow x 2)))))>
#<alt (* 2 (atan (+ 1 (+ (* -1 x) (pow x 2)))))>
#<alt (* 2 (atan (+ 1 (+ (* -1 x) (pow x 2)))))>
#<alt (* 2 (atan (+ 1 (+ (* -1 x) (pow x 2)))))>
#<alt (atan (+ 1 (* x (- x 1))))>
#<alt (atan (+ 1 (* x (- x 1))))>
#<alt (atan (+ 1 (* x (- x 1))))>
#<alt (atan (+ 1 (* x (- x 1))))>
#<alt (atan (- (+ 1 (pow x 2)) x))>
#<alt (atan (- (+ 1 (pow x 2)) x))>
#<alt (atan (- (+ 1 (pow x 2)) x))>
#<alt (atan (- (+ 1 (pow x 2)) x))>
#<alt (atan (+ 1 (+ (* -1 x) (pow x 2))))>
#<alt (atan (+ 1 (+ (* -1 x) (pow x 2))))>
#<alt (atan (+ 1 (+ (* -1 x) (pow x 2))))>
#<alt (atan (+ 1 (+ (* -1 x) (pow x 2))))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* x (- x 1)))>
#<alt (+ 1 (* x (- x 1)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (/ 1 x)))>
#<alt (* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)))>
#<alt (* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (- 1 (/ 1 x)) x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (- 1 (/ 1 x)) x))))>
#<alt (* -1 x)>
#<alt (* x (- x 1))>
#<alt (* x (- x 1))>
#<alt (* x (- x 1))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (/ 1 x)))>
#<alt (* (pow x 2) (- 1 (/ 1 x)))>
#<alt (* (pow x 2) (- 1 (/ 1 x)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (/ 1 x)))>
#<alt (* (pow x 2) (- 1 (/ 1 x)))>
#<alt (* (pow x 2) (- 1 (/ 1 x)))>

Calls

12 calls:

Time	Variable		Point	Expression
31.0ms	x	@	inf	(* x (+ x -1))
2.0ms	x	@	0	(* x (+ x -1))
1.0ms	x	@	-inf	(* 2 (atan (+ 1 (* x (+ x -1)))))
0.0ms	x	@	inf	(* 2 (atan (+ 1 (* x (+ x -1)))))
0.0ms	x	@	0	(* 2 (atan (+ 1 (* x (+ x -1)))))

rewrite199.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1838×	`sum4-define`
1626×	`prod-diff`
1274×	`--lowering--.f32`
1274×	`--lowering--.f64`
1172×	`fnmadd-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	20	27
2	38	26
3	57	26
4	82	26
5	141	26
6	260	26
7	546	26
8	1635	26
9	4948	26
0	8245	26

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 229

Calls

Call 1

Inputs
(* 2 (atan (+ 1 (* x (+ x -1)))))
(atan (+ 1 (* x (+ x -1))))
(+ 1 (* x (+ x -1)))
(* x (+ x -1))

Outputs
(+.f64 (.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))))) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))))))
(-.f64 #s(literal 0 binary64) (.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal 1 binary64) x))))))
(neg.f64 (.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal 1 binary64) x))))))
(neg.f64 (.f64 (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))) #s(literal -2 binary64)))
(neg.f64 (.f64 #s(literal -2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))))))
(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
(.f64 #s(literal -1 binary64) (.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))
(.f64 (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
(.f64 (atan.f64 (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))) #s(literal -1 binary64))
(.f64 #s(literal -2 binary64) (atan.f64 (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal 1 binary64) x)))))
(+.f64 (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))))
(-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))
(-.f64 #s(literal 0 binary64) (-.f64 (atan.f64 (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) #s(literal 0 binary64)))
(atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(fma.f64 #s(literal -1 binary64) (atan.f64 (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) #s(literal 0 binary64))
(fma.f64 (atan.f64 (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64) #s(literal 0 binary64))
(neg.f64 (atan.f64 (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))
(.f64 #s(literal -1 binary64) (atan.f64 (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal 1 binary64) x)))))
(.f64 (atan.f64 (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))
(+.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))
(+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) #s(literal 0 binary64))
(+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))))
(+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (neg.f64 (+.f64 (+.f64 x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x))))
(+.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))) (.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))))
(+.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))) (.f64 #s(literal -1 binary64) (+.f64 (+.f64 x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x))))
(+.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))) (.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)))
(+.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))) (.f64 (+.f64 (+.f64 x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(+.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(+.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x))
(+.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 0 binary64) x))
(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x))
(+.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) #s(literal -2 binary64))) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (*.f64 x x)))
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(+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))) (-.f64 #s(literal 1 binary64) x)) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) x)))
(+.f64 (.f64 (.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 x #s(literal -1 binary64))) (.f64 (.f64 x x) (+.f64 x #s(literal -1 binary64))))
(+.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal 1 binary64) x))) (+.f64 x #s(literal -1 binary64))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 x #s(literal -1 binary64))))
(+.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))) (-.f64 #s(literal -1 binary64) (*.f64 x x)))
(+.f64 (+.f64 #s(literal 0 binary64) (-.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) #s(literal -2 binary64)))) (-.f64 #s(literal -1 binary64) (*.f64 x x)))
(+.f64 (+.f64 #s(literal 0 binary64) (.f64 x (+.f64 (+.f64 x #s(literal -1 binary64)) x))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(+.f64 (+.f64 (.f64 x x) (.f64 x (+.f64 x #s(literal -1 binary64)))) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(+.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) (.f64 #s(literal 2 binary64) (.f64 x x))) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(+.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1 binary64))) (-.f64 #s(literal -1 binary64) (*.f64 x x)))
(+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) #s(literal -2 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) #s(literal -2 binary64))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) #s(literal -2 binary64))) (-.f64 (.f64 (.f64 x x) #s(literal -2 binary64)) #s(literal 1 binary64))) (*.f64 x x))
(+.f64 (+.f64 (.f64 x (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (-.f64 (.f64 (.f64 x x) #s(literal -2 binary64)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (.f64 x x)))
(+.f64 (+.f64 (.f64 x (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (.f64 (.f64 x x) #s(literal -2 binary64))) (.f64 x x))
(-.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))) #s(literal 0 binary64))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) #s(literal 1 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))
(-.f64 (*.f64 x x) x)
(-.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(-.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) (-.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) x)))
(-.f64 (+.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1 binary64)) (-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 0 binary64) x)))
(-.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) #s(literal -2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 (.f64 x (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (.f64 x x))
(-.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))) (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 (+.f64 #s(literal 0 binary64) (-.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) #s(literal -2 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 (+.f64 #s(literal 0 binary64) (.f64 x (+.f64 (+.f64 x #s(literal -1 binary64)) x))) (.f64 x x))
(-.f64 (+.f64 (.f64 x x) (.f64 x (+.f64 x #s(literal -1 binary64)))) (*.f64 x x))
(-.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) (.f64 #s(literal 2 binary64) (.f64 x x))) (*.f64 x x))
(-.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) #s(literal -2 binary64))) #s(literal -1 binary64)) (*.f64 x x))
(-.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) #s(literal -2 binary64))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -2 binary64))) (-.f64 #s(literal -1 binary64) (*.f64 x x)))
(-.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) #s(literal -2 binary64))) (-.f64 (.f64 (.f64 x x) #s(literal -2 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(-.f64 (+.f64 (.f64 x (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (-.f64 (.f64 (.f64 x x) #s(literal -2 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal -1 binary64) (.f64 x x)))
(-.f64 (+.f64 (.f64 x (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (.f64 (.f64 x x) #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(-.f64 (-.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) #s(literal -2 binary64))) (.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x)))) (-.f64 #s(literal -1 binary64) (*.f64 x x)))
(-.f64 (-.f64 (.f64 x (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (+.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1 binary64))) (-.f64 #s(literal -1 binary64) (.f64 x x)))
(fma.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) (-.f64 #s(literal 0 binary64) x))
(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x) (*.f64 x x))
(fma.f64 x x (-.f64 #s(literal 0 binary64) x))
(fma.f64 x #s(literal -1 binary64) (*.f64 x x))
(fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) x (*.f64 x x))
(fma.f64 #s(literal -1 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 x #s(literal -1 binary64))))
(fma.f64 (*.f64 x x) #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64) (*.f64 x x))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 1 binary64) x) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 0 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))
(fma.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) x) #s(literal 0 binary64))
(fma.f64 (+.f64 x #s(literal -1 binary64)) x #s(literal 0 binary64))
(fma.f64 (*.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x))
(neg.f64 (*.f64 x (-.f64 #s(literal 1 binary64) x)))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (.f64 x (-.f64 #s(literal 1 binary64) x)))
(.f64 (.f64 x (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 1 binary64) x))
(*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) x))
(*.f64 (+.f64 x #s(literal -1 binary64)) x)
(.f64 (.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))

simplify132.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

2594×	`fnmadd-define`
1922×	`fma-lowering-fma.f32`
1922×	`fma-lowering-fma.f64`
1840×	`sum3-define`
1838×	`fnmsub-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	365
1	77	319
2	180	319
3	492	319
4	1382	286
5	3513	286
6	6925	286
0	8166	286

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
(* 2 (atan (+ 1 (* x (- x 1)))))
(* 2 (atan (+ 1 (* x (- x 1)))))
(* 2 (atan (+ 1 (* x (- x 1)))))
(* 2 (atan (+ 1 (* x (- x 1)))))
(* 2 (atan (- (+ 1 (pow x 2)) x)))
(* 2 (atan (- (+ 1 (pow x 2)) x)))
(* 2 (atan (- (+ 1 (pow x 2)) x)))
(* 2 (atan (- (+ 1 (pow x 2)) x)))
(* 2 (atan (+ 1 (+ (* -1 x) (pow x 2)))))
(* 2 (atan (+ 1 (+ (* -1 x) (pow x 2)))))
(* 2 (atan (+ 1 (+ (* -1 x) (pow x 2)))))
(* 2 (atan (+ 1 (+ (* -1 x) (pow x 2)))))
(atan (+ 1 (* x (- x 1))))
(atan (+ 1 (* x (- x 1))))
(atan (+ 1 (* x (- x 1))))
(atan (+ 1 (* x (- x 1))))
(atan (- (+ 1 (pow x 2)) x))
(atan (- (+ 1 (pow x 2)) x))
(atan (- (+ 1 (pow x 2)) x))
(atan (- (+ 1 (pow x 2)) x))
(atan (+ 1 (+ (* -1 x) (pow x 2))))
(atan (+ 1 (+ (* -1 x) (pow x 2))))
(atan (+ 1 (+ (* -1 x) (pow x 2))))
(atan (+ 1 (+ (* -1 x) (pow x 2))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- x 1)))
(+ 1 (* x (- x 1)))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)))
(* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (+ 1 (* -1 (/ (- 1 (/ 1 x)) x))))
(* (pow x 2) (+ 1 (* -1 (/ (- 1 (/ 1 x)) x))))
(* -1 x)
(* x (- x 1))
(* x (- x 1))
(* x (- x 1))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))

Outputs
(* 2 (atan (+ 1 (* x (- x 1)))))
(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
(* 2 (atan (+ 1 (* x (- x 1)))))
(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
(* 2 (atan (+ 1 (* x (- x 1)))))
(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
(* 2 (atan (+ 1 (* x (- x 1)))))
(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
(* 2 (atan (- (+ 1 (pow x 2)) x)))
(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
(* 2 (atan (- (+ 1 (pow x 2)) x)))
(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
(* 2 (atan (- (+ 1 (pow x 2)) x)))
(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
(* 2 (atan (- (+ 1 (pow x 2)) x)))
(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
(* 2 (atan (+ 1 (+ (* -1 x) (pow x 2)))))
(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
(* 2 (atan (+ 1 (+ (* -1 x) (pow x 2)))))
(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
(* 2 (atan (+ 1 (+ (* -1 x) (pow x 2)))))
(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
(* 2 (atan (+ 1 (+ (* -1 x) (pow x 2)))))
(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
(atan (+ 1 (* x (- x 1))))
(atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(atan (+ 1 (* x (- x 1))))
(atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(atan (+ 1 (* x (- x 1))))
(atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(atan (+ 1 (* x (- x 1))))
(atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(atan (- (+ 1 (pow x 2)) x))
(atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(atan (- (+ 1 (pow x 2)) x))
(atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(atan (- (+ 1 (pow x 2)) x))
(atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(atan (- (+ 1 (pow x 2)) x))
(atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(atan (+ 1 (+ (* -1 x) (pow x 2))))
(atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(atan (+ 1 (+ (* -1 x) (pow x 2))))
(atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(atan (+ 1 (+ (* -1 x) (pow x 2))))
(atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(atan (+ 1 (+ (* -1 x) (pow x 2))))
(atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- x 1)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))
(+ 1 (* x (- x 1)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))
(* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(* (pow x 2) (+ 1 (* -1 (/ (- 1 (/ 1 x)) x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))
(* (pow x 2) (+ 1 (* -1 (/ (- 1 (/ 1 x)) x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* x (- x 1))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(* x (- x 1))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(* x (- x 1))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal -1 binary64)))

eval36.0ms (0.6%)

Compiler: Compiled 4294 to 870 computations (79.7% saved)

prune30.0ms (0.5%)

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	276	1	277
Fresh	0	0	0
Picked	1	0	1
Done	0	7	7
Total	277	8	285

Accuracy

100.0%

Counts

285 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(.f64 (atan.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x))))) #s(literal 2 binary64))
✓	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))
✓	99.3%	(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
	99.3%	(.f64 #s(literal 2 binary64) (atan.f64 (-.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) x)))
✓	99.3%	(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
✓	99.7%	(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
✓	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
✓	97.8%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))

Compiler

Compiled 202 to 122 computations (39.6% saved)

regimes16.0ms (0.3%)

Counts

11 → 1

Calls

Call 1

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

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

Calls

5 calls:

4.0ms	x
3.0ms	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
3.0ms	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
3.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
3.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
100.0%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
100.0%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
100.0%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 41 to 28 computations (31.7% saved)

regimes17.0ms (0.3%)

Counts

10 → 1

Calls

Call 1

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

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

Calls

5 calls:

3.0ms	x
3.0ms	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
3.0ms	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
3.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
3.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
100.0%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
100.0%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
100.0%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 41 to 28 computations (31.7% saved)

regimes15.0ms (0.3%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

5 calls:

3.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
3.0ms	x
3.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
3.0ms	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
2.0ms	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
100.0%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
100.0%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
100.0%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 41 to 28 computations (31.7% saved)

regimes3.0ms (0.1%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0.1%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0.1%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

2 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))

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

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
99.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))

Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
97.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

36×	`*-commutative_binary64`
22×	`+-commutative_binary64`
10×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	96
1	76	96
2	87	96
3	93	96
4	97	96
5	98	96

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.1s (19.4%)

Rules

3528×	`-lowering-.f32`
3528×	`-lowering-.f64`
2580×	`fma-lowering-fma.f32`
2580×	`fma-lowering-fma.f64`
2544×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	164
1	82	150
2	258	145
3	818	140
4	3236	140
0	8057	140
0	200	1968
1	588	1687
2	1906	1646
3	6411	1645
0	8729	1645
0	107	519
1	313	442
2	910	432
3	2498	428
0	8482	428
0	9	35
1	29	35
2	105	35
3	533	35
0	2544	35

Stop Event

1×	fuel
1×	iter 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 207 to 132 computations (36.2% saved)

preprocess48.0ms (0.8%)

Compiler: Compiled 218 to 110 computations (49.5% saved)

analyze8.0ms (0.1%)

sample933.0ms (16.1%)

preprocess67.0ms (1.1%)

explain103.0ms (1.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify31.0ms (0.5%)

localize47.0ms (0.8%)

series4.0ms (0.1%)

rewrite136.0ms (2.3%)

simplify205.0ms (3.5%)

eval32.0ms (0.6%)

prune27.0ms (0.5%)

simplify187.0ms (3.2%)

localize432.0ms (7.4%)

series18.0ms (0.3%)

rewrite282.0ms (4.9%)

simplify257.0ms (4.4%)

eval127.0ms (2.2%)

prune111.0ms (1.9%)

simplify151.0ms (2.6%)

localize228.0ms (3.9%)

series8.0ms (0.1%)

rewrite228.0ms (3.9%)

simplify237.0ms (4.1%)

eval104.0ms (1.8%)

prune79.0ms (1.4%)

simplify39.0ms (0.7%)

localize46.0ms (0.8%)

series36.0ms (0.6%)

rewrite199.0ms (3.4%)

simplify132.0ms (2.3%)

eval36.0ms (0.6%)

prune30.0ms (0.5%)

regimes16.0ms (0.3%)

regimes17.0ms (0.3%)

regimes15.0ms (0.3%)

regimes3.0ms (0.1%)

regimes3.0ms (0.1%)

regimes4.0ms (0.1%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify10.0ms (0.2%)

soundness1.1s (19.4%)

preprocess48.0ms (0.8%)

end0.0ms (0%)

Profiling