Metrics for arccos

analyze9.0ms (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: 6.0ms

ival-sub: 4.0ms (64.9% of total)

ival-mult: 1.0ms (16.2% of total)

ival-sqrt: 1.0ms (16.2% of total)

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

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

const: 0.0ms (0% of total)

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

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

sample853.0ms (10.7%)

Results

639.0ms	8256×	0	valid
3.0ms	23×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 415.0ms

ival-atan: 88.0ms (21.2% of total)

ival-sqrt: 71.0ms (17.1% of total)

ival-mult: 64.0ms (15.4% of total)

ival-sub: 62.0ms (14.9% of total)

ival-div: 62.0ms (14.9% of total)

ival-add: 54.0ms (13% of total)

const: 13.0ms (3.1% of total)

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

Bogosity

preprocess64.0ms (0.8%)

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)

explain135.0ms (1.7%)

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

100.0ms

512×

valid

Compiler

Compiled 104 to 29 computations (72.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-atan: 6.0ms (23.6% of total)

ival-sub: 5.0ms (19.6% of total)

ival-mult: 4.0ms (15.7% of total)

ival-sqrt: 4.0ms (15.7% of total)

ival-div: 3.0ms (11.8% of total)

ival-add: 3.0ms (11.8% of total)

const: 1.0ms (3.9% 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 (0.4%)

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)

localize43.0ms (0.5%)

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

29.0ms

256×

valid

Compiler

Compiled 46 to 10 computations (78.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-sub: 2.0ms (16.8% of total)

ival-div: 2.0ms (16.8% of total)

ival-mult: 2.0ms (16.8% of total)

ival-sqrt: 2.0ms (16.8% of total)

ival-atan: 2.0ms (16.8% of total)

ival-add: 1.0ms (8.4% of total)

const: 0.0ms (0% of total)

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

series4.0ms (0%)

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)))

rewrite230.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

2432×	`/-lowering-/.f32`
2432×	`/-lowering-/.f64`
2382×	`-lowering-.f32`
2382×	`-lowering-.f64`
1310×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	35
1	46	35
2	347	35
3	4811	35
0	8133	35

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 237

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))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.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 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.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 (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))
(/.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) (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.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) (sqrt.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 (-.f64 #s(literal -1 binary64) x) x))) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 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 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 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 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))) (neg.f64 (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x)))))
(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))
(pow.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.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))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.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 (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 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.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)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(*.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 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 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
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(.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (-.f64 #s(literal -1 binary64) x) x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))
(.f64 (.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 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 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 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 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (+.f64 x #s(literal -1 binary64)))
(.f64 (.f64 (+.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 #s(literal 1 binary64) x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.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) (*.f64 x (+.f64 x #s(literal -1 binary64)))))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.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) (.f64 x (.f64 x x)))) (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.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 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 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) (.f64 x (.f64 x x))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x)))))
(.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))))))
(.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 (+.f64 #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 (-.f64 #s(literal 1 binary64) x) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 x #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal -1 binary64) (.f64 x x))) (+.f64 x #s(literal -1 binary64)))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.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) (.f64 x (.f64 x x)))) (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 x (+.f64 x #s(literal -1 binary64))))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))) (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 x (+.f64 x #s(literal -1 binary64))))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (.f64 x x) #s(literal -1 binary64))) (+.f64 x #s(literal -1 binary64)))
(.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 (+.f64 #s(literal 1 binary64) x) (.f64 x (+.f64 #s(literal 1 binary64) x))))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) (-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))))
(.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 (+.f64 #s(literal 1 binary64) x) (.f64 x (+.f64 #s(literal 1 binary64) x)))))) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))))

simplify218.0ms (2.7%)

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	449
2	908	437
3	2496	429
0	8510	429

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 (-.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 (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 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (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 x #s(literal -2 binary64)))))))
-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))

eval39.0ms (0.5%)

Compiler: Compiled 6693 to 1310 computations (80.4% saved)

prune30.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	280	5	285
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	280	6	286

Accuracy

100.0%

Counts

286 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	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))))))
▶	99.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
▶	99.4%	(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))))
▶	99.2%	(.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)))))))
✓	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
▶	97.9%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))

Compiler

Compiled 124 to 99 computations (20.2% saved)

simplify200.0ms (2.5%)

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 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
✓	cost-diff	128	(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))
✓	cost-diff	128	(atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))))
✓	cost-diff	128	(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 (-.f64 #s(literal 1 binary64) 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

2604×	`sum5-define`
2464×	`sum3-define`
1912×	`fnmsub-define`
1736×	`sum4-define`
1182×	`fnmadd-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	210
1	62	194
2	140	194
3	256	187
4	700	187
5	1823	187
6	4225	187
7	5993	187
8	6159	187
9	6363	187
10	6430	187
0	8406	187

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

localize158.0ms (2%)

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

Results

103.0ms	255×	0	valid
1.0ms	1×	2	valid

Compiler

Compiled 218 to 30 computations (86.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-mult: 20.0ms (45.5% of total)

ival-atan: 10.0ms (22.7% of total)

ival-add: 7.0ms (15.9% of total)

ival-div: 3.0ms (6.8% of total)

ival-sqrt: 2.0ms (4.5% of total)

const: 1.0ms (2.3% of total)

ival-sub: 1.0ms (2.3% of total)

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

series13.0ms (0.2%)

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 (* 2 (atan (+ 1 (* x (+ -1 (* x (* (- 1 x) 1/2)))))))>
#<alt (atan (+ 1 (* x (+ -1 (* x (* (- 1 x) 1/2))))))>
#<alt (+ 1 (* x (+ -1 (* x (* (- 1 x) 1/2)))))>
#<alt (* x (+ -1 (* x (* (- 1 x) 1/2))))>
#<alt (/ (+ 1 x) (- 1 x))>
#<alt (* x 1/2)>
#<alt (* x (* (- 1 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 (* 2 (atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x)))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x)))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x)))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x)))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))>
#<alt (atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))>
#<alt (atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))>
#<alt (atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))>
#<alt (atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))>
#<alt (atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x))>
#<alt (atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x))>
#<alt (atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x))>
#<alt (atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x))>
#<alt (atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))>
#<alt (atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))>
#<alt (atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))>
#<alt (atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))>
#<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 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	(* 2 (atan (+ 1 (* x (+ -1 (* x (* (- 1 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 x) 1/2)))))))
0.0ms	x	@	inf	(* 2 (atan (+ 1 (* x (+ -1 (* x 1/2))))))

rewrite317.0ms (4%)

Algorithm

1×	batch-egg-rewrite

Rules

3930×	`/-lowering-/.f32`
3930×	`/-lowering-/.f64`
3756×	`-lowering-.f32`
3756×	`-lowering-.f64`
1542×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	164
1	139	150
2	1175	150
0	8661	150

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 441

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

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 (/.f64 #s(literal -1 binary64) (sqrt.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 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 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 -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 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))
(/.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 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 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 (-.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 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 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))))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(pow.f64 (sqrt.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 1/2 binary64))
(pow.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.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)))) #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 (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 -1 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 #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 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64)) (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/4 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 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.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 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.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 #s(literal -1 binary64) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) x)) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x))) (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) (.f64 x (.f64 x x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #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)))))
(exp.f64 (neg.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))))
(-.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 #s(literal 0 binary64) (/.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)))
(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) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 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) (neg.f64 (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 (-.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) (.f64 x x)) #s(literal 1/2 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 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.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 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 #s(literal -1 binary64)) (sqrt.f64 (-.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))))
(/.f64 (.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)) #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 (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 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))) (neg.f64 (pow.f64 (+.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #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)))))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(pow.f64 (sqrt.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 -1/2 binary64))
(pow.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.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))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.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 (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) (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 (-.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)))
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(/.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 x x)) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (+.f64 #s(literal -1 binary64) x) (+.f64 #s(literal -1 binary64) x)))
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(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))
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(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (+.f64 #s(literal -1 binary64) x) (+.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) x))))
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(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))) (-.f64 #s(literal 1 binary64) x))))
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(/.f64 (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))))
(pow.f64 (/.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 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (-.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 #s(literal -1 binary64) (/.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) (+.f64 #s(literal -1 binary64) x)))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.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 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x 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) (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x))))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x))))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.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) (*.f64 x (+.f64 #s(literal 1 binary64) x))))))
(.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))) (-.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))))
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(.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))))
(.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 1 binary64) x)))
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(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) x))
(neg.f64 (*.f64 #s(literal -1/2 binary64) x))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
(.f64 #s(literal -1 binary64) (.f64 #s(literal -1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
(-.f64 #s(literal 0 binary64) (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) x))))
(neg.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) x))))
(/.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) x)))
(.f64 (-.f64 #s(literal 1 binary64) x) (.f64 x #s(literal 1/2 binary64)))
(.f64 #s(literal -1 binary64) (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(.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 #s(literal -1/2 binary64) x)) x)
(.f64 (.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))

simplify284.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

3600×	`-lowering-.f32`
3600×	`-lowering-.f64`
1500×	`sum3-define`
1478×	`+-lowering-+.f64`
1478×	`+-lowering-+.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	206	1968
1	609	1749
2	1976	1680
3	6569	1679
0	8023	1679

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

eval121.0ms (1.5%)

Compiler: Compiled 18797 to 3044 computations (83.8% saved)

prune80.0ms (1%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	775	6	781
Fresh	0	0	0
Picked	2	3	5
Done	0	1	1
Total	777	10	787

Accuracy

100.0%

Counts

787 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.4%	(.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (-.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) x))))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) x)))))) (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) x))))) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) x)))))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) x)))))) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))))))
▶	99.4%	(.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.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))))))))
▶	99.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
✓	99.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
▶	99.2%	(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x #s(literal 1/2 binary64))))))
✓	99.2%	(.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)))))))
▶	99.4%	(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))))
▶	34.0%	(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (.f64 x x) (.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))))
✓	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
✓	97.9%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))

Compiler

Compiled 373 to 189 computations (49.3% saved)

simplify197.0ms (2.5%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	256	(.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
✓	cost-diff	768	(.f64 (.f64 x x) (.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
✓	cost-diff	768	(atan.f64 (.f64 (.f64 x x) (.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))
✓	cost-diff	768	(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (.f64 x x) (.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64))))
✓	cost-diff	0	(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(atan.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(+.f64 (-.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x #s(literal 1/2 binary64))))
✓	cost-diff	0	(atan.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x #s(literal 1/2 binary64)))))
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x #s(literal 1/2 binary64))))))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
✓	cost-diff	128	(+.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)))))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (+.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))))))
✓	cost-diff	128	(atan.f64 (/.f64 #s(literal 1 binary64) (+.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)))))))
✓	cost-diff	128	(.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.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))))))))

Rules

2598×	`-lowering-.f32`
2598×	`-lowering-.f64`
1576×	`fnmsub-define`
1172×	`/-lowering-/.f32`
1172×	`/-lowering-/.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	40	330
1	99	310
2	267	302
3	822	299
4	2224	297
5	6178	296
0	8303	296

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize196.0ms (2.5%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)
✓	accuracy	86.2%	(.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
✓	accuracy	81.3%	(+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
✓	accuracy	48.0%	(.f64 (.f64 x x) (.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))))
✓	accuracy	100.0%	(atan.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x)))
✓	accuracy	100.0%	(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x #s(literal 1/2 binary64))))))
✓	accuracy	100.0%	(+.f64 (-.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(atan.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (.f64 x (.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) (+.f64 #s(literal 1 binary64) x))))
✓	accuracy	100.0%	(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) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))))))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.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))))))
✓	accuracy	100.0%	(*.f64 x (+.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))

Results

115.0ms

256×

valid

Compiler

Compiled 387 to 41 computations (89.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 67.0ms

ival-mult: 34.0ms (50.5% of total)

ival-atan: 12.0ms (17.8% of total)

ival-add: 10.0ms (14.8% of total)

ival-div: 9.0ms (13.4% of total)

ival-sub: 1.0ms (1.5% of total)

const: 1.0ms (1.5% of total)

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

series19.0ms (0.2%)

Counts

25 → 300

Calls

Call 1

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

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

Calls

75 calls:

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

rewrite1.9s (24.1%)

Algorithm

1×	batch-egg-rewrite

Rules

5022×	`-lowering-.f32`
5022×	`-lowering-.f64`
2830×	`+-lowering-+.f64`
2830×	`+-lowering-+.f32`
2792×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	265
1	221	238
2	2233	232
0	9967	232

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 543

Calls

Call 1

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

Outputs
(.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))))))
(.f64 (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))))) #s(literal 2 binary64))
(atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))))
(neg.f64 (atan.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))))))
(exp.f64 (.f64 (log1p.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))) #s(literal -1 binary64)))
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(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))) (*.f64 x (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) x)))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))))
(/.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) x))) x))
(/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))
(/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) #s(literal 1 binary64)) x)
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)))) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) x))))
(/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)))
(pow.f64 (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x))
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) x)))))
(.f64 (pow.f64 (/.f64 x (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))))

simplify241.0ms (3%)

Algorithm

1×	egg-herbie

Rules

3228×	`-lowering-.f32`
3228×	`-lowering-.f64`
2174×	`/-lowering-/.f32`
2174×	`/-lowering-/.f64`
1520×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	220	2879
1	677	2602
2	2166	2393
0	8436	2393

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 300

Calls

Call 1

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

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

eval130.0ms (1.6%)

Compiler: Compiled 29567 to 3630 computations (87.7% saved)

prune79.0ms (1%)

Pruning

11 alts after pruning (4 fresh and 7 done)

	Pruned	Kept	Total
New	931	4	935
Fresh	1	0	1
Picked	2	3	5
Done	0	4	4
Total	934	11	945

Accuracy

100.0%

Counts

945 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) (.f64 x #s(literal 1/2 binary64)))))))
✓	99.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
▶	99.4%	(.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64))))))))
✓	99.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
✓	99.2%	(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x #s(literal 1/2 binary64))))))
▶	99.0%	(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
✓	99.2%	(.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)))))))
✓	99.4%	(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))))
▶	46.2%	(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal -1 binary64) x))))))
✓	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
✓	97.9%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))

Compiler

Compiled 144 to 108 computations (25% saved)

simplify176.0ms (2.2%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Rules

2780×	`-lowering-.f32`
2780×	`-lowering-.f64`
2000×	`+-lowering-+.f64`
2000×	`+-lowering-+.f32`
1250×	`distribute-lft-in`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	285
1	99	262
2	267	257
3	894	247
4	2260	247
5	3340	247
6	7448	247
0	8031	247

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize147.0ms (1.8%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) (*.f64 x #s(literal 1/2 binary64))))))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) (*.f64 x #s(literal 1/2 binary64)))))
✓	accuracy	100.0%	(.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) (*.f64 x #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x (+.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64))))))))
✓	accuracy	100.0%	(atan.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64)))))))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64))))))
✓	accuracy	100.0%	(.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64)))))
✓	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%	(*.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 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal -1 binary64) x)))
✓	accuracy	100.0%	(atan.f64 (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal -1 binary64) x)))))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	accuracy	48.0%	(.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal -1 binary64) x))))

Results

91.0ms

256×

valid

Compiler

Compiled 311 to 36 computations (88.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-mult: 24.0ms (45.5% of total)

ival-add: 10.0ms (19% of total)

ival-atan: 10.0ms (19% of total)

ival-div: 7.0ms (13.3% of total)

const: 1.0ms (1.9% of total)

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

series10.0ms (0.1%)

Counts

20 → 240

Calls

Call 1

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

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

Calls

60 calls:

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

rewrite302.0ms (3.8%)

Algorithm

1×	batch-egg-rewrite

Rules

2560×	`fma-lowering-fma.f32`
2560×	`fma-lowering-fma.f64`
2148×	`-lowering-.f32`
2148×	`-lowering-.f64`
2064×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	35	221
1	215	197
2	2308	192
0	8556	192

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 579

Calls

Call 1

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

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

simplify261.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

4298×	`-lowering-.f32`
4298×	`-lowering-.f64`
1554×	`+-lowering-+.f64`
1554×	`+-lowering-+.f32`
1354×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	2436
1	570	2305
2	1894	2153
3	7757	2153
0	8068	2153

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

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

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

eval103.0ms (1.3%)

Compiler: Compiled 23373 to 2492 computations (89.3% saved)

prune63.0ms (0.8%)

Pruning

11 alts after pruning (3 fresh and 8 done)

	Pruned	Kept	Total
New	846	3	849
Fresh	0	0	0
Picked	3	1	4
Done	0	7	7
Total	849	11	860

Accuracy

100.0%

Counts

860 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.4%	(.f64 (atan.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
✓	99.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
	99.0%	(.f64 #s(literal 2 binary64) (atan.f64 (-.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) x)))
✓	99.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
✓	99.2%	(.f64 #s(literal 2 binary64) (atan.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x #s(literal 1/2 binary64))))))
✓	99.2%	(.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)))))))
	99.4%	(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64))))))))
✓	99.4%	(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))))
✓	46.2%	(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal -1 binary64) x))))))
✓	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
✓	97.9%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))

Compiler

Compiled 479 to 222 computations (53.7% saved)

regimes27.0ms (0.3%)

Counts

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

Calls

5 calls:

5.0ms	x
5.0ms	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
5.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
5.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
4.0ms	(*.f64 #s(literal 2 binary64) (atan.f64 (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)

regimes7.0ms (0.1%)

Counts

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

Outputs

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

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
99.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0.1%)

Counts

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

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
99.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

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 #s(literal 2 binary64) (atan.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (.f64 x (*.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
99.2%	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
99.0%	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
99.0%	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
97.9%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	73
1	62	73
2	65	73
3	67	73
4	68	73

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.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 #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))))))))
(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))) (-.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 #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 (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 #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))))))))
(.f64 #s(literal 2 binary64) (atan.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) 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)))))))
(.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 x (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 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 (13.5%)

Rules

3600×	`-lowering-.f32`
3600×	`-lowering-.f64`
2544×	`-lowering-.f32`
2544×	`-lowering-.f64`
2432×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	206	1968
1	609	1749
2	1976	1680
3	6569	1679
0	8023	1679
0	107	519
1	313	449
2	908	437
3	2496	429
0	8510	429
0	9	35
1	46	35
2	347	35
3	4811	35
0	8133	35

Stop Event

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

Compiler

Compiled 170 to 110 computations (35.3% saved)

preprocess147.0ms (1.9%)

Compiler: Compiled 172 to 92 computations (46.5% saved)

analyze9.0ms (0.1%)

sample853.0ms (10.7%)

preprocess64.0ms (0.8%)

explain135.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify31.0ms (0.4%)

localize43.0ms (0.5%)

series4.0ms (0%)

rewrite230.0ms (2.9%)

simplify218.0ms (2.7%)

eval39.0ms (0.5%)

prune30.0ms (0.4%)

simplify200.0ms (2.5%)

localize158.0ms (2%)

series13.0ms (0.2%)

rewrite317.0ms (4%)

simplify284.0ms (3.6%)

eval121.0ms (1.5%)

prune80.0ms (1%)

simplify197.0ms (2.5%)

localize196.0ms (2.5%)

series19.0ms (0.2%)

rewrite1.9s (24.1%)

simplify241.0ms (3%)

eval130.0ms (1.6%)

prune79.0ms (1%)

simplify176.0ms (2.2%)

localize147.0ms (1.8%)

series10.0ms (0.1%)

rewrite302.0ms (3.8%)

simplify261.0ms (3.3%)

eval103.0ms (1.3%)

prune63.0ms (0.8%)

regimes27.0ms (0.3%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify10.0ms (0.1%)

soundness1.1s (13.5%)

preprocess147.0ms (1.9%)

end0.0ms (0%)

Profiling