Ian Simplification

Time bar (total: 2.5min)

analyze5.0ms (0%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
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%50%0%0%50%0%3
50%25%25%0%0%50%0%4
75%37.5%12.5%0%0%50%0%5
87.5%43.7%6.2%0%0%50%0%6
93.8%46.9%3.1%0%0%50%0%7
96.9%48.4%1.6%0%0%50%0%8
98.4%49.2%0.8%0%0%50%0%9
99.2%49.6%0.4%0%0%50%0%10
99.6%49.8%0.2%0%0%50%0%11
99.8%49.9%0.1%0%0%50%0%12
Compiler

Compiled 15 to 12 computations (20% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-div: 1.0ms (39.3% of total)
ival-asin: 1.0ms (39.3% of total)
ival-pi: 0.0ms (0% of total)
ival-sub: 0.0ms (0% of total)
ival-mult: 0.0ms (0% of total)
const: 0.0ms (0% of total)
ival-sqrt: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample3.6s (2.4%)

Results
1.7s3371×2valid
1.4s4675×1valid
20.0ms210×0valid
0.0ms4×0invalid
Precisions
Click to see histograms. Total time spent on operations: 2.6s
ival-asin: 1.2s (45.5% of total)
ival-div: 373.0ms (14.1% of total)
ival-sub: 353.0ms (13.3% of total)
ival-sqrt: 199.0ms (7.5% of total)
ival-mult: 191.0ms (7.2% of total)
backward-pass: 181.0ms (6.8% of total)
ival-pi: 118.0ms (4.5% of total)
const: 30.0ms (1.1% of total)
Bogosity

preprocess73.0ms (0%)

Algorithm
2×egg-herbie
Rules
770×fnmadd-define
612×fmsub-define
590×fnmsub-define
466×fmm-def
362×fma-define
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01942
14740
29737
322433
446133
590433
6144533
7190733
8228233
9241533
10243933
01113
12613
24012
36712
410511
517211
629211
744111
856011
985011
10104111
11106311
0106311
Stop Event
1×iter limit
1×saturated
1×saturated
Calls
Call 1
Inputs
(- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2)))))
Outputs
(- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2)))))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))))) #s(literal -2 binary64)))
Call 2
Inputs
(- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2)))))
(- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 (neg x)) 2)))))
(neg (- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 (neg x)) 2))))))
Outputs
(- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2)))))
(fnmsub 2 (asin (sqrt (fnmsub x 1/2 -1/2))) (* (PI) -1/2))
(- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 (neg x)) 2)))))
(fnmsub 2 (asin (sqrt (fnmsub x -1/2 -1/2))) (* (PI) -1/2))
(neg (- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 (neg x)) 2))))))
(fnmsub (asin (sqrt (fnmsub x -1/2 -1/2))) -2 (* (PI) 1/2))

explain309.0ms (0.2%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2540-0-(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
00-0-(PI.f64)
00-0-x
00-0-(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
00-0-#s(literal 2 binary64)
00-0-(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
00-0-(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
00-0-(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
00-0-(-.f64 #s(literal 1 binary64) x)
00-0-(/.f64 (PI.f64) #s(literal 2 binary64))
00-0-#s(literal 1 binary64)
Results
147.0ms250×2valid
93.0ms248×1valid
2.0ms14×0valid
Compiler

Compiled 118 to 35 computations (70.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 179.0ms
ival-asin: 68.0ms (38% of total)
ival-sub: 33.0ms (18.5% of total)
ival-mult: 19.0ms (10.6% of total)
ival-div: 18.0ms (10.1% of total)
backward-pass: 17.0ms (9.5% of total)
ival-sqrt: 15.0ms (8.4% of total)
ival-pi: 7.0ms (3.9% of total)
const: 2.0ms (1.1% of total)

eval0.0ms (0%)

Compiler

Compiled 14 to 12 computations (14.3% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶6.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
Compiler

Compiled 14 to 11 computations (21.4% saved)

simplify31.0ms (0%)

Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
✓cost-diff0
(PI.f64)
✓cost-diff0
(/.f64 (PI.f64) #s(literal 2 binary64))
✓cost-diff0
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
Rules
292×fnmadd-define
232×sum3-define
212×fma-lowering-fma.f32
212×fma-define
212×fmsub-define
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01150
12650
24049
36749
410544
517244
629244
744144
856044
985044
10104144
11106344
0106344
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2)))))
(/ (PI) 2)
(PI)
2
(* 2 (asin (sqrt (/ (- 1 x) 2))))
(asin (sqrt (/ (- 1 x) 2)))
(sqrt (/ (- 1 x) 2))
(/ (- 1 x) 2)
(- 1 x)
1
x
Outputs
(- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2)))))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))))) #s(literal -2 binary64)))
(/ (PI) 2)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI)
(PI.f64)
2
#s(literal 2 binary64)
(* 2 (asin (sqrt (/ (- 1 x) 2))))
(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))))))
(asin (sqrt (/ (- 1 x) 2)))
(asin.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64)))))
(sqrt (/ (- 1 x) 2))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))))
(/ (- 1 x) 2)
(-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64)))
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x

localize131.0ms (0.1%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(PI.f64)
✓accuracy100.0%
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
✓accuracy98.5%
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
✓accuracy8.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
Results
72.0ms125×2valid
38.0ms124×1valid
1.0ms7×0valid
Compiler

Compiled 52 to 12 computations (76.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 82.0ms
ival-asin: 36.0ms (43.9% of total)
backward-pass: 10.0ms (12.2% of total)
ival-div: 9.0ms (11% of total)
ival-mult: 9.0ms (11% of total)
ival-sub: 7.0ms (8.5% of total)
ival-sqrt: 6.0ms (7.3% of total)
ival-pi: 5.0ms (6.1% of total)
const: 1.0ms (1.2% of total)

series7.0ms (0%)

Counts
6 → 48
Calls
Call 1
Inputs
#<alt (- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2)))))>
#<alt (/ (PI) 2)>
#<alt (PI)>
#<alt (* 2 (asin (sqrt (/ (- 1 x) 2))))>
#<alt (asin (sqrt (/ (- 1 x) 2)))>
#<alt (sqrt (/ (- 1 x) 2))>
Outputs
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))>
#<alt (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))>
#<alt (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))>
#<alt (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))>
#<alt (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))>
#<alt (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))>
#<alt (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))>
#<alt (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))>
#<alt (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))>
#<alt (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))>
#<alt (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))>
#<alt (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))>
#<alt (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))>
#<alt (asin (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (asin (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (asin (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (asin (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (asin (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (asin (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (asin (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (asin (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))>
#<alt (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))>
#<alt (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))>
#<alt (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* -1/8 (* x (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* x (+ (* -1/8 (sqrt 1/2)) (* -1/16 (* x (sqrt 1/2))))))))>
#<alt (* (sqrt x) (* (sqrt -1) (sqrt 1/2)))>
#<alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt 1/2) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))>
Calls

12 calls:

TimeVariablePointExpression
3.0ms
x
@0
(sqrt (/ (- 1 x) 2))
1.0ms
x
@inf
(sqrt (/ (- 1 x) 2))
1.0ms
x
@-inf
(sqrt (/ (- 1 x) 2))
1.0ms
x
@0
(- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2)))))
0.0ms
x
@inf
(- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2)))))

rewrite312.0ms (0.2%)

Algorithm
1×batch-egg-rewrite
Rules
4800×*-lowering-*.f32
4800×*-lowering-*.f64
3020×/-lowering-/.f32
3020×/-lowering-/.f64
1152×+-lowering-+.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01139
18538
265638
0813438
Stop Event
1×iter limit
1×node limit
Counts
6 → 286
Calls
Call 1
Inputs
(- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2)))))
(/ (PI) 2)
(PI)
(* 2 (asin (sqrt (/ (- 1 x) 2))))
(asin (sqrt (/ (- 1 x) 2)))
(sqrt (/ (- 1 x) 2))
Outputs
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))))
(+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))
(+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))))
(+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
(+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64))) (+.f64 (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))))
(+.f64 (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64))))
(+.f64 (/.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64))))) (neg.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64)))))))
(+.f64 (/.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))))
(-.f64 #s(literal 0 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))))
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(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) (-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (-.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (pow.f64 (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(/.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 3 binary64))) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))))
(/.f64 (-.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (pow.f64 (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))))))
(/.f64 (neg.f64 (-.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (pow.f64 (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
(/.f64 (+.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (-.f64 (*.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))))))
(/.f64 (-.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
(asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(*.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))))))
(*.f64 (-.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (pow.f64 (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))))
(neg.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 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 #s(literal 2 binary64)) (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 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64)))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) #s(literal 4 binary64)))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (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 #s(literal 1 binary64) x)))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64)) (*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 #s(literal -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 #s(literal 2 binary64)))))
(/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal 1/2 binary64))) (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 x))) (sqrt.f64 #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)))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) (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 x))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64)))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 #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 #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -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 #s(literal 2 binary64)))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))

simplify211.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
4346×*-lowering-*.f32
4346×*-lowering-*.f64
2544×+-lowering-+.f64
2544×+-lowering-+.f32
1670×fnmadd-define
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
094667
1284641
2975619
33438611
08107611
Stop Event
1×iter limit
1×node limit
Counts
48 → 48
Calls
Call 1
Inputs
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* -1/8 (* x (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* x (+ (* -1/8 (sqrt 1/2)) (* -1/16 (* x (sqrt 1/2))))))))
(* (sqrt x) (* (sqrt -1) (sqrt 1/2)))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt 1/2) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))
Outputs
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(*.f64 #s(literal 2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(*.f64 #s(literal 2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(*.f64 #s(literal 2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(*.f64 #s(literal 2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(*.f64 #s(literal 2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(*.f64 #s(literal 2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(*.f64 #s(literal 2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(*.f64 #s(literal 2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64))))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* -1/8 (* x (sqrt 1/2))))))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal -1/8 binary64))))))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* x (+ (* -1/8 (sqrt 1/2)) (* -1/16 (* x (sqrt 1/2))))))))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (*.f64 (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64))) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))))
(* (sqrt x) (* (sqrt -1) (sqrt 1/2)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))
(*.f64 x (+.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(*.f64 x (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (/.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) #s(literal -1 binary64))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt 1/2) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(*.f64 x (+.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (/.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) #s(literal -1 binary64)))) (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (-.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(*.f64 x (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))
(*.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))

eval85.0ms (0.1%)

Compiler

Compiled 10128 to 1187 computations (88.3% saved)

prune68.0ms (0%)

Pruning

22 alts after pruning (21 fresh and 1 done)

PrunedKeptTotal
New31321334
Fresh000
Picked011
Done000
Total31322335
Accuracy
9.3%
Counts
335 → 22
Alt Table
Click to see full alt table
StatusAccuracyProgram
6.0%
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)))
▶6.0%
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)))
6.1%
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64)))) (-.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
6.1%
(/.f64 (-.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))))) #s(literal 64 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 6 binary64))) (*.f64 (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64)))) (+.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 3 binary64)))))
6.1%
(/.f64 (-.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) #s(literal 16 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 4 binary64))) (*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))))
6.1%
(/.f64 (-.f64 (*.f64 (/.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) (/.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))))) (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))))) (+.f64 (/.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))))))
6.1%
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))))) #s(literal 64 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 9 binary64))) (*.f64 (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64)))) (+.f64 (+.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 6 binary64)) (pow.f64 (*.f64 (PI.f64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))))) #s(literal 64 binary64)))))
6.0%
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64))))) (*.f64 (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64)))) (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 3 binary64)))) (*.f64 (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64)))) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64))))))
▶6.1%
(/.f64 (-.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) (*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))) (*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))))
6.1%
(/.f64 (+.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)) #s(literal 3 binary64))) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64)))))
6.1%
(/.f64 (*.f64 (-.f64 (*.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))))) #s(literal 64 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 9 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64)))))) (+.f64 (+.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 6 binary64)) (pow.f64 (*.f64 (PI.f64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))))) #s(literal 64 binary64))))
6.1%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)))))
6.0%
(-.f64 (/.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
6.1%
(-.f64 (/.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))))
▶8.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 (PI.f64) (*.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64))))
6.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))))
6.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)))))))
✓6.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
▶3.8%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
6.1%
(*.f64 (/.f64 (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 #s(literal -4 binary64) (pow.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (+.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 3 binary64)))) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (-.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64)))))
▶6.1%
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64))))) (+.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)) #s(literal 3 binary64))))
6.1%
(*.f64 (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64)))) (*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64)))))))
Compiler

Compiled 2328 to 901 computations (61.3% saved)

simplify240.0ms (0.2%)

Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff128
(*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
✓cost-diff128
(*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
✓cost-diff13760
(-.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) (*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64))))
✓cost-diff41024
(/.f64 (-.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) (*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))) (*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))))
✓cost-diff128
(*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64)))
✓cost-diff128
(+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64))))
✓cost-diff128
(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64)))))
✓cost-diff320
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64))))) (+.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)) #s(literal 3 binary64))))
✓cost-diff64
(pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))
✓cost-diff64
(asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
✓cost-diff64
(*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64))
✓cost-diff19264
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64))))
✓cost-diff0
(PI.f64)
✓cost-diff0
(/.f64 (PI.f64) #s(literal 2 binary64))
✓cost-diff0
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
✓cost-diff64
(-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))
✓cost-diff192
(*.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
✓cost-diff192
(+.f64 (PI.f64) (*.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
✓cost-diff192
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 (PI.f64) (*.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64))))
Rules
3482×*-lowering-*.f32
3482×*-lowering-*.f64
1754×fma-define
1614×fma-lowering-fma.f32
1614×fma-lowering-fma.f64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
050602
1143545
2462529
32095525
47072525
08257525
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(- (/ (PI) 2) (+ (PI) (* (- 0 (acos (pow (- 1/2 (/ x 2)) 1/2))) 2)))
(/ (PI) 2)
(PI)
2
(+ (PI) (* (- 0 (acos (pow (- 1/2 (/ x 2)) 1/2))) 2))
(* (- 0 (acos (pow (- 1/2 (/ x 2)) 1/2))) 2)
(- 0 (acos (pow (- 1/2 (/ x 2)) 1/2)))
0
(acos (pow (- 1/2 (/ x 2)) 1/2))
(pow (- 1/2 (/ x 2)) 1/2)
(- 1/2 (/ x 2))
1/2
(/ x 2)
x
(- (/ (PI) 2) (* 2 (asin (sqrt 1/2))))
(/ (PI) 2)
(PI)
2
(* 2 (asin (sqrt 1/2)))
(asin (sqrt 1/2))
(sqrt 1/2)
1/2
(+ (* (sqrt (PI)) (/ (sqrt (PI)) 2)) (* (asin (pow (- 1/2 (/ x 2)) 1/2)) -2))
(sqrt (PI))
(PI)
(/ (sqrt (PI)) 2)
2
(* (asin (pow (- 1/2 (/ x 2)) 1/2)) -2)
(asin (pow (- 1/2 (/ x 2)) 1/2))
(pow (- 1/2 (/ x 2)) 1/2)
(- 1/2 (/ x 2))
1/2
(/ x 2)
x
-2
(* (/ 1 (+ (/ (PI) (/ 4 (PI))) (* (asin (pow (- 1/2 (/ x 2)) 1/2)) (+ (* (asin (pow (- 1/2 (/ x 2)) 1/2)) 4) (PI))))) (+ (/ (* (PI) (* (PI) (PI))) 8) (pow (* (asin (pow (- 1/2 (/ x 2)) 1/2)) -2) 3)))
(/ 1 (+ (/ (PI) (/ 4 (PI))) (* (asin (pow (- 1/2 (/ x 2)) 1/2)) (+ (* (asin (pow (- 1/2 (/ x 2)) 1/2)) 4) (PI)))))
1
(+ (/ (PI) (/ 4 (PI))) (* (asin (pow (- 1/2 (/ x 2)) 1/2)) (+ (* (asin (pow (- 1/2 (/ x 2)) 1/2)) 4) (PI))))
(/ (PI) (/ 4 (PI)))
(PI)
(/ 4 (PI))
4
(* (asin (pow (- 1/2 (/ x 2)) 1/2)) (+ (* (asin (pow (- 1/2 (/ x 2)) 1/2)) 4) (PI)))
(asin (pow (- 1/2 (/ x 2)) 1/2))
(pow (- 1/2 (/ x 2)) 1/2)
(- 1/2 (/ x 2))
1/2
(/ x 2)
x
2
(+ (* (asin (pow (- 1/2 (/ x 2)) 1/2)) 4) (PI))
(* (asin (pow (- 1/2 (/ x 2)) 1/2)) 4)
(+ (/ (* (PI) (* (PI) (PI))) 8) (pow (* (asin (pow (- 1/2 (/ x 2)) 1/2)) -2) 3))
(/ (* (PI) (* (PI) (PI))) 8)
(* (PI) (* (PI) (PI)))
(* (PI) (PI))
8
(pow (* (asin (pow (- 1/2 (/ x 2)) 1/2)) -2) 3)
(* (asin (pow (- 1/2 (/ x 2)) 1/2)) -2)
-2
3
(/ (- (* (/ (PI) (/ 4 (PI))) (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))))) (* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (pow (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))) 2))) (* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))))))
(- (* (/ (PI) (/ 4 (PI))) (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))))) (* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (pow (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))) 2)))
(* (/ (PI) (/ 4 (PI))) (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))))
(/ (PI) (/ 4 (PI)))
(PI)
(/ 4 (PI))
4
(+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))))
(/ (PI) 2)
2
(* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))
(asin (pow (- 1/2 (/ x 2)) 1/2))
(pow (- 1/2 (/ x 2)) 1/2)
(- 1/2 (/ x 2))
1/2
(/ x 2)
x
(* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (pow (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))) 2))
(pow (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))) 2)
(* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))))
Outputs
(- (/ (PI) 2) (+ (PI) (* (- 0 (acos (pow (- 1/2 (/ x 2)) 1/2))) 2)))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (PI.f64)))
(/ (PI) 2)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI)
(PI.f64)
2
#s(literal 2 binary64)
(+ (PI) (* (- 0 (acos (pow (- 1/2 (/ x 2)) 1/2))) 2))
(+.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
(* (- 0 (acos (pow (- 1/2 (/ x 2)) 1/2))) 2)
(*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64))
(- 0 (acos (pow (- 1/2 (/ x 2)) 1/2)))
(-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
0
#s(literal 0 binary64)
(acos (pow (- 1/2 (/ x 2)) 1/2))
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(pow (- 1/2 (/ x 2)) 1/2)
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
(- 1/2 (/ x 2))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))
1/2
#s(literal 1/2 binary64)
(/ x 2)
(/.f64 x #s(literal 2 binary64))
x
(- (/ (PI) 2) (* 2 (asin (sqrt 1/2))))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(/ (PI) 2)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI)
(PI.f64)
2
#s(literal 2 binary64)
(* 2 (asin (sqrt 1/2)))
(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(asin (sqrt 1/2))
(asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(+ (* (sqrt (PI)) (/ (sqrt (PI)) 2)) (* (asin (pow (- 1/2 (/ x 2)) 1/2)) -2))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
(sqrt (PI))
(sqrt.f64 (PI.f64))
(PI)
(PI.f64)
(/ (sqrt (PI)) 2)
(/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
2
#s(literal 2 binary64)
(* (asin (pow (- 1/2 (/ x 2)) 1/2)) -2)
(*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64))
(asin (pow (- 1/2 (/ x 2)) 1/2))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(pow (- 1/2 (/ x 2)) 1/2)
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
(- 1/2 (/ x 2))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))
1/2
#s(literal 1/2 binary64)
(/ x 2)
(/.f64 x #s(literal 2 binary64))
x
-2
#s(literal -2 binary64)
(* (/ 1 (+ (/ (PI) (/ 4 (PI))) (* (asin (pow (- 1/2 (/ x 2)) 1/2)) (+ (* (asin (pow (- 1/2 (/ x 2)) 1/2)) 4) (PI))))) (+ (/ (* (PI) (* (PI) (PI))) 8) (pow (* (asin (pow (- 1/2 (/ x 2)) 1/2)) -2) 3)))
(/.f64 (+.f64 (pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal 3 binary64)) (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64))) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 4 binary64))))))
(/ 1 (+ (/ (PI) (/ 4 (PI))) (* (asin (pow (- 1/2 (/ x 2)) 1/2)) (+ (* (asin (pow (- 1/2 (/ x 2)) 1/2)) 4) (PI)))))
(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 4 binary64))))))
1
#s(literal 1 binary64)
(+ (/ (PI) (/ 4 (PI))) (* (asin (pow (- 1/2 (/ x 2)) 1/2)) (+ (* (asin (pow (- 1/2 (/ x 2)) 1/2)) 4) (PI))))
(+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 4 binary64)))))
(/ (PI) (/ 4 (PI)))
(/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64)))
(PI)
(PI.f64)
(/ 4 (PI))
(/.f64 #s(literal 4 binary64) (PI.f64))
4
#s(literal 4 binary64)
(* (asin (pow (- 1/2 (/ x 2)) 1/2)) (+ (* (asin (pow (- 1/2 (/ x 2)) 1/2)) 4) (PI)))
(*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 4 binary64))))
(asin (pow (- 1/2 (/ x 2)) 1/2))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(pow (- 1/2 (/ x 2)) 1/2)
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
(- 1/2 (/ x 2))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))
1/2
#s(literal 1/2 binary64)
(/ x 2)
(/.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
(+ (* (asin (pow (- 1/2 (/ x 2)) 1/2)) 4) (PI))
(+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 4 binary64)))
(* (asin (pow (- 1/2 (/ x 2)) 1/2)) 4)
(*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 4 binary64))
(+ (/ (* (PI) (* (PI) (PI))) 8) (pow (* (asin (pow (- 1/2 (/ x 2)) 1/2)) -2) 3))
(+.f64 (pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal 3 binary64)) (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)))
(/ (* (PI) (* (PI) (PI))) 8)
(/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64))
(* (PI) (* (PI) (PI)))
(*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))
(* (PI) (PI))
(*.f64 (PI.f64) (PI.f64))
8
#s(literal 8 binary64)
(pow (* (asin (pow (- 1/2 (/ x 2)) 1/2)) -2) 3)
(pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal 3 binary64))
(* (asin (pow (- 1/2 (/ x 2)) 1/2)) -2)
(*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64))
-2
#s(literal -2 binary64)
3
#s(literal 3 binary64)
(/ (- (* (/ (PI) (/ 4 (PI))) (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))))) (* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (pow (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))) 2))) (* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))))))
(/.f64 (-.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))))
(- (* (/ (PI) (/ 4 (PI))) (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))))) (* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (pow (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))) 2)))
(*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) (-.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64))))
(* (/ (PI) (/ 4 (PI))) (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))))
(/.f64 (*.f64 (PI.f64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))) (/.f64 #s(literal 4 binary64) (PI.f64)))
(/ (PI) (/ 4 (PI)))
(/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64)))
(PI)
(PI.f64)
(/ 4 (PI))
(/.f64 #s(literal 4 binary64) (PI.f64))
4
#s(literal 4 binary64)
(+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(/ (PI) 2)
(/.f64 (PI.f64) #s(literal 2 binary64))
2
#s(literal 2 binary64)
(* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))
(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(asin (pow (- 1/2 (/ x 2)) 1/2))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(pow (- 1/2 (/ x 2)) 1/2)
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
(- 1/2 (/ x 2))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))
1/2
#s(literal 1/2 binary64)
(/ x 2)
(/.f64 x #s(literal 2 binary64))
x
(* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (pow (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))) 2))
(*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64)))
(pow (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))) 2)
(pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64))
(* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))))
(*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))))

localize3.0s (2%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
✓accuracy100.0%
(*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
✓accuracy99.5%
(-.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) (*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64))))
✓accuracy5.8%
(PI.f64)
✓accuracy100.0%
(pow.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)) #s(literal 3 binary64))
✓accuracy100.0%
(*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))
✓accuracy99.5%
(+.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)) #s(literal 3 binary64)))
✓accuracy5.8%
(PI.f64)
✓accuracy100.0%
(pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))
✓accuracy100.0%
(sqrt.f64 (PI.f64))
✓accuracy99.4%
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)))
✓accuracy5.8%
(PI.f64)
✓accuracy100.0%
(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64))))
✓accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
✓accuracy100.0%
(asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))
✓accuracy5.8%
(PI.f64)
✓accuracy100.0%
(+.f64 (PI.f64) (*.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
✓accuracy100.0%
(acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
✓accuracy99.5%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 (PI.f64) (*.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64))))
✓accuracy5.8%
(PI.f64)
Results
2.8s249×5exit
12.0ms6×2valid
11.0ms1×3valid
Compiler

Compiled 696 to 50 computations (92.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.5s
ival-asin: 876.0ms (35.5% of total)
ival-pow: 824.0ms (33.4% of total)
ival-mult: 158.0ms (6.4% of total)
backward-pass: 155.0ms (6.3% of total)
ival-acos: 126.0ms (5.1% of total)
ival-div: 105.0ms (4.3% of total)
ival-sub: 58.0ms (2.4% of total)
ival-add: 52.0ms (2.1% of total)
ival-pi: 40.0ms (1.6% of total)
ival-sqrt: 34.0ms (1.4% of total)
compiled-spec: 33.0ms (1.3% of total)
const: 5.0ms (0.2% of total)

series35.0ms (0%)

Counts
27 → 228
Calls
Call 1
Inputs
#<alt (- (/ (PI) 2) (+ (PI) (* (- 0 (acos (pow (- 1/2 (/ x 2)) 1/2))) 2)))>
#<alt (+ (PI) (* (- 0 (acos (pow (- 1/2 (/ x 2)) 1/2))) 2))>
#<alt (* (- 0 (acos (pow (- 1/2 (/ x 2)) 1/2))) 2)>
#<alt (- 0 (acos (pow (- 1/2 (/ x 2)) 1/2)))>
#<alt (- (/ (PI) 2) (* 2 (asin (sqrt 1/2))))>
#<alt (/ (PI) 2)>
#<alt (PI)>
#<alt (* 2 (asin (sqrt 1/2)))>
#<alt (+ (* (sqrt (PI)) (/ (sqrt (PI)) 2)) (* (asin (pow (- 1/2 (/ x 2)) 1/2)) -2))>
#<alt (* (asin (pow (- 1/2 (/ x 2)) 1/2)) -2)>
#<alt (asin (pow (- 1/2 (/ x 2)) 1/2))>
#<alt (pow (- 1/2 (/ x 2)) 1/2)>
#<alt (* (/ 1 (+ (/ (PI) (/ 4 (PI))) (* (asin (pow (- 1/2 (/ x 2)) 1/2)) (+ (* (asin (pow (- 1/2 (/ x 2)) 1/2)) 4) (PI))))) (+ (/ (* (PI) (* (PI) (PI))) 8) (pow (* (asin (pow (- 1/2 (/ x 2)) 1/2)) -2) 3)))>
#<alt (/ 1 (+ (/ (PI) (/ 4 (PI))) (* (asin (pow (- 1/2 (/ x 2)) 1/2)) (+ (* (asin (pow (- 1/2 (/ x 2)) 1/2)) 4) (PI)))))>
#<alt (+ (/ (PI) (/ 4 (PI))) (* (asin (pow (- 1/2 (/ x 2)) 1/2)) (+ (* (asin (pow (- 1/2 (/ x 2)) 1/2)) 4) (PI))))>
#<alt (* (asin (pow (- 1/2 (/ x 2)) 1/2)) (+ (* (asin (pow (- 1/2 (/ x 2)) 1/2)) 4) (PI)))>
#<alt (/ (- (* (/ (PI) (/ 4 (PI))) (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))))) (* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (pow (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))) 2))) (* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))))))>
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Outputs
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#<alt (/ (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (* 4 (* (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x))))))))) (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))) 2))>
#<alt (/ (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (* 4 (* (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x))))))))) (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))) 2))>
#<alt (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))))>
#<alt (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))))>
#<alt (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))))>
#<alt (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))))>
#<alt (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))))>
#<alt (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))))>
#<alt (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))))>
#<alt (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))))>
#<alt (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (* 4 (* (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))>
#<alt (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (* 4 (* (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))>
#<alt (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (* 4 (* (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))>
#<alt (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (* 4 (* (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))>
#<alt (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (* 4 (* (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (* 4 (* (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (* 4 (* (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (* 4 (* (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2)>
#<alt (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2)>
#<alt (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2)>
#<alt (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2)>
#<alt (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2)>
#<alt (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2)>
#<alt (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2)>
#<alt (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2)>
#<alt (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))) 2)>
#<alt (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))) 2)>
#<alt (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))) 2)>
#<alt (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))) 2)>
#<alt (acos (sqrt (- 1/2 (* 1/2 x))))>
#<alt (acos (sqrt (- 1/2 (* 1/2 x))))>
#<alt (acos (sqrt (- 1/2 (* 1/2 x))))>
#<alt (acos (sqrt (- 1/2 (* 1/2 x))))>
#<alt (acos (sqrt (- 1/2 (* 1/2 x))))>
#<alt (acos (sqrt (- 1/2 (* 1/2 x))))>
#<alt (acos (sqrt (- 1/2 (* 1/2 x))))>
#<alt (acos (sqrt (- 1/2 (* 1/2 x))))>
#<alt (acos (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (acos (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (acos (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (acos (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))>
#<alt (+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))>
#<alt (+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))>
#<alt (+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))>
#<alt (+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))>
#<alt (+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))>
#<alt (+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))>
#<alt (+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))>
#<alt (+ (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))>
#<alt (+ (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))>
#<alt (+ (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))>
#<alt (+ (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))>
#<alt (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3))>
#<alt (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3))>
#<alt (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3))>
#<alt (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3))>
#<alt (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3))>
#<alt (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3))>
#<alt (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3))>
#<alt (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3))>
#<alt (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3))>
#<alt (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3))>
#<alt (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3))>
#<alt (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3))>
Calls

57 calls:

TimeVariablePointExpression
5.0ms
x
@0
(/ (- (* (/ (PI) (/ 4 (PI))) (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))))) (* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (pow (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))) 2))) (* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))))))
3.0ms
x
@0
(* (/ 1 (+ (/ (PI) (/ 4 (PI))) (* (asin (pow (- 1/2 (/ x 2)) 1/2)) (+ (* (asin (pow (- 1/2 (/ x 2)) 1/2)) 4) (PI))))) (+ (/ (* (PI) (* (PI) (PI))) 8) (pow (* (asin (pow (- 1/2 (/ x 2)) 1/2)) -2) 3)))
3.0ms
x
@inf
(/ 1 (+ (/ (PI) (/ 4 (PI))) (* (asin (pow (- 1/2 (/ x 2)) 1/2)) (+ (* (asin (pow (- 1/2 (/ x 2)) 1/2)) 4) (PI)))))
3.0ms
x
@-inf
(/ (- (* (/ (PI) (/ 4 (PI))) (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))))) (* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (pow (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))) 2))) (* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))))))
3.0ms
x
@inf
(/ (- (* (/ (PI) (/ 4 (PI))) (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))))) (* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (pow (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))) 2))) (* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))))))

rewrite502.0ms (0.3%)

Algorithm
1×batch-egg-rewrite
Rules
4370×*-lowering-*.f32
4370×*-lowering-*.f64
2220×pow-lowering-pow.f64
2220×pow-lowering-pow.f32
1694×unpow-prod-down
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
050396
1373346
24177316
08273316
Stop Event
1×iter limit
1×node limit
Counts
27 → 564
Calls
Call 1
Inputs
(- (/ (PI) 2) (+ (PI) (* (- 0 (acos (pow (- 1/2 (/ x 2)) 1/2))) 2)))
(+ (PI) (* (- 0 (acos (pow (- 1/2 (/ x 2)) 1/2))) 2))
(* (- 0 (acos (pow (- 1/2 (/ x 2)) 1/2))) 2)
(- 0 (acos (pow (- 1/2 (/ x 2)) 1/2)))
(- (/ (PI) 2) (* 2 (asin (sqrt 1/2))))
(/ (PI) 2)
(PI)
(* 2 (asin (sqrt 1/2)))
(+ (* (sqrt (PI)) (/ (sqrt (PI)) 2)) (* (asin (pow (- 1/2 (/ x 2)) 1/2)) -2))
(* (asin (pow (- 1/2 (/ x 2)) 1/2)) -2)
(asin (pow (- 1/2 (/ x 2)) 1/2))
(pow (- 1/2 (/ x 2)) 1/2)
(* (/ 1 (+ (/ (PI) (/ 4 (PI))) (* (asin (pow (- 1/2 (/ x 2)) 1/2)) (+ (* (asin (pow (- 1/2 (/ x 2)) 1/2)) 4) (PI))))) (+ (/ (* (PI) (* (PI) (PI))) 8) (pow (* (asin (pow (- 1/2 (/ x 2)) 1/2)) -2) 3)))
(/ 1 (+ (/ (PI) (/ 4 (PI))) (* (asin (pow (- 1/2 (/ x 2)) 1/2)) (+ (* (asin (pow (- 1/2 (/ x 2)) 1/2)) 4) (PI)))))
(+ (/ (PI) (/ 4 (PI))) (* (asin (pow (- 1/2 (/ x 2)) 1/2)) (+ (* (asin (pow (- 1/2 (/ x 2)) 1/2)) 4) (PI))))
(* (asin (pow (- 1/2 (/ x 2)) 1/2)) (+ (* (asin (pow (- 1/2 (/ x 2)) 1/2)) 4) (PI)))
(/ (- (* (/ (PI) (/ 4 (PI))) (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))))) (* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (pow (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))) 2))) (* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))))))
(- (* (/ (PI) (/ 4 (PI))) (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))))) (* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (pow (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))) 2)))
(* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (pow (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2))) 2))
(* (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))) (+ (/ (PI) 2) (* 2 (asin (pow (- 1/2 (/ x 2)) 1/2)))))
(acos (pow (- 1/2 (/ x 2)) 1/2))
(asin (sqrt 1/2))
(sqrt 1/2)
(sqrt (PI))
(+ (/ (* (PI) (* (PI) (PI))) 8) (pow (* (asin (pow (- 1/2 (/ x 2)) 1/2)) -2) 3))
(* (PI) (* (PI) (PI)))
(pow (* (asin (pow (- 1/2 (/ x 2)) 1/2)) -2) 3)
Outputs
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))))
(+.f64 (-.f64 #s(literal 0 binary64) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64)))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (neg.f64 (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal -2 binary64) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) #s(literal 2 binary64)))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))))
(-.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))))
(-.f64 (/.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))))))) (/.f64 (pow.f64 (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) #s(literal 3 binary64)) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))))))))
(-.f64 (/.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))))) (/.f64 (pow.f64 (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))))))
(-.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))) (PI.f64))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))))
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (-.f64 #s(literal 0 binary64) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))))) (-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) #s(literal 2 binary64)))))
(/.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) #s(literal 3 binary64))) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))))))
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(*.f64 (*.f64 (pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal 2 binary64)) #s(literal -2 binary64)) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(*.f64 (pow.f64 (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 1 binary64)) #s(literal 3 binary64)) #s(literal 8 binary64))
(*.f64 (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 1/2 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 3/2 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 3 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64)) (pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))) #s(literal 3/2 binary64)) (pow.f64 (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64)) #s(literal 3/2 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 3/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (*.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 3/2 binary64)) (pow.f64 #s(literal -2 binary64) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (*.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal -2 binary64)) #s(literal 3/2 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal -2 binary64) #s(literal 3/2 binary64)) #s(literal 2 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 3 binary64)))

simplify235.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
4218×*-lowering-*.f32
4218×*-lowering-*.f64
1628×fma-lowering-fma.f32
1628×fma-lowering-fma.f64
1334×fnmadd-define
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01644480
15043667
214243502
347593475
081873475
Stop Event
1×iter limit
1×node limit
Counts
228 → 228
Calls
Call 1
Inputs
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))))
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))))
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))))
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))))
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))))
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))))
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))))
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))))
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+ (PI) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+ (PI) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+ (PI) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+ (PI) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(* -1 (acos (sqrt (- 1/2 (* 1/2 x)))))
(* -1 (acos (sqrt (- 1/2 (* 1/2 x)))))
(* -1 (acos (sqrt (- 1/2 (* 1/2 x)))))
(* -1 (acos (sqrt (- 1/2 (* 1/2 x)))))
(* -1 (acos (sqrt (- 1/2 (* 1/2 x)))))
(* -1 (acos (sqrt (- 1/2 (* 1/2 x)))))
(* -1 (acos (sqrt (- 1/2 (* 1/2 x)))))
(* -1 (acos (sqrt (- 1/2 (* 1/2 x)))))
(* -1 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(* -1 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(* -1 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(* -1 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(* -2 (asin (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (asin (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (asin (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (asin (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (asin (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (asin (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (asin (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (asin (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (asin (sqrt (+ 1/2 (* -1/2 x)))))
(* -2 (asin (sqrt (+ 1/2 (* -1/2 x)))))
(* -2 (asin (sqrt (+ 1/2 (* -1/2 x)))))
(* -2 (asin (sqrt (+ 1/2 (* -1/2 x)))))
(asin (sqrt (- 1/2 (* 1/2 x))))
(asin (sqrt (- 1/2 (* 1/2 x))))
(asin (sqrt (- 1/2 (* 1/2 x))))
(asin (sqrt (- 1/2 (* 1/2 x))))
(asin (sqrt (- 1/2 (* 1/2 x))))
(asin (sqrt (- 1/2 (* 1/2 x))))
(asin (sqrt (- 1/2 (* 1/2 x))))
(asin (sqrt (- 1/2 (* 1/2 x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/4 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/32 (/ x (pow (sqrt 1/2) 3))) (* 1/4 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 5))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/4 (/ 1 (sqrt 1/2))))))
(* (sqrt x) (sqrt -1/2))
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2)))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/2) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/2) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2))))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))
(* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt 1/2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt 1/2) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt 1/2) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))
(/ (+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ (+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ (+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ (+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ (+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ (+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ (+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ (+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ (+ (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)) (* 1/8 (pow (PI) 3))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(/ (+ (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)) (* 1/8 (pow (PI) 3))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(/ (+ (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)) (* 1/8 (pow (PI) 3))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(/ (+ (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)) (* 1/8 (pow (PI) 3))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x))))))))
(* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))
(* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))
(* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))
(* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))
(* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))
(* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))
(* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))
(* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))
(* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))
(* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))
(* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))
(* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))
(/ (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))) (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2))
(/ (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))) (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2))
(/ (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))) (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2))
(/ (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))) (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2))
(/ (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))) (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2))
(/ (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))) (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2))
(/ (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))) (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2))
(/ (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))) (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2))
(/ (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (* 4 (* (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x))))))))) (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))) 2))
(/ (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (* 4 (* (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x))))))))) (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))) 2))
(/ (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (* 4 (* (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x))))))))) (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))) 2))
(/ (- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (* 4 (* (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x))))))))) (pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))) 2))
(- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (* 4 (* (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (* 4 (* (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (* 4 (* (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(- (* 1/4 (* (pow (PI) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (* 4 (* (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))
(* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))
(* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))
(* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))
(* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))
(* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))
(* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))
(* 4 (* (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x))))))))
(* 4 (* (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x))))))))
(* 4 (* (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x))))))))
(* 4 (* (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x))))))))
(* 4 (* (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 2) (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x))))))))
(pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2)
(pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2)
(pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2)
(pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2)
(pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2)
(pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2)
(pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2)
(pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (- 1/2 (* 1/2 x)))))) 2)
(pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))) 2)
(pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))) 2)
(pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))) 2)
(pow (+ (* 1/2 (PI)) (* 2 (asin (sqrt (+ 1/2 (* -1/2 x)))))) 2)
(acos (sqrt (- 1/2 (* 1/2 x))))
(acos (sqrt (- 1/2 (* 1/2 x))))
(acos (sqrt (- 1/2 (* 1/2 x))))
(acos (sqrt (- 1/2 (* 1/2 x))))
(acos (sqrt (- 1/2 (* 1/2 x))))
(acos (sqrt (- 1/2 (* 1/2 x))))
(acos (sqrt (- 1/2 (* 1/2 x))))
(acos (sqrt (- 1/2 (* 1/2 x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))
(+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))
(+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))
(+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))
(+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))
(+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))
(+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))
(+ (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))
(+ (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))
(+ (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))
(+ (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))
(+ (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)) (* 1/8 (pow (PI) 3)))
(* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3))
(* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3))
(* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3))
(* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3))
(* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3))
(* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3))
(* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3))
(* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3))
(* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3))
(* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3))
(* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3))
(* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3))
Outputs
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (PI.f64)))
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (PI.f64)))
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (PI.f64)))
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (PI.f64)))
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (PI.f64)))
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (PI.f64)))
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (PI.f64)))
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (PI.f64)))
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (PI.f64)))
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (PI.f64)))
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (PI.f64)))
(- (* 1/2 (PI)) (+ (PI) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (PI.f64)))
(+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+.f64 (PI.f64) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
(+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+.f64 (PI.f64) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
(+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+.f64 (PI.f64) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
(+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+.f64 (PI.f64) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
(+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+.f64 (PI.f64) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
(+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+.f64 (PI.f64) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
(+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+.f64 (PI.f64) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
(+ (PI) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+.f64 (PI.f64) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
(+ (PI) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (PI.f64) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
(+ (PI) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (PI.f64) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
(+ (PI) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (PI.f64) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
(+ (PI) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (PI.f64) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* -1 (acos (sqrt (- 1/2 (* 1/2 x)))))
(-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* -1 (acos (sqrt (- 1/2 (* 1/2 x)))))
(-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* -1 (acos (sqrt (- 1/2 (* 1/2 x)))))
(-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* -1 (acos (sqrt (- 1/2 (* 1/2 x)))))
(-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* -1 (acos (sqrt (- 1/2 (* 1/2 x)))))
(-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* -1 (acos (sqrt (- 1/2 (* 1/2 x)))))
(-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* -1 (acos (sqrt (- 1/2 (* 1/2 x)))))
(-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* -1 (acos (sqrt (- 1/2 (* 1/2 x)))))
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eval368.0ms (0.2%)

Compiler

Compiled 117209 to 5876 computations (95% saved)

prune265.0ms (0.2%)

Pruning

28 alts after pruning (26 fresh and 2 done)

PrunedKeptTotal
New2034222056
Fresh12416
Picked415
Done011
Total2050282078
Accuracy
9.4%
Counts
2078 → 28
Alt Table
Click to see full alt table
StatusAccuracyProgram
6.0%
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)))
6.1%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (-.f64 #s(literal 0 binary64) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))))
▶6.0%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
▶6.0%
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))) #s(literal -2 binary64)))
6.1%
(/.f64 (fma.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) (*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) (*.f64 #s(literal -4 binary64) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))))) (*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))))
6.1%
(/.f64 (-.f64 (pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal 2 binary64)) (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64))) (-.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
8.1%
(/.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))))
3.8%
(/.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (*.f64 (asin.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -2 binary64)) #s(literal 2 binary64))) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -2 binary64))))
6.1%
(/.f64 (-.f64 (*.f64 (/.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) (/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) (PI.f64)))) (pow.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) #s(literal 2 binary64))) (*.f64 (pow.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) #s(literal 2 binary64)) (*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) (pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal 2 binary64))))) (pow.f64 (pow.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) #s(literal 2 binary64)) #s(literal 2 binary64)))
8.1%
(/.f64 (-.f64 (*.f64 (/.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) (/.f64 #s(literal 4 binary64) (PI.f64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) (*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))) (*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))))
6.1%
(/.f64 (-.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) (*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))) (/.f64 (-.f64 (pow.f64 (/.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) (/.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))) #s(literal 2 binary64))) (-.f64 (/.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) (/.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))))))
6.1%
(/.f64 (-.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) (*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))) (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 #s(literal -4 binary64) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))))
▶8.1%
(/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))) (pow.f64 (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) #s(literal 2 binary64))) (+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))))
▶6.1%
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 4 binary64)))))) (-.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/64 binary64))) (pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal 6 binary64)))) (-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal 3 binary64))))
6.1%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)))))
6.1%
(-.f64 (/.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))) (/.f64 (pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal 2 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))))
3.8%
(-.f64 (/.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))))
8.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))))
8.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 (PI.f64) (*.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) #s(literal 4 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) #s(literal 2 binary64))))
▶5.7%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 (PI.f64) (*.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64))))
6.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))))
6.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)))))))
✓6.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
✓3.8%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
6.1%
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64))))) (-.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/64 binary64))) (-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal 3 binary64)))) (/.f64 (pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal 6 binary64)) (-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal 3 binary64))))))
6.0%
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64))))) (+.f64 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)) #s(literal 3 binary64))))
6.1%
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64))))) (+.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)) #s(literal 3 binary64))))
6.0%
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64))))) (+.f64 (/.f64 (exp.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 3 binary64))) #s(literal 8 binary64)) (pow.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)) #s(literal 3 binary64))))
Compiler

Compiled 2462 to 1134 computations (53.9% saved)

simplify199.0ms (0.1%)

Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 4 binary64)))))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 4 binary64))))))
✓cost-diff128
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 4 binary64)))))) (-.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/64 binary64))) (pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal 6 binary64))))
✓cost-diff128
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 4 binary64)))))) (-.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/64 binary64))) (pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal 6 binary64)))) (-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal 3 binary64))))
✓cost-diff6528
(pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓cost-diff6528
(asin.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
✓cost-diff6528
(*.f64 (asin.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))) #s(literal -2 binary64))
✓cost-diff25728
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))) #s(literal -2 binary64)))
✓cost-diff0
(PI.f64)
✓cost-diff0
(sqrt.f64 (PI.f64))
✓cost-diff0
(/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
✓cost-diff19200
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
✓cost-diff0
(/.f64 (PI.f64) #s(literal 2 binary64))
✓cost-diff128
(*.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64))
✓cost-diff128
(+.f64 (PI.f64) (*.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
✓cost-diff128
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 (PI.f64) (*.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64))))
✓cost-diff64
(neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))
✓cost-diff64
(pow.f64 (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) #s(literal 2 binary64))
✓cost-diff64
(-.f64 (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))) (pow.f64 (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) #s(literal 2 binary64)))
✓cost-diff20544
(/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))) (pow.f64 (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) #s(literal 2 binary64))) (+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))))
Rules
3690×*-lowering-*.f32
3690×*-lowering-*.f64
1404×fnmadd-define
1360×fma-lowering-fma.f32
1360×fma-lowering-fma.f64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
061625
1148582
2430575
31482575
44522560
08246560
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ (- (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2)) (+ (- (/ (PI) 2) (PI)) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))))
(- (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2))
(* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI)))
(- (/ (PI) 2) (PI))
(/ (PI) 2)
(PI)
2
(pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2)
(neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))
(* (acos (sqrt (+ 1/2 (/ x -2)))) 2)
(acos (sqrt (+ 1/2 (/ x -2))))
(sqrt (+ 1/2 (/ x -2)))
(+ 1/2 (/ x -2))
1/2
(/ x -2)
x
-2
(+ (- (/ (PI) 2) (PI)) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)))
(- (/ (PI) 2) (+ (PI) (* (- 0 (acos (sqrt 1/2))) 2)))
(/ (PI) 2)
(PI)
2
(+ (PI) (* (- 0 (acos (sqrt 1/2))) 2))
(* (- 0 (acos (sqrt 1/2))) 2)
(- 0 (acos (sqrt 1/2)))
0
(acos (sqrt 1/2))
(sqrt 1/2)
1/2
(+ (* (/ (sqrt (PI)) 2) (sqrt (PI))) (* (asin (sqrt (+ 1/2 (/ x -2)))) -2))
(/ (sqrt (PI)) 2)
(sqrt (PI))
(PI)
2
(* (asin (sqrt (+ 1/2 (/ x -2)))) -2)
(asin (sqrt (+ 1/2 (/ x -2))))
(sqrt (+ 1/2 (/ x -2)))
(+ 1/2 (/ x -2))
1/2
(/ x -2)
x
-2
(+ (* (sqrt (PI)) (/ (sqrt (PI)) 2)) (* (asin (pow (pow (+ 1/2 (/ x -2)) 1/4) 2)) -2))
(sqrt (PI))
(PI)
(/ (sqrt (PI)) 2)
2
(* (asin (pow (pow (+ 1/2 (/ x -2)) 1/4) 2)) -2)
(asin (pow (pow (+ 1/2 (/ x -2)) 1/4) 2))
(pow (pow (+ 1/2 (/ x -2)) 1/4) 2)
(pow (+ 1/2 (/ x -2)) 1/4)
(+ 1/2 (/ x -2))
1/2
(/ x -2)
x
-2
1/4
(/ (* (/ 1 (+ (/ (* (PI) (PI)) 4) (* (asin (sqrt (+ 1/2 (/ x -2)))) (+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4))))) (- (* (* (PI) (* (PI) (PI))) (* (* (PI) (* (PI) (PI))) 1/64)) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 6))) (- (/ (* (PI) (* (PI) (PI))) 8) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 3)))
(* (/ 1 (+ (/ (* (PI) (PI)) 4) (* (asin (sqrt (+ 1/2 (/ x -2)))) (+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4))))) (- (* (* (PI) (* (PI) (PI))) (* (* (PI) (* (PI) (PI))) 1/64)) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 6)))
(/ 1 (+ (/ (* (PI) (PI)) 4) (* (asin (sqrt (+ 1/2 (/ x -2)))) (+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4)))))
1
(+ (/ (* (PI) (PI)) 4) (* (asin (sqrt (+ 1/2 (/ x -2)))) (+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4))))
(/ (* (PI) (PI)) 4)
(* (PI) (PI))
(PI)
4
(* (asin (sqrt (+ 1/2 (/ x -2)))) (+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4)))
(asin (sqrt (+ 1/2 (/ x -2))))
(sqrt (+ 1/2 (/ x -2)))
(+ 1/2 (/ x -2))
1/2
(/ x -2)
x
-2
(+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4))
(* (asin (sqrt (+ 1/2 (/ x -2)))) 4)
(- (* (* (PI) (* (PI) (PI))) (* (* (PI) (* (PI) (PI))) 1/64)) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 6))
(* (* (PI) (* (PI) (PI))) (* (* (PI) (* (PI) (PI))) 1/64))
(* (PI) (* (PI) (PI)))
(* (* (PI) (* (PI) (PI))) 1/64)
1/64
(pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 6)
(* (asin (sqrt (+ 1/2 (/ x -2)))) -2)
6
(- (/ (* (PI) (* (PI) (PI))) 8) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 3))
(/ (* (PI) (* (PI) (PI))) 8)
8
(pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 3)
3
Outputs
(/ (- (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2)) (+ (- (/ (PI) 2) (PI)) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))))
(*.f64 (+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) #s(literal 1 binary64))
(- (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2))
(-.f64 (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))) (pow.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64)))
(* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI)))
(*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)))
(- (/ (PI) 2) (PI))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))
(/ (PI) 2)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI)
(PI.f64)
2
#s(literal 2 binary64)
(pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2)
(pow.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64))
(neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(* (acos (sqrt (+ 1/2 (/ x -2)))) 2)
(*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(acos (sqrt (+ 1/2 (/ x -2))))
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(sqrt (+ 1/2 (/ x -2)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
(+ 1/2 (/ x -2))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))
1/2
#s(literal 1/2 binary64)
(/ x -2)
(/.f64 x #s(literal -2 binary64))
x
-2
#s(literal -2 binary64)
(+ (- (/ (PI) 2) (PI)) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(- (/ (PI) 2) (+ (PI) (* (- 0 (acos (sqrt 1/2))) 2)))
(-.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (PI.f64) (/.f64 (PI.f64) #s(literal -2 binary64))))
(/ (PI) 2)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI)
(PI.f64)
2
#s(literal 2 binary64)
(+ (PI) (* (- 0 (acos (sqrt 1/2))) 2))
(+.f64 (PI.f64) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(* (- 0 (acos (sqrt 1/2))) 2)
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(- 0 (acos (sqrt 1/2)))
(-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64))))
0
#s(literal 0 binary64)
(acos (sqrt 1/2))
(acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(+ (* (/ (sqrt (PI)) 2) (sqrt (PI))) (* (asin (sqrt (+ 1/2 (/ x -2)))) -2))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(/ (sqrt (PI)) 2)
(/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
(sqrt (PI))
(sqrt.f64 (PI.f64))
(PI)
(PI.f64)
2
#s(literal 2 binary64)
(* (asin (sqrt (+ 1/2 (/ x -2)))) -2)
(*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(asin (sqrt (+ 1/2 (/ x -2))))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(sqrt (+ 1/2 (/ x -2)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
(+ 1/2 (/ x -2))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))
1/2
#s(literal 1/2 binary64)
(/ x -2)
(/.f64 x #s(literal -2 binary64))
x
-2
#s(literal -2 binary64)
(+ (* (sqrt (PI)) (/ (sqrt (PI)) 2)) (* (asin (pow (pow (+ 1/2 (/ x -2)) 1/4) 2)) -2))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(sqrt (PI))
(sqrt.f64 (PI.f64))
(PI)
(PI.f64)
(/ (sqrt (PI)) 2)
(/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
2
#s(literal 2 binary64)
(* (asin (pow (pow (+ 1/2 (/ x -2)) 1/4) 2)) -2)
(*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(asin (pow (pow (+ 1/2 (/ x -2)) 1/4) 2))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(pow (pow (+ 1/2 (/ x -2)) 1/4) 2)
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
(pow (+ 1/2 (/ x -2)) 1/4)
(pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/4 binary64))
(+ 1/2 (/ x -2))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))
1/2
#s(literal 1/2 binary64)
(/ x -2)
(/.f64 x #s(literal -2 binary64))
x
-2
#s(literal -2 binary64)
1/4
#s(literal 1/4 binary64)
(/ (* (/ 1 (+ (/ (* (PI) (PI)) 4) (* (asin (sqrt (+ 1/2 (/ x -2)))) (+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4))))) (- (* (* (PI) (* (PI) (PI))) (* (* (PI) (* (PI) (PI))) 1/64)) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 6))) (- (/ (* (PI) (* (PI) (PI))) 8) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 3)))
(/.f64 (-.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) (*.f64 (PI.f64) (*.f64 #s(literal 1/64 binary64) (*.f64 (PI.f64) (PI.f64))))) (pow.f64 (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 6 binary64))) (*.f64 (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 4 binary64))))) (+.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (*.f64 #s(literal 8 binary64) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 3 binary64))))))
(* (/ 1 (+ (/ (* (PI) (PI)) 4) (* (asin (sqrt (+ 1/2 (/ x -2)))) (+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4))))) (- (* (* (PI) (* (PI) (PI))) (* (* (PI) (* (PI) (PI))) 1/64)) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 6)))
(/.f64 (-.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) (*.f64 (PI.f64) (*.f64 #s(literal 1/64 binary64) (*.f64 (PI.f64) (PI.f64))))) (pow.f64 (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 6 binary64))) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 4 binary64))))))
(/ 1 (+ (/ (* (PI) (PI)) 4) (* (asin (sqrt (+ 1/2 (/ x -2)))) (+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4)))))
(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 4 binary64))))))
1
#s(literal 1 binary64)
(+ (/ (* (PI) (PI)) 4) (* (asin (sqrt (+ 1/2 (/ x -2)))) (+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4))))
(+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 4 binary64)))))
(/ (* (PI) (PI)) 4)
(/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64))
(* (PI) (PI))
(*.f64 (PI.f64) (PI.f64))
(PI)
(PI.f64)
4
#s(literal 4 binary64)
(* (asin (sqrt (+ 1/2 (/ x -2)))) (+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4)))
(*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 4 binary64))))
(asin (sqrt (+ 1/2 (/ x -2))))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(sqrt (+ 1/2 (/ x -2)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
(+ 1/2 (/ x -2))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))
1/2
#s(literal 1/2 binary64)
(/ x -2)
(/.f64 x #s(literal -2 binary64))
x
-2
#s(literal -2 binary64)
(+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4))
(+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 4 binary64)))
(* (asin (sqrt (+ 1/2 (/ x -2)))) 4)
(*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 4 binary64))
(- (* (* (PI) (* (PI) (PI))) (* (* (PI) (* (PI) (PI))) 1/64)) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 6))
(-.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) (*.f64 (PI.f64) (*.f64 #s(literal 1/64 binary64) (*.f64 (PI.f64) (PI.f64))))) (pow.f64 (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 6 binary64)))
(* (* (PI) (* (PI) (PI))) (* (* (PI) (* (PI) (PI))) 1/64))
(*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) (*.f64 (PI.f64) (*.f64 #s(literal 1/64 binary64) (*.f64 (PI.f64) (PI.f64)))))
(* (PI) (* (PI) (PI)))
(*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))
(* (* (PI) (* (PI) (PI))) 1/64)
(*.f64 (PI.f64) (*.f64 #s(literal 1/64 binary64) (*.f64 (PI.f64) (PI.f64))))
1/64
#s(literal 1/64 binary64)
(pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 6)
(pow.f64 (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 6 binary64))
(* (asin (sqrt (+ 1/2 (/ x -2)))) -2)
(*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
6
#s(literal 6 binary64)
(- (/ (* (PI) (* (PI) (PI))) 8) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 3))
(+.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (*.f64 #s(literal 8 binary64) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 3 binary64))))
(/ (* (PI) (* (PI) (PI))) 8)
(/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64))
8
#s(literal 8 binary64)
(pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 3)
(pow.f64 (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 3 binary64))
3
#s(literal 3 binary64)

localize2.7s (1.8%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))
✓accuracy100.0%
(pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal 6 binary64))
✓accuracy99.5%
(-.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/64 binary64))) (pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal 6 binary64)))
✓accuracy5.8%
(PI.f64)
✓accuracy100.0%
(pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓accuracy100.0%
(sqrt.f64 (PI.f64))
✓accuracy99.4%
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))) #s(literal -2 binary64)))
✓accuracy5.8%
(PI.f64)
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
✓accuracy100.0%
(sqrt.f64 (PI.f64))
✓accuracy99.4%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
✓accuracy5.8%
(PI.f64)
✓accuracy100.0%
(*.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64))
✓accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
✓accuracy100.0%
(acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))
✓accuracy5.8%
(PI.f64)
✓accuracy100.0%
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
✓accuracy100.0%
(pow.f64 (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) #s(literal 2 binary64))
✓accuracy99.5%
(-.f64 (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))) (pow.f64 (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) #s(literal 2 binary64)))
✓accuracy5.8%
(PI.f64)
Results
2.4s249×5exit
18.0ms7×2valid
Compiler

Compiled 702 to 60 computations (91.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.0s
ival-pow: 592.0ms (29.1% of total)
ival-acos: 575.0ms (28.3% of total)
backward-pass: 210.0ms (10.3% of total)
ival-mult: 173.0ms (8.5% of total)
ival-asin: 123.0ms (6% of total)
ival-div: 94.0ms (4.6% of total)
ival-add: 73.0ms (3.6% of total)
compiled-spec: 66.0ms (3.2% of total)
ival-sub: 55.0ms (2.7% of total)
ival-sqrt: 42.0ms (2.1% of total)
ival-neg: 14.0ms (0.7% of total)
ival-pi: 11.0ms (0.5% of total)
const: 6.0ms (0.3% of total)

series31.0ms (0%)

Counts
27 → 204
Calls
Call 1
Inputs
#<alt (/ (- (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2)) (+ (- (/ (PI) 2) (PI)) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))))>
#<alt (- (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2))>
#<alt (pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2)>
#<alt (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))>
#<alt (- (/ (PI) 2) (+ (PI) (* (- 0 (acos (sqrt 1/2))) 2)))>
#<alt (+ (PI) (* (- 0 (acos (sqrt 1/2))) 2))>
#<alt (* (- 0 (acos (sqrt 1/2))) 2)>
#<alt (/ (PI) 2)>
#<alt (+ (* (/ (sqrt (PI)) 2) (sqrt (PI))) (* (asin (sqrt (+ 1/2 (/ x -2)))) -2))>
#<alt (/ (sqrt (PI)) 2)>
#<alt (sqrt (PI))>
#<alt (PI)>
#<alt (+ (* (sqrt (PI)) (/ (sqrt (PI)) 2)) (* (asin (pow (pow (+ 1/2 (/ x -2)) 1/4) 2)) -2))>
#<alt (* (asin (pow (pow (+ 1/2 (/ x -2)) 1/4) 2)) -2)>
#<alt (asin (pow (pow (+ 1/2 (/ x -2)) 1/4) 2))>
#<alt (pow (pow (+ 1/2 (/ x -2)) 1/4) 2)>
#<alt (/ (* (/ 1 (+ (/ (* (PI) (PI)) 4) (* (asin (sqrt (+ 1/2 (/ x -2)))) (+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4))))) (- (* (* (PI) (* (PI) (PI))) (* (* (PI) (* (PI) (PI))) 1/64)) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 6))) (- (/ (* (PI) (* (PI) (PI))) 8) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 3)))>
#<alt (* (/ 1 (+ (/ (* (PI) (PI)) 4) (* (asin (sqrt (+ 1/2 (/ x -2)))) (+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4))))) (- (* (* (PI) (* (PI) (PI))) (* (* (PI) (* (PI) (PI))) 1/64)) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 6)))>
#<alt (/ 1 (+ (/ (* (PI) (PI)) 4) (* (asin (sqrt (+ 1/2 (/ x -2)))) (+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4)))))>
#<alt (+ (/ (* (PI) (PI)) 4) (* (asin (sqrt (+ 1/2 (/ x -2)))) (+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4))))>
#<alt (acos (sqrt (+ 1/2 (/ x -2))))>
#<alt (acos (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (sqrt (+ 1/2 (/ x -2)))>
#<alt (- (* (* (PI) (* (PI) (PI))) (* (* (PI) (* (PI) (PI))) 1/64)) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 6))>
#<alt (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 6)>
#<alt (* (PI) (* (PI) (PI)))>
Outputs
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))>
#<alt (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))>
#<alt (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))>
#<alt (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))>
#<alt (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))>
#<alt (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))>
#<alt (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))>
#<alt (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))>
#<alt (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))>
#<alt (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))>
#<alt (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))>
#<alt (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))>
#<alt (* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))>
#<alt (* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))>
#<alt (* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))>
#<alt (* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))>
#<alt (* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (* -2 (asin (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (* -2 (asin (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (* -2 (asin (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (* -2 (asin (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (* -2 (asin (sqrt (- 1/2 (* 1/2 x)))))>
#<alt (* -2 (asin (sqrt (- 1/2 (* 1/2 x)))))>
#<alt (* -2 (asin (sqrt (- 1/2 (* 1/2 x)))))>
#<alt (* -2 (asin (sqrt (- 1/2 (* 1/2 x)))))>
#<alt (* -2 (asin (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (* -2 (asin (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (* -2 (asin (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (* -2 (asin (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (asin (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (asin (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (asin (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (asin (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (asin (sqrt (- 1/2 (* 1/2 x))))>
#<alt (asin (sqrt (- 1/2 (* 1/2 x))))>
#<alt (asin (sqrt (- 1/2 (* 1/2 x))))>
#<alt (asin (sqrt (- 1/2 (* 1/2 x))))>
#<alt (asin (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (asin (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (asin (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (asin (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/4 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/32 (/ x (pow (sqrt 1/2) 3))) (* 1/4 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 5))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/4 (/ 1 (sqrt 1/2))))))>
#<alt (* (sqrt x) (sqrt -1/2))>
#<alt (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2)))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/2) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/2) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2))))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))>
#<alt (* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt 1/2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt 1/2) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt 1/2) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))>
#<alt (/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))>
#<alt (/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))>
#<alt (/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))>
#<alt (/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))>
#<alt (/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))>
#<alt (/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))>
#<alt (/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))>
#<alt (/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))>
#<alt (/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))>
#<alt (/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))>
#<alt (/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))>
#<alt (/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))>
#<alt (/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))>
#<alt (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (acos (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (acos (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (acos (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (acos (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (acos (sqrt (- 1/2 (* 1/2 x))))>
#<alt (acos (sqrt (- 1/2 (* 1/2 x))))>
#<alt (acos (sqrt (- 1/2 (* 1/2 x))))>
#<alt (acos (sqrt (- 1/2 (* 1/2 x))))>
#<alt (acos (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (acos (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (acos (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (acos (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/4 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/32 (/ x (pow (sqrt 1/2) 3))) (* 1/4 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 5))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/4 (/ 1 (sqrt 1/2))))))>
#<alt (* (sqrt x) (sqrt -1/2))>
#<alt (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2)))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/2) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/2) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2))))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))>
#<alt (* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt 1/2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt 1/2) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt 1/2) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))>
#<alt (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))>
#<alt (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))>
#<alt (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))>
#<alt (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))>
#<alt (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6)))>
#<alt (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6)))>
#<alt (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6)))>
#<alt (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6)))>
#<alt (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))>
#<alt (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))>
#<alt (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))>
#<alt (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))>
#<alt (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))>
#<alt (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))>
#<alt (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))>
#<alt (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))>
#<alt (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))>
#<alt (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))>
#<alt (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))>
#<alt (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))>
#<alt (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))>
#<alt (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))>
#<alt (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))>
#<alt (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))>
Calls

51 calls:

TimeVariablePointExpression
8.0ms
x
@-inf
(/ (* (/ 1 (+ (/ (* (PI) (PI)) 4) (* (asin (sqrt (+ 1/2 (/ x -2)))) (+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4))))) (- (* (* (PI) (* (PI) (PI))) (* (* (PI) (* (PI) (PI))) 1/64)) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 6))) (- (/ (* (PI) (* (PI) (PI))) 8) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 3)))
4.0ms
x
@0
(/ (* (/ 1 (+ (/ (* (PI) (PI)) 4) (* (asin (sqrt (+ 1/2 (/ x -2)))) (+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4))))) (- (* (* (PI) (* (PI) (PI))) (* (* (PI) (* (PI) (PI))) 1/64)) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 6))) (- (/ (* (PI) (* (PI) (PI))) 8) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 3)))
3.0ms
x
@inf
(/ (* (/ 1 (+ (/ (* (PI) (PI)) 4) (* (asin (sqrt (+ 1/2 (/ x -2)))) (+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4))))) (- (* (* (PI) (* (PI) (PI))) (* (* (PI) (* (PI) (PI))) 1/64)) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 6))) (- (/ (* (PI) (* (PI) (PI))) 8) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 3)))
2.0ms
x
@0
(/ (- (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2)) (+ (- (/ (PI) 2) (PI)) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))))
2.0ms
x
@inf
(/ (- (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2)) (+ (- (/ (PI) 2) (PI)) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))))

rewrite344.0ms (0.2%)

Algorithm
1×batch-egg-rewrite
Rules
3618×*-lowering-*.f32
3618×*-lowering-*.f64
2358×pow-lowering-pow.f64
2358×pow-lowering-pow.f32
1860×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
061367
1420276
23864273
08321273
Stop Event
1×iter limit
1×node limit
Counts
27 → 555
Calls
Call 1
Inputs
(/ (- (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2)) (+ (- (/ (PI) 2) (PI)) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))))
(- (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2))
(pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2)
(neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))
(- (/ (PI) 2) (+ (PI) (* (- 0 (acos (sqrt 1/2))) 2)))
(+ (PI) (* (- 0 (acos (sqrt 1/2))) 2))
(* (- 0 (acos (sqrt 1/2))) 2)
(/ (PI) 2)
(+ (* (/ (sqrt (PI)) 2) (sqrt (PI))) (* (asin (sqrt (+ 1/2 (/ x -2)))) -2))
(/ (sqrt (PI)) 2)
(sqrt (PI))
(PI)
(+ (* (sqrt (PI)) (/ (sqrt (PI)) 2)) (* (asin (pow (pow (+ 1/2 (/ x -2)) 1/4) 2)) -2))
(* (asin (pow (pow (+ 1/2 (/ x -2)) 1/4) 2)) -2)
(asin (pow (pow (+ 1/2 (/ x -2)) 1/4) 2))
(pow (pow (+ 1/2 (/ x -2)) 1/4) 2)
(/ (* (/ 1 (+ (/ (* (PI) (PI)) 4) (* (asin (sqrt (+ 1/2 (/ x -2)))) (+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4))))) (- (* (* (PI) (* (PI) (PI))) (* (* (PI) (* (PI) (PI))) 1/64)) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 6))) (- (/ (* (PI) (* (PI) (PI))) 8) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 3)))
(* (/ 1 (+ (/ (* (PI) (PI)) 4) (* (asin (sqrt (+ 1/2 (/ x -2)))) (+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4))))) (- (* (* (PI) (* (PI) (PI))) (* (* (PI) (* (PI) (PI))) 1/64)) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 6)))
(/ 1 (+ (/ (* (PI) (PI)) 4) (* (asin (sqrt (+ 1/2 (/ x -2)))) (+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4)))))
(+ (/ (* (PI) (PI)) 4) (* (asin (sqrt (+ 1/2 (/ x -2)))) (+ (PI) (* (asin (sqrt (+ 1/2 (/ x -2)))) 4))))
(acos (sqrt (+ 1/2 (/ x -2))))
(acos (sqrt 1/2))
(sqrt 1/2)
(sqrt (+ 1/2 (/ x -2)))
(- (* (* (PI) (* (PI) (PI))) (* (* (PI) (* (PI) (PI))) 1/64)) (pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 6))
(pow (* (asin (sqrt (+ 1/2 (/ x -2)))) -2) 6)
(* (PI) (* (PI) (PI)))
Outputs
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal 2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (neg.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal -2 binary64)))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))) #s(literal 2 binary64)))
(+.f64 (/.f64 (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))) (+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal -2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal -2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))))))
(+.f64 (-.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) #s(literal 0 binary64)) (*.f64 #s(literal 2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal 2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))))) #s(literal -1 binary64)))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 (PI.f64) (*.f64 #s(literal -2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(-.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal -2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))))
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(cbrt.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) (*.f64 (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))))))
(pow.f64 (PI.f64) #s(literal 3 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 6 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 3/2 binary64))
(pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 9 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 2 binary64))
(*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 5/2 binary64)))
(*.f64 #s(literal 1 binary64) (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))))
(*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64))
(*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1 binary64))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (PI.f64) #s(literal 7/3 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) (pow.f64 (PI.f64) #s(literal 3/2 binary64)))
(*.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1 binary64)) (PI.f64))
(*.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))

simplify260.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
4266×*-lowering-*.f32
4266×*-lowering-*.f64
2090×+-lowering-+.f64
2090×+-lowering-+.f32
1304×fma-lowering-fma.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01694076
15043614
213343548
341803530
084443530
Stop Event
1×iter limit
1×node limit
Counts
204 → 204
Calls
Call 1
Inputs
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))
(* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))
(* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))
(* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(* -2 (asin (sqrt (+ 1/2 (* -1/2 x)))))
(* -2 (asin (sqrt (+ 1/2 (* -1/2 x)))))
(* -2 (asin (sqrt (+ 1/2 (* -1/2 x)))))
(* -2 (asin (sqrt (+ 1/2 (* -1/2 x)))))
(* -2 (asin (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (asin (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (asin (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (asin (sqrt (- 1/2 (* 1/2 x)))))
(* -2 (asin (sqrt (+ 1/2 (* -1/2 x)))))
(* -2 (asin (sqrt (+ 1/2 (* -1/2 x)))))
(* -2 (asin (sqrt (+ 1/2 (* -1/2 x)))))
(* -2 (asin (sqrt (+ 1/2 (* -1/2 x)))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin (sqrt (- 1/2 (* 1/2 x))))
(asin (sqrt (- 1/2 (* 1/2 x))))
(asin (sqrt (- 1/2 (* 1/2 x))))
(asin (sqrt (- 1/2 (* 1/2 x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/4 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/32 (/ x (pow (sqrt 1/2) 3))) (* 1/4 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 5))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/4 (/ 1 (sqrt 1/2))))))
(* (sqrt x) (sqrt -1/2))
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2)))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/2) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/2) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2))))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))
(* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt 1/2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt 1/2) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt 1/2) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 3)))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (* (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))) (- (* 1/8 (pow (PI) 3)) (* -8 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 3)))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(/ (- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))) (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(/ 1 (+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x)))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (- 1/2 (* 1/2 x)))) (+ (PI) (* 4 (asin (sqrt (- 1/2 (* 1/2 x))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x))))))))
(+ (* 1/4 (pow (PI) 2)) (* (asin (sqrt (+ 1/2 (* -1/2 x)))) (+ (PI) (* 4 (asin (sqrt (+ 1/2 (* -1/2 x))))))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos (sqrt (- 1/2 (* 1/2 x))))
(acos (sqrt (- 1/2 (* 1/2 x))))
(acos (sqrt (- 1/2 (* 1/2 x))))
(acos (sqrt (- 1/2 (* 1/2 x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/4 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/32 (/ x (pow (sqrt 1/2) 3))) (* 1/4 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 5))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/4 (/ 1 (sqrt 1/2))))))
(* (sqrt x) (sqrt -1/2))
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2)))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/2) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/2) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2))))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))
(* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt 1/2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt 1/2) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt 1/2) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6)))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6)))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6)))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6)))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))
(* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))
(* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))
(* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))
(* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))
(* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))
(* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))
(* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))
(* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))
(* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))
(* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))
(* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))
(* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))
Outputs
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal -2 binary64))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal -2 binary64))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal -2 binary64))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal -2 binary64))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal -2 binary64))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal -2 binary64))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal -2 binary64))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal -2 binary64))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal -2 binary64))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal -2 binary64))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal -2 binary64))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal -2 binary64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(*.f64 #s(literal 4 binary64) (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(*.f64 #s(literal 4 binary64) (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(*.f64 #s(literal 4 binary64) (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(*.f64 #s(literal 4 binary64) (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))
(*.f64 #s(literal 4 binary64) (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))
(*.f64 #s(literal 4 binary64) (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))
(*.f64 #s(literal 4 binary64) (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))
(*.f64 #s(literal 4 binary64) (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(*.f64 #s(literal 4 binary64) (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(*.f64 #s(literal 4 binary64) (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(*.f64 #s(literal 4 binary64) (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(*.f64 #s(literal 4 binary64) (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal -2 binary64))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
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(+ (sqrt 1/2) (* x (- (* -1/32 (/ x (pow (sqrt 1/2) 3))) (* 1/4 (/ 1 (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (*.f64 x (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(+ (sqrt 1/2) (* x (- (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 5))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/4 (/ 1 (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 #s(literal -1/128 binary64) (/.f64 x (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(* (sqrt x) (sqrt -1/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1/2 binary64)))
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2))))
(*.f64 x (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1/2 binary64)))) (*.f64 (sqrt.f64 #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2)))))
(*.f64 x (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1/2 binary64)))) (+.f64 (*.f64 (sqrt.f64 #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal -1/2 binary64)))))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/2) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/2) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2))))))
(*.f64 x (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1/2 binary64)))) (+.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal -1/2 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/128 binary64) (pow.f64 (sqrt.f64 #s(literal -1/2 binary64)) #s(literal 5 binary64)))))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(*.f64 x (-.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt 1/2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(*.f64 x (-.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt 1/2) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt 1/2) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))
(*.f64 x (+.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (*.f64 #s(literal -1/128 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64)))))))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))
(+.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 (PI.f64) #s(literal 6 binary64))) (*.f64 (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)) #s(literal -64 binary64)))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))
(+.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 (PI.f64) #s(literal 6 binary64))) (*.f64 (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)) #s(literal -64 binary64)))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))
(+.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 (PI.f64) #s(literal 6 binary64))) (*.f64 (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)) #s(literal -64 binary64)))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))
(+.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 (PI.f64) #s(literal 6 binary64))) (*.f64 (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)) #s(literal -64 binary64)))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6)))
(+.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 (PI.f64) #s(literal 6 binary64))) (*.f64 (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)) #s(literal -64 binary64)))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6)))
(+.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 (PI.f64) #s(literal 6 binary64))) (*.f64 (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)) #s(literal -64 binary64)))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6)))
(+.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 (PI.f64) #s(literal 6 binary64))) (*.f64 (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)) #s(literal -64 binary64)))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6)))
(+.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 (PI.f64) #s(literal 6 binary64))) (*.f64 (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)) #s(literal -64 binary64)))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))
(+.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 (PI.f64) #s(literal 6 binary64))) (*.f64 (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)) #s(literal -64 binary64)))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))
(+.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 (PI.f64) #s(literal 6 binary64))) (*.f64 (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)) #s(literal -64 binary64)))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))
(+.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 (PI.f64) #s(literal 6 binary64))) (*.f64 (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)) #s(literal -64 binary64)))
(- (* 1/64 (pow (PI) 6)) (* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6)))
(+.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 (PI.f64) #s(literal 6 binary64))) (*.f64 (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)) #s(literal -64 binary64)))
(* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))
(*.f64 #s(literal 64 binary64) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)))
(* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))
(*.f64 #s(literal 64 binary64) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)))
(* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))
(*.f64 #s(literal 64 binary64) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)))
(* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))
(*.f64 #s(literal 64 binary64) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)))
(* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))
(*.f64 #s(literal 64 binary64) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)))
(* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))
(*.f64 #s(literal 64 binary64) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)))
(* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))
(*.f64 #s(literal 64 binary64) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)))
(* 64 (pow (asin (sqrt (- 1/2 (* 1/2 x)))) 6))
(*.f64 #s(literal 64 binary64) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)))
(* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))
(*.f64 #s(literal 64 binary64) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)))
(* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))
(*.f64 #s(literal 64 binary64) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)))
(* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))
(*.f64 #s(literal 64 binary64) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)))
(* 64 (pow (asin (sqrt (+ 1/2 (* -1/2 x)))) 6))
(*.f64 #s(literal 64 binary64) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 6 binary64)))

eval421.0ms (0.3%)

Compiler

Compiled 110785 to 6465 computations (94.2% saved)

prune293.0ms (0.2%)

Pruning

34 alts after pruning (30 fresh and 4 done)

PrunedKeptTotal
New1998152013
Fresh61521
Picked325
Done022
Total2007342041
Accuracy
9.5%
Counts
2041 → 34
Alt Table
Click to see full alt table
StatusAccuracyProgram
6.0%
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)))
▶6.1%
(fma.f64 (/.f64 (sqrt.f64 (*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
6.1%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (-.f64 #s(literal 0 binary64) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))))
3.8%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (-.f64 #s(literal 0 binary64) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
✓6.0%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
▶6.1%
(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
✓6.0%
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))) #s(literal -2 binary64)))
▶6.1%
(/.f64 (fma.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))) (+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))))
6.1%
(/.f64 (/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))))) (pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) #s(literal 2 binary64))) (-.f64 (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64))))) (+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))))
8.1%
(/.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))))
3.8%
(/.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (*.f64 (asin.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -2 binary64)) #s(literal 2 binary64))) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -2 binary64))))
6.1%
(/.f64 (-.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) (*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))) (/.f64 (-.f64 (pow.f64 (/.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) (/.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))) #s(literal 2 binary64))) (-.f64 (/.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) (/.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))))))
6.1%
(/.f64 (-.f64 (*.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) (*.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))) (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 #s(literal -4 binary64) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))))
6.1%
(/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))))) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))) (pow.f64 (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) #s(literal 2 binary64))) (+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))))
6.1%
(/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))) (pow.f64 (neg.f64 (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) #s(literal 2 binary64))) (+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))))
▶8.1%
(/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))) (pow.f64 (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) #s(literal 2 binary64))) (+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))) (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))))
8.1%
(/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))) (pow.f64 (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) #s(literal 2 binary64))) (+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))))) (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))))
8.1%
(/.f64 (-.f64 (*.f64 (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))) (+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal -2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))))) (*.f64 (+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal -2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))) (pow.f64 (+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal -2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))))) #s(literal 2 binary64)))
8.1%
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal -2 binary64))))
6.1%
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 4 binary64)))))) (-.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))) (*.f64 (PI.f64) (PI.f64))) (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/64 binary64))) (pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal 6 binary64)))) (-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal 3 binary64))))
6.1%
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) (+.f64 (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 4 binary64)))))) (-.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) (*.f64 (exp.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 3 binary64))) #s(literal 1/64 binary64))) (pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal 6 binary64)))) (-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal 3 binary64))))
6.1%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)))))
6.1%
(-.f64 (/.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))) (/.f64 (pow.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) #s(literal 2 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))))
3.8%
(-.f64 (/.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))))
8.1%
(-.f64 (/.f64 (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))) (+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal -2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))))) (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal -2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))))))
8.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))))
▶5.7%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 2 binary64))))
8.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 (PI.f64) (*.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) #s(literal 4 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) #s(literal 2 binary64))))
6.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))))
6.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)))))))
✓6.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
✓3.8%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
6.0%
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64))))) (+.f64 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)) #s(literal 3 binary64))))
6.1%
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal 4 binary64)) (PI.f64))))) (+.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (*.f64 (asin.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -2 binary64)) #s(literal 3 binary64))))
Compiler

Compiled 2731 to 1318 computations (51.7% saved)

simplify232.0ms (0.2%)

Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
✓cost-diff12992
(sqrt.f64 (*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))))
✓cost-diff12992
(/.f64 (sqrt.f64 (*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))) #s(literal 2 binary64))
✓cost-diff19264
(fma.f64 (/.f64 (sqrt.f64 (*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
✓cost-diff128
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))
✓cost-diff192
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))))
✓cost-diff6848
(fma.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64))))
✓cost-diff27072
(/.f64 (fma.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))) (+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))))
✓cost-diff0
(sqrt.f64 (PI.f64))
✓cost-diff0
(/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))
✓cost-diff128
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))))
✓cost-diff19328
(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
✓cost-diff0
(-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 2 binary64)))
✓cost-diff0
(PI.f64)
✓cost-diff0
(/.f64 (PI.f64) #s(literal 2 binary64))
✓cost-diff128
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 2 binary64))))
✓cost-diff128
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))
✓cost-diff384
(*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)))
✓cost-diff448
(-.f64 (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))) (pow.f64 (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) #s(literal 2 binary64)))
✓cost-diff512
(/.f64 (-.f64 (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))) (pow.f64 (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) #s(literal 2 binary64))) (+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))) (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))))
Rules
2446×*-lowering-*.f32
2446×*-lowering-*.f64
1464×fmsub-define
1382×fma-lowering-fma.f32
1382×fma-lowering-fma.f64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
049509
1119497
2313486
31040463
44193450
08631450
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ (- (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2)) (+ (- (/ (PI) 2) (* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2)))) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))))
(- (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2))
(* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI)))
(- (/ (PI) 2) (PI))
(/ (PI) 2)
(PI)
2
(pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2)
(neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))
(* (acos (sqrt (+ 1/2 (/ x -2)))) 2)
(acos (sqrt (+ 1/2 (/ x -2))))
(sqrt (+ 1/2 (/ x -2)))
(+ 1/2 (/ x -2))
1/2
(/ x -2)
x
-2
(+ (- (/ (PI) 2) (* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2)))) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)))
(- (/ (PI) 2) (* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2))))
(* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2)))
(cbrt (pow (PI) 3/2))
(pow (PI) 3/2)
3/2
(- (/ (PI) 2) (- (PI) (* (acos (sqrt 1/2)) 2)))
(/ (PI) 2)
(PI)
2
(- (PI) (* (acos (sqrt 1/2)) 2))
(* (acos (sqrt 1/2)) 2)
(acos (sqrt 1/2))
(sqrt 1/2)
1/2
(+ (* (/ 1 (/ 2 (sqrt (PI)))) (sqrt (PI))) (* (asin (sqrt (+ 1/2 (/ x -2)))) -2))
(/ 1 (/ 2 (sqrt (PI))))
1
(/ 2 (sqrt (PI)))
2
(sqrt (PI))
(PI)
(* (asin (sqrt (+ 1/2 (/ x -2)))) -2)
(asin (sqrt (+ 1/2 (/ x -2))))
(sqrt (+ 1/2 (/ x -2)))
(+ 1/2 (/ x -2))
1/2
(/ x -2)
x
-2
(/ (+ (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (- 0 (pow (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) 2))) (+ (- (/ (PI) 2) (PI)) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))))
(+ (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (- 0 (pow (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) 2)))
(- (/ (PI) 2) (PI))
(/ (PI) 2)
(PI)
2
(- 0 (pow (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) 2))
0
(pow (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) 2)
(* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2)))
(acos (pow (+ 1/2 (/ x -2)) 1/2))
(pow (+ 1/2 (/ x -2)) 1/2)
(+ 1/2 (/ x -2))
1/2
(/ x -2)
x
-2
(+ (- (/ (PI) 2) (PI)) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)))
(neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))
(* (acos (sqrt (+ 1/2 (/ x -2)))) 2)
(acos (sqrt (+ 1/2 (/ x -2))))
(sqrt (+ 1/2 (/ x -2)))
(+ (* (/ (sqrt (* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2)))) 2) (sqrt (PI))) (* (asin (sqrt (+ 1/2 (/ x -2)))) -2))
(/ (sqrt (* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2)))) 2)
(sqrt (* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2))))
(* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2)))
(cbrt (pow (PI) 3/2))
(pow (PI) 3/2)
(PI)
3/2
2
(sqrt (PI))
(* (asin (sqrt (+ 1/2 (/ x -2)))) -2)
(asin (sqrt (+ 1/2 (/ x -2))))
(sqrt (+ 1/2 (/ x -2)))
(+ 1/2 (/ x -2))
1/2
(/ x -2)
x
-2
Outputs
(/ (- (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2)) (+ (- (/ (PI) 2) (* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2)))) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))))
(/.f64 (-.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64))) (+.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))))))
(- (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2))
(-.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64)))
(* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI)))
(*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))
(- (/ (PI) 2) (PI))
(/.f64 (PI.f64) #s(literal -2 binary64))
(/ (PI) 2)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI)
(PI.f64)
2
#s(literal 2 binary64)
(pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2)
(pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64))
(neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(* (acos (sqrt (+ 1/2 (/ x -2)))) 2)
(*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(acos (sqrt (+ 1/2 (/ x -2))))
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(sqrt (+ 1/2 (/ x -2)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
(+ 1/2 (/ x -2))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))
1/2
#s(literal 1/2 binary64)
(/ x -2)
(/.f64 x #s(literal -2 binary64))
x
-2
#s(literal -2 binary64)
(+ (- (/ (PI) 2) (* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2)))) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)))
(+.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))))
(- (/ (PI) 2) (* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))))
(* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2)))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(cbrt (pow (PI) 3/2))
(cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))
(pow (PI) 3/2)
(pow.f64 (PI.f64) #s(literal 3/2 binary64))
3/2
#s(literal 3/2 binary64)
(- (/ (PI) 2) (- (PI) (* (acos (sqrt 1/2)) 2)))
(+.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(/ (PI) 2)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI)
(PI.f64)
2
#s(literal 2 binary64)
(- (PI) (* (acos (sqrt 1/2)) 2))
(+.f64 (PI.f64) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(* (acos (sqrt 1/2)) 2)
(*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(acos (sqrt 1/2))
(acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(+ (* (/ 1 (/ 2 (sqrt (PI)))) (sqrt (PI))) (* (asin (sqrt (+ 1/2 (/ x -2)))) -2))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(/ 1 (/ 2 (sqrt (PI))))
(/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
1
#s(literal 1 binary64)
(/ 2 (sqrt (PI)))
(/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))
2
#s(literal 2 binary64)
(sqrt (PI))
(sqrt.f64 (PI.f64))
(PI)
(PI.f64)
(* (asin (sqrt (+ 1/2 (/ x -2)))) -2)
(*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(asin (sqrt (+ 1/2 (/ x -2))))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(sqrt (+ 1/2 (/ x -2)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
(+ 1/2 (/ x -2))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))
1/2
#s(literal 1/2 binary64)
(/ x -2)
(/.f64 x #s(literal -2 binary64))
x
-2
#s(literal -2 binary64)
(/ (+ (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (- 0 (pow (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) 2))) (+ (- (/ (PI) 2) (PI)) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))))
(*.f64 (+.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) #s(literal 1 binary64))
(+ (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (- 0 (pow (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) 2)))
(-.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64)))
(- (/ (PI) 2) (PI))
(/.f64 (PI.f64) #s(literal -2 binary64))
(/ (PI) 2)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI)
(PI.f64)
2
#s(literal 2 binary64)
(- 0 (pow (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) 2))
(-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64)))
0
#s(literal 0 binary64)
(pow (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) 2)
(pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64))
(* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2)))
(*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(acos (pow (+ 1/2 (/ x -2)) 1/2))
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(pow (+ 1/2 (/ x -2)) 1/2)
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
(+ 1/2 (/ x -2))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))
1/2
#s(literal 1/2 binary64)
(/ x -2)
(/.f64 x #s(literal -2 binary64))
x
-2
#s(literal -2 binary64)
(+ (- (/ (PI) 2) (PI)) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)))
(+.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(* (acos (sqrt (+ 1/2 (/ x -2)))) 2)
(*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(acos (sqrt (+ 1/2 (/ x -2))))
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(sqrt (+ 1/2 (/ x -2)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
(+ (* (/ (sqrt (* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2)))) 2) (sqrt (PI))) (* (asin (sqrt (+ 1/2 (/ x -2)))) -2))
(+.f64 (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (/.f64 (fabs.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))) (/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))))
(/ (sqrt (* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2)))) 2)
(/.f64 (fabs.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))) #s(literal 2 binary64))
(sqrt (* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2))))
(fabs.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2)))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(cbrt (pow (PI) 3/2))
(cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))
(pow (PI) 3/2)
(pow.f64 (PI.f64) #s(literal 3/2 binary64))
(PI)
(PI.f64)
3/2
#s(literal 3/2 binary64)
2
#s(literal 2 binary64)
(sqrt (PI))
(sqrt.f64 (PI.f64))
(* (asin (sqrt (+ 1/2 (/ x -2)))) -2)
(*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(asin (sqrt (+ 1/2 (/ x -2))))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(sqrt (+ 1/2 (/ x -2)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
(+ 1/2 (/ x -2))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))
1/2
#s(literal 1/2 binary64)
(/ x -2)
(/.f64 x #s(literal -2 binary64))
x
-2
#s(literal -2 binary64)

localize2.9s (1.9%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(sqrt.f64 (PI.f64))
✓accuracy100.0%
(cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))
✓accuracy99.4%
(fma.f64 (/.f64 (sqrt.f64 (*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
✓accuracy5.8%
(PI.f64)
✓accuracy100.0%
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
✓accuracy100.0%
(pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
✓accuracy97.6%
(fma.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64))))
✓accuracy5.8%
(PI.f64)
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
✓accuracy100.0%
(sqrt.f64 (PI.f64))
✓accuracy99.4%
(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
✓accuracy5.8%
(PI.f64)
✓accuracy100.0%
(*.f64 (acos.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 2 binary64))
✓accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
✓accuracy100.0%
(acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))
✓accuracy5.8%
(PI.f64)
✓accuracy100.0%
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
✓accuracy100.0%
(cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))
✓accuracy99.5%
(-.f64 (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))) (pow.f64 (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) #s(literal 2 binary64)))
✓accuracy5.8%
(PI.f64)
Results
2.6s249×5exit
13.0ms6×2valid
4.0ms1×3valid
Compiler

Compiled 593 to 48 computations (91.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.0s
ival-pow: 678.0ms (33.7% of total)
ival-acos: 576.0ms (28.6% of total)
backward-pass: 314.0ms (15.6% of total)
ival-mult: 95.0ms (4.7% of total)
ival-div: 88.0ms (4.4% of total)
compiled-spec: 67.0ms (3.3% of total)
ival-sqrt: 57.0ms (2.8% of total)
ival-sub: 51.0ms (2.5% of total)
ival-add: 37.0ms (1.8% of total)
ival-asin: 15.0ms (0.7% of total)
ival-cbrt: 12.0ms (0.6% of total)
ival-pi: 11.0ms (0.5% of total)
ival-neg: 8.0ms (0.4% of total)
const: 3.0ms (0.1% of total)

series18.0ms (0%)

Counts
26 → 120
Calls
Call 1
Inputs
#<alt (/ (- (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2)) (+ (- (/ (PI) 2) (* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2)))) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))))>
#<alt (- (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2))>
#<alt (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI)))>
#<alt (- (/ (PI) 2) (PI))>
#<alt (- (/ (PI) 2) (- (PI) (* (acos (sqrt 1/2)) 2)))>
#<alt (/ (PI) 2)>
#<alt (PI)>
#<alt (- (PI) (* (acos (sqrt 1/2)) 2))>
#<alt (+ (* (/ 1 (/ 2 (sqrt (PI)))) (sqrt (PI))) (* (asin (sqrt (+ 1/2 (/ x -2)))) -2))>
#<alt (/ 1 (/ 2 (sqrt (PI))))>
#<alt (/ 2 (sqrt (PI)))>
#<alt (sqrt (PI))>
#<alt (/ (+ (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (- 0 (pow (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) 2))) (+ (- (/ (PI) 2) (PI)) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))))>
#<alt (+ (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (- 0 (pow (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) 2)))>
#<alt (+ (- (/ (PI) 2) (PI)) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)))>
#<alt (+ (* (/ (sqrt (* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2)))) 2) (sqrt (PI))) (* (asin (sqrt (+ 1/2 (/ x -2)))) -2))>
#<alt (/ (sqrt (* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2)))) 2)>
#<alt (sqrt (* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2))))>
#<alt (* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2)))>
#<alt (cbrt (pow (PI) 3/2))>
#<alt (acos (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (* (acos (sqrt 1/2)) 2)>
#<alt (sqrt (+ 1/2 (/ x -2)))>
#<alt (pow (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) 2)>
#<alt (acos (sqrt (+ 1/2 (/ x -2))))>
Outputs
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))>
#<alt (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))>
#<alt (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))>
#<alt (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))>
#<alt (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))>
#<alt (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))))>
#<alt (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))))>
#<alt (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))))>
#<alt (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))))>
#<alt (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))>
#<alt (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))>
#<alt (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))>
#<alt (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/4 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/32 (/ x (pow (sqrt 1/2) 3))) (* 1/4 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 5))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/4 (/ 1 (sqrt 1/2))))))>
#<alt (* (sqrt x) (sqrt -1/2))>
#<alt (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2)))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/2) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/2) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2))))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))>
#<alt (* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt 1/2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt 1/2) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt 1/2) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))>
#<alt (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))>
#<alt (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))>
#<alt (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))>
#<alt (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))>
#<alt (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))>
#<alt (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))>
#<alt (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))>
#<alt (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))>
#<alt (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))>
#<alt (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))>
#<alt (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))>
#<alt (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))>
#<alt (acos (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (acos (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (acos (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (acos (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (acos (sqrt (- 1/2 (* 1/2 x))))>
#<alt (acos (sqrt (- 1/2 (* 1/2 x))))>
#<alt (acos (sqrt (- 1/2 (* 1/2 x))))>
#<alt (acos (sqrt (- 1/2 (* 1/2 x))))>
#<alt (acos (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (acos (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (acos (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (acos (sqrt (+ 1/2 (* -1/2 x))))>
Calls

30 calls:

TimeVariablePointExpression
8.0ms
x
@0
(+ (* (/ 1 (/ 2 (sqrt (PI)))) (sqrt (PI))) (* (asin (sqrt (+ 1/2 (/ x -2)))) -2))
5.0ms
x
@0
(/ (+ (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (- 0 (pow (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) 2))) (+ (- (/ (PI) 2) (PI)) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))))
1.0ms
x
@inf
(/ (+ (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (- 0 (pow (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) 2))) (+ (- (/ (PI) 2) (PI)) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))))
1.0ms
x
@-inf
(/ (+ (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (- 0 (pow (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) 2))) (+ (- (/ (PI) 2) (PI)) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))))
0.0ms
x
@0
(/ (- (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2)) (+ (- (/ (PI) 2) (* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2)))) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))))

rewrite309.0ms (0.2%)

Algorithm
1×batch-egg-rewrite
Rules
2574×*-lowering-*.f32
2574×*-lowering-*.f64
1562×pow-lowering-pow.f64
1562×pow-lowering-pow.f32
1382×fmsub-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
049245
1358169
23647165
08312165
Stop Event
1×iter limit
1×node limit
Counts
26 → 793
Calls
Call 1
Inputs
(/ (- (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2)) (+ (- (/ (PI) 2) (* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2)))) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))))
(- (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (pow (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)) 2))
(* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI)))
(- (/ (PI) 2) (PI))
(- (/ (PI) 2) (- (PI) (* (acos (sqrt 1/2)) 2)))
(/ (PI) 2)
(PI)
(- (PI) (* (acos (sqrt 1/2)) 2))
(+ (* (/ 1 (/ 2 (sqrt (PI)))) (sqrt (PI))) (* (asin (sqrt (+ 1/2 (/ x -2)))) -2))
(/ 1 (/ 2 (sqrt (PI))))
(/ 2 (sqrt (PI)))
(sqrt (PI))
(/ (+ (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (- 0 (pow (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) 2))) (+ (- (/ (PI) 2) (PI)) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))))
(+ (* (- (/ (PI) 2) (PI)) (- (/ (PI) 2) (PI))) (- 0 (pow (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) 2)))
(+ (- (/ (PI) 2) (PI)) (neg (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)))
(+ (* (/ (sqrt (* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2)))) 2) (sqrt (PI))) (* (asin (sqrt (+ 1/2 (/ x -2)))) -2))
(/ (sqrt (* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2)))) 2)
(sqrt (* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2))))
(* (cbrt (pow (PI) 3/2)) (cbrt (pow (PI) 3/2)))
(cbrt (pow (PI) 3/2))
(acos (sqrt 1/2))
(sqrt 1/2)
(* (acos (sqrt 1/2)) 2)
(sqrt (+ 1/2 (/ x -2)))
(pow (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) 2)
(acos (sqrt (+ 1/2 (/ x -2))))
Outputs
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (neg.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal -2 binary64)))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) #s(literal 2 binary64)))
(+.f64 (/.f64 (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64))) (+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))) (neg.f64 (/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64)) (+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))))))
(+.f64 (-.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) #s(literal 0 binary64)) (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
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(*.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(*.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(*.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(*.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(*.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (neg.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64)))
(*.f64 #s(literal -1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64)))
(*.f64 #s(literal 4 binary64) (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))
(*.f64 #s(literal 4 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64)))
(*.f64 #s(literal 4 binary64) (neg.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))))
(*.f64 #s(literal 4 binary64) (pow.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64))))
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 6 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 4 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (*.f64 #s(literal 2 binary64) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))))
(*.f64 (neg.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 1 binary64)) (pow.f64 (*.f64 #s(literal -2 binary64) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 1 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 1 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64)) #s(literal 4 binary64))
(*.f64 (exp.f64 (log.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))) (exp.f64 (log.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))))
(*.f64 (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))) (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))))
(*.f64 #s(literal -4 binary64) (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal -2 binary64))
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal -1 binary64)) (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(*.f64 (*.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64))
(*.f64 (pow.f64 (pow.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal 4 binary64))
(*.f64 (pow.f64 (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 4 binary64))
(*.f64 (pow.f64 (pow.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 4 binary64))
(*.f64 (pow.f64 (exp.f64 (log.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))) #s(literal 1 binary64)) (pow.f64 (exp.f64 (log.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))) #s(literal 1 binary64)) (pow.f64 (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 1 binary64)) #s(literal -2 binary64))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 2 binary64)) #s(literal 1 binary64)) (pow.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 1 binary64)) #s(literal 2 binary64))
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (neg.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (neg.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(fma.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (neg.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (sqrt.f64 (PI.f64)) (neg.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (neg.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(fma.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) #s(literal -1/2 binary64) (neg.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (neg.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))) (neg.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(/.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 3 binary64))) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (+.f64 (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)) (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))))
(/.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))

simplify20.5s (13.6%)

Algorithm
1×egg-herbie
Rules
4174×*-lowering-*.f32
4174×*-lowering-*.f64
1774×+-lowering-+.f64
1774×+-lowering-+.f32
1710×/-lowering-/.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01282176
13641891
210621786
335021742
085111742
Stop Event
1×iter limit
1×node limit
Counts
120 → 120
Calls
Call 1
Inputs
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))))
(- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))))
(- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))))
(- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))))
(- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/4 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/32 (/ x (pow (sqrt 1/2) 3))) (* 1/4 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 5))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/4 (/ 1 (sqrt 1/2))))))
(* (sqrt x) (sqrt -1/2))
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2)))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/2) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/2) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2))))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))
(* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt 1/2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt 1/2) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt 1/2) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))
(* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))
(* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))
(* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos (sqrt (- 1/2 (* 1/2 x))))
(acos (sqrt (- 1/2 (* 1/2 x))))
(acos (sqrt (- 1/2 (* 1/2 x))))
(acos (sqrt (- 1/2 (* 1/2 x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
Outputs
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))))
(/ (- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2))) (- (* 1/2 (PI)) (+ (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))))
(/.f64 (+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64)))) (+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal -2 binary64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (- 1/2 (* 1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64))))
(- (pow (- (* 1/2 (PI)) (PI)) 2) (* 4 (pow (acos (sqrt (+ 1/2 (* -1/2 x)))) 2)))
(+.f64 (*.f64 (pow.f64 (acos.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) x)))) #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64))))
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eval1.9min (75%)

Compiler

Compiled 106445 to 6533 computations (93.9% saved)

end0.0ms (0%)

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