Ian Simplification

Time bar (total: 20.1s)

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 (39.6% of total)
ival-asin: 1.0ms (39.6% 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)

sample3.5s (17.4%)

Results
1.7s3300×2valid
1.3s4774×1valid
19.0ms182×0valid
0.0ms1×0invalid
Precisions
Click to see histograms. Total time spent on operations: 2.5s
ival-asin: 1.1s (46.5% of total)
ival-div: 344.0ms (14% of total)
backward-pass: 253.0ms (10.3% of total)
ival-sub: 228.0ms (9.3% of total)
ival-sqrt: 189.0ms (7.7% of total)
ival-mult: 166.0ms (6.7% of total)
ival-pi: 111.0ms (4.5% of total)
const: 25.0ms (1% of total)
Bogosity

preprocess72.0ms (0.4%)

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))

explain366.0ms (1.8%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2550-0-(-.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
169.0ms212×2valid
116.0ms292×1valid
1.0ms8×0valid
Compiler

Compiled 118 to 35 computations (70.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 191.0ms
ival-asin: 65.0ms (34.1% of total)
ival-sub: 47.0ms (24.7% of total)
backward-pass: 24.0ms (12.6% of total)
ival-div: 19.0ms (10% of total)
ival-mult: 14.0ms (7.3% of total)
ival-sqrt: 11.0ms (5.8% of total)
ival-pi: 9.0ms (4.7% of total)
const: 2.0ms (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
▶5.9%
(-.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)

simplify29.0ms (0.1%)

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

localize177.0ms (0.9%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
✓accuracy100.0%
(PI.f64)
✓accuracy98.5%
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
✓accuracy7.6%
(-.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
95.0ms106×2valid
61.0ms146×1valid
1.0ms4×0valid
Compiler

Compiled 52 to 12 computations (76.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 74.0ms
ival-asin: 31.0ms (42.2% of total)
backward-pass: 11.0ms (15% of total)
ival-div: 10.0ms (13.6% of total)
ival-sub: 6.0ms (8.2% of total)
ival-sqrt: 6.0ms (8.2% of total)
ival-mult: 5.0ms (6.8% of total)
ival-pi: 3.0ms (4.1% of total)
const: 1.0ms (1.4% 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
(- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2)))))
1.0ms
x
@inf
(sqrt (/ (- 1 x) 2))
1.0ms
x
@-inf
(sqrt (/ (- 1 x) 2))
1.0ms
x
@0
(sqrt (/ (- 1 x) 2))
0.0ms
x
@inf
(- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2)))))

rewrite218.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
2202×*-lowering-*.f32
2202×*-lowering-*.f64
1480×prod-diff
1168×pow-lowering-pow.f64
1168×pow-lowering-pow.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01139
16038
226738
3148134
0844934
Stop Event
1×iter limit
1×node limit
Counts
6 → 352
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 2 binary64) (-.f64 #s(literal 1 binary64) x)) #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 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)) (+.f64 (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))))))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))) (+.f64 (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))))))
(+.f64 #s(literal 0 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64))))
(+.f64 (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #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 2 binary64) (-.f64 #s(literal 1 binary64) x)) #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 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))))))
(+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64))) #s(literal 0 binary64))
(+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64))) (+.f64 (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))))
(+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64))) (+.f64 (+.f64 (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))) (+.f64 (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))))))
(+.f64 (+.f64 (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64))))
(+.f64 (fma.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))) (neg.f64 (*.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal -2 binary64)) (cbrt.f64 (PI.f64))))) (fma.f64 (neg.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal -2 binary64))) (cbrt.f64 (PI.f64)) (*.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal -2 binary64)) (cbrt.f64 (PI.f64)))))
(+.f64 (fma.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal -2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal -2 binary64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal -2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(+.f64 (fma.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal -2 binary64)) (sqrt.f64 (PI.f64))))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal -2 binary64))) (sqrt.f64 (PI.f64)) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal -2 binary64)) (sqrt.f64 (PI.f64)))))
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(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 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))))))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -2 binary64) #s(literal -1/2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal -1/2 binary64)) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 x #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -2 binary64)))))

simplify234.0ms (1.2%)

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)))))))

eval54.0ms (0.3%)

Compiler

Compiled 8792 to 1181 computations (86.6% saved)

prune81.0ms (0.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New3946400
Fresh000
Picked011
Done000
Total3947401
Accuracy
9.0%
Counts
401 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶5.8%
(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 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)))
5.9%
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)))
▶5.8%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)))
▶7.6%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))))
▶6.0%
(-.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)))))))
✓5.9%
(-.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))))))
▶4.0%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
Compiler

Compiled 224 to 173 computations (22.8% saved)

simplify196.0ms (1%)

Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))
✓cost-diff0
(PI.f64)
✓cost-diff0
(pow.f64 (PI.f64) #s(literal 2/3 binary64))
✓cost-diff6272
(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 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 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 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)))
✓cost-diff0
(*.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))))))
✓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 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)))))))
✓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-diff0
(PI.f64)
✓cost-diff0
(/.f64 (PI.f64) #s(literal 2 binary64))
✓cost-diff128
(*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))))
✓cost-diff256
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))))
Rules
2662×+-lowering-+.f64
2662×+-lowering-+.f32
2258×--lowering--.f32
2258×--lowering--.f64
1794×*-lowering-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0368589934854
1718589934850
21278589934847
33028589934843
46448589934840
515298589934840
639858589934839
08108270
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (pow (/ 2 (- 1 x)) -1/2)))))
(/ (PI) 2)
(PI)
2
(* 2 (- (/ (PI) 2) (acos (pow (/ 2 (- 1 x)) -1/2))))
(- (/ (PI) 2) (acos (pow (/ 2 (- 1 x)) -1/2)))
(acos (pow (/ 2 (- 1 x)) -1/2))
(pow (/ 2 (- 1 x)) -1/2)
(/ 2 (- 1 x))
(- 1 x)
1
x
-1/2
(- (/ (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
(- (/ (PI) 2) (* 2 (asin (/ 1 (sqrt (/ 2 (- 1 x)))))))
(/ (PI) 2)
(PI)
2
(* 2 (asin (/ 1 (sqrt (/ 2 (- 1 x))))))
(asin (/ 1 (sqrt (/ 2 (- 1 x)))))
(/ 1 (sqrt (/ 2 (- 1 x))))
1
(sqrt (/ 2 (- 1 x)))
(/ 2 (- 1 x))
(- 1 x)
x
(+ (* (/ (sqrt (PI)) 2) (sqrt (PI))) (* (asin (pow (/ 2 (- 1 x)) -1/2)) -2))
(/ (sqrt (PI)) 2)
(sqrt (PI))
(PI)
2
(* (asin (pow (/ 2 (- 1 x)) -1/2)) -2)
(asin (pow (/ 2 (- 1 x)) -1/2))
(pow (/ 2 (- 1 x)) -1/2)
(/ 2 (- 1 x))
(- 1 x)
1
x
-1/2
-2
(+ (* (pow (PI) 2/3) (/ (cbrt (PI)) 2)) (* (asin (pow (/ 2 (- 1 x)) -1/2)) -2))
(pow (PI) 2/3)
(PI)
2/3
(/ (cbrt (PI)) 2)
(cbrt (PI))
2
(* (asin (pow (/ 2 (- 1 x)) -1/2)) -2)
(asin (pow (/ 2 (- 1 x)) -1/2))
(pow (/ 2 (- 1 x)) -1/2)
(/ 2 (- 1 x))
(- 1 x)
1
x
-1/2
-2
Outputs
(- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (pow (/ 2 (- 1 x)) -1/2)))))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))) (/.f64 (PI.f64) #s(literal -2 binary64)))
(/ (PI) 2)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI)
(PI.f64)
2
#s(literal 2 binary64)
(* 2 (- (/ (PI) 2) (acos (pow (/ 2 (- 1 x)) -1/2))))
(+.f64 (*.f64 (acos.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)) (PI.f64))
(- (/ (PI) 2) (acos (pow (/ 2 (- 1 x)) -1/2)))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))
(acos (pow (/ 2 (- 1 x)) -1/2))
(acos.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
(pow (/ 2 (- 1 x)) -1/2)
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(/ 2 (- 1 x))
(/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
-1/2
#s(literal -1/2 binary64)
(- (/ (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)
(- (/ (PI) 2) (* 2 (asin (/ 1 (sqrt (/ 2 (- 1 x)))))))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))))) #s(literal -2 binary64)))
(/ (PI) 2)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI)
(PI.f64)
2
#s(literal 2 binary64)
(* 2 (asin (/ 1 (sqrt (/ 2 (- 1 x))))))
(*.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))))))
(asin (/ 1 (sqrt (/ 2 (- 1 x)))))
(asin.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)))))
(/ 1 (sqrt (/ 2 (- 1 x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))))
1
#s(literal 1 binary64)
(sqrt (/ 2 (- 1 x)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)))
(/ 2 (- 1 x))
(/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
x
(+ (* (/ (sqrt (PI)) 2) (sqrt (PI))) (* (asin (pow (/ 2 (- 1 x)) -1/2)) -2))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #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 (pow (/ 2 (- 1 x)) -1/2)) -2)
(*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64))
(asin (pow (/ 2 (- 1 x)) -1/2))
(asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
(pow (/ 2 (- 1 x)) -1/2)
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(/ 2 (- 1 x))
(/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
-1/2
#s(literal -1/2 binary64)
-2
#s(literal -2 binary64)
(+ (* (pow (PI) 2/3) (/ (cbrt (PI)) 2)) (* (asin (pow (/ 2 (- 1 x)) -1/2)) -2))
(+.f64 (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))))
(pow (PI) 2/3)
(pow.f64 (PI.f64) #s(literal 2/3 binary64))
(PI)
(PI.f64)
2/3
#s(literal 2/3 binary64)
(/ (cbrt (PI)) 2)
(/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))
(cbrt (PI))
(cbrt.f64 (PI.f64))
2
#s(literal 2 binary64)
(* (asin (pow (/ 2 (- 1 x)) -1/2)) -2)
(*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64))
(asin (pow (/ 2 (- 1 x)) -1/2))
(asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
(pow (/ 2 (- 1 x)) -1/2)
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(/ 2 (- 1 x))
(/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
-1/2
#s(literal -1/2 binary64)
-2
#s(literal -2 binary64)

localize3.1s (15.3%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
✓accuracy100.0%
(cbrt.f64 (PI.f64))
✓accuracy99.8%
(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 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)))
✓accuracy4.6%
(PI.f64)
✓accuracy100.0%
(asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
✓accuracy100.0%
(sqrt.f64 (PI.f64))
✓accuracy99.8%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)))
✓accuracy4.6%
(PI.f64)
✓accuracy100.0%
(asin.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)))))
✓accuracy100.0%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))))
✓accuracy99.8%
(-.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)))))))
✓accuracy4.6%
(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)))
✓accuracy4.6%
(PI.f64)
✓accuracy100.0%
(acos.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
✓accuracy100.0%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))
✓accuracy99.8%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))))
✓accuracy4.6%
(PI.f64)
Results
2.9s252×5exit
9.0ms4×2valid
Compiler

Compiled 295 to 35 computations (88.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.4s
ival-asin: 857.0ms (36.2% of total)
ival-pow: 770.0ms (32.5% of total)
backward-pass: 204.0ms (8.6% of total)
ival-acos: 110.0ms (4.6% of total)
ival-div: 88.0ms (3.7% of total)
compiled-spec: 82.0ms (3.5% of total)
ival-mult: 80.0ms (3.4% of total)
ival-sub: 73.0ms (3.1% of total)
ival-sqrt: 46.0ms (1.9% of total)
ival-add: 18.0ms (0.8% of total)
...c/correct-round.rkt:119:19: 14.0ms (0.6% of total)
ival-cbrt: 13.0ms (0.5% of total)
ival-pi: 11.0ms (0.5% of total)
const: 3.0ms (0.1% of total)

series9.0ms (0%)

Counts
22 → 132
Calls
Call 1
Inputs
#<alt (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (pow (/ 2 (- 1 x)) -1/2)))))>
#<alt (* 2 (- (/ (PI) 2) (acos (pow (/ 2 (- 1 x)) -1/2))))>
#<alt (/ (PI) 2)>
#<alt (PI)>
#<alt (- (/ (PI) 2) (* 2 (asin (sqrt 1/2))))>
#<alt (* 2 (asin (sqrt 1/2)))>
#<alt (- (/ (PI) 2) (* 2 (asin (/ 1 (sqrt (/ 2 (- 1 x)))))))>
#<alt (* 2 (asin (/ 1 (sqrt (/ 2 (- 1 x))))))>
#<alt (+ (* (/ (sqrt (PI)) 2) (sqrt (PI))) (* (asin (pow (/ 2 (- 1 x)) -1/2)) -2))>
#<alt (/ (sqrt (PI)) 2)>
#<alt (sqrt (PI))>
#<alt (+ (* (pow (PI) 2/3) (/ (cbrt (PI)) 2)) (* (asin (pow (/ 2 (- 1 x)) -1/2)) -2))>
#<alt (pow (PI) 2/3)>
#<alt (/ (cbrt (PI)) 2)>
#<alt (- (/ (PI) 2) (acos (pow (/ 2 (- 1 x)) -1/2)))>
#<alt (acos (pow (/ 2 (- 1 x)) -1/2))>
#<alt (asin (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (/ 1 (sqrt (/ 2 (- 1 x))))>
#<alt (asin (/ 1 (sqrt (/ 2 (- 1 x)))))>
#<alt (asin (pow (/ 2 (- 1 x)) -1/2))>
#<alt (cbrt (PI))>
Outputs
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))>
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))>
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))>
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x)))))))>
#<alt (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))>
#<alt (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))>
#<alt (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))>
#<alt (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))>
#<alt (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))>
#<alt (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))>
#<alt (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))>
#<alt (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))>
#<alt (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x))))))>
#<alt (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x))))))>
#<alt (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x))))))>
#<alt (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x))))))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))>
#<alt (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))>
#<alt (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))>
#<alt (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))>
#<alt (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))>
#<alt (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))>
#<alt (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))>
#<alt (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))>
#<alt (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))>
#<alt (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))>
#<alt (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))>
#<alt (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))>
#<alt (acos (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (acos (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (acos (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (acos (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (acos (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (acos (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (acos (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (acos (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))>
#<alt (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))>
#<alt (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))>
#<alt (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))>
#<alt (/ 1 (sqrt 2))>
#<alt (+ (* -1/2 (/ x (sqrt 2))) (/ 1 (sqrt 2)))>
#<alt (+ (* x (- (* -1/8 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))>
#<alt (+ (* x (- (* x (- (* -1/16 (/ x (sqrt 2))) (* 1/8 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))>
#<alt (* (sqrt x) (/ (sqrt -1) (sqrt 2)))>
#<alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt 2)))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (* (pow (sqrt -1) 3) (sqrt 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt 2))))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (* (pow (sqrt -1) 3) (sqrt 2))))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (* (pow (sqrt -1) 5) (sqrt 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt 2)))))))>
#<alt (* -1 (* (sqrt x) (/ (sqrt -1) (sqrt 2))))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt 2)))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (sqrt 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt 2))))))))>
#<alt (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))>
#<alt (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))>
#<alt (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))>
#<alt (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))>
#<alt (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))>
#<alt (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))>
#<alt (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))>
#<alt (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))>
#<alt (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x)))))>
#<alt (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x)))))>
#<alt (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x)))))>
#<alt (asin (* (/ 1 (sqrt 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)))))>
Calls

33 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
(/ 1 (sqrt (/ 2 (- 1 x))))
1.0ms
x
@0
(- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (pow (/ 2 (- 1 x)) -1/2)))))
1.0ms
x
@inf
(/ 1 (sqrt (/ 2 (- 1 x))))
1.0ms
x
@inf
(- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (pow (/ 2 (- 1 x)) -1/2)))))
0.0ms
x
@-inf
(- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (pow (/ 2 (- 1 x)) -1/2)))))

rewrite329.0ms (1.6%)

Algorithm
1×batch-egg-rewrite
Rules
1774×fma-lowering-fma.f32
1774×fma-lowering-fma.f64
1770×fmsub-define
1740×fmm-def
1638×*-lowering-*.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
036154
1135137
2580137
33312137
08200137
Stop Event
1×iter limit
1×node limit
Counts
22 → 1313
Calls
Call 1
Inputs
(- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (pow (/ 2 (- 1 x)) -1/2)))))
(* 2 (- (/ (PI) 2) (acos (pow (/ 2 (- 1 x)) -1/2))))
(/ (PI) 2)
(PI)
(- (/ (PI) 2) (* 2 (asin (sqrt 1/2))))
(* 2 (asin (sqrt 1/2)))
(- (/ (PI) 2) (* 2 (asin (/ 1 (sqrt (/ 2 (- 1 x)))))))
(* 2 (asin (/ 1 (sqrt (/ 2 (- 1 x))))))
(+ (* (/ (sqrt (PI)) 2) (sqrt (PI))) (* (asin (pow (/ 2 (- 1 x)) -1/2)) -2))
(/ (sqrt (PI)) 2)
(sqrt (PI))
(+ (* (pow (PI) 2/3) (/ (cbrt (PI)) 2)) (* (asin (pow (/ 2 (- 1 x)) -1/2)) -2))
(pow (PI) 2/3)
(/ (cbrt (PI)) 2)
(- (/ (PI) 2) (acos (pow (/ 2 (- 1 x)) -1/2)))
(acos (pow (/ 2 (- 1 x)) -1/2))
(asin (sqrt 1/2))
(sqrt 1/2)
(/ 1 (sqrt (/ 2 (- 1 x))))
(asin (/ 1 (sqrt (/ 2 (- 1 x)))))
(asin (pow (/ 2 (- 1 x)) -1/2))
(cbrt (PI))
Outputs
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #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))))))))
(+.f64 (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))
(+.f64 (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #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))))))))
(+.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64))) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #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)))))))
(+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64))) (+.f64 (+.f64 (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #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)))))) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #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))))))))
(+.f64 (+.f64 (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #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)))))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64))))
(+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(-.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))))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #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))))))))
(-.f64 (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)) (/.f64 (PI.f64) #s(literal -2 binary64)))
(-.f64 (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal -2 binary64)) (sqrt.f64 (PI.f64))))
(-.f64 (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)) (*.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal -2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(-.f64 (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (PI.f64))))
(-.f64 #s(literal 0 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 0 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) 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 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #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)))))))))
(fma.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))) (/.f64 (PI.f64) #s(literal 2 binary64)))
(fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
(fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1 binary64) (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #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)))))))))
(fma.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #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)))))))))
(fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (PI.f64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (PI.f64)) (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #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)))))))))
(fma.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))) #s(literal -1 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #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)))))))))
(fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal -1 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
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(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (cbrt.f64 (PI.f64)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (cbrt.f64 (PI.f64)) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) (cbrt.f64 (PI.f64)))) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (/.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal -1/3 binary64))) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 #s(literal -1 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64)))
(fma.f64 #s(literal -1 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) 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)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (PI.f64))) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (-.f64 #s(literal 0 binary64) (cbrt.f64 (PI.f64))) (*.f64 #s(literal -1/2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (-.f64 #s(literal 0 binary64) (cbrt.f64 (PI.f64))) (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (*.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 4/9 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 4/9 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (/.f64 #s(literal 2 binary64) (cbrt.f64 (PI.f64)))) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (cbrt.f64 (PI.f64)) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) 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))) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 4/9 binary64)) #s(literal 2 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (pow.f64 (PI.f64) #s(literal -1/3 binary64))) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal -1/3 binary64))) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (*.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 4/9 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(fma.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (cbrt.f64 (PI.f64))) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(neg.f64 (-.f64 #s(literal 0 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(neg.f64 (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal -2 binary64))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) #s(literal 2/3 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 2/3 binary64) (log.f64 (PI.f64))) #s(literal 1/2 binary64)))
(fabs.f64 (cbrt.f64 (PI.f64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (cbrt.f64 (PI.f64))))
(sqrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(cbrt.f64 (PI.f64))
(neg.f64 (-.f64 #s(literal 0 binary64) (cbrt.f64 (PI.f64))))
(pow.f64 (PI.f64) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2/3 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/6 binary64))
(pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/9 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (cbrt.f64 (PI.f64)))
(*.f64 (cbrt.f64 (PI.f64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2/3 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (PI.f64) #s(literal 2/9 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 2/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 2/3 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 4/9 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 4/9 binary64))) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))))

simplify285.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
4420×*-lowering-*.f32
4420×*-lowering-*.f64
1968×+-lowering-+.f64
1968×+-lowering-+.f32
1466×/-lowering-/.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01171654
13551629
210121610
335071552
082021552
Stop Event
1×iter limit
1×node limit
Counts
132 → 132
Calls
Call 1
Inputs
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x)))))))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x)))))))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x)))))))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x)))))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x))))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x))))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x))))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x))))))
(+ (* -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)))))) (* 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)))))) (* 1/2 (PI)))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(/ 1 (sqrt 2))
(+ (* -1/2 (/ x (sqrt 2))) (/ 1 (sqrt 2)))
(+ (* x (- (* -1/8 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))
(+ (* x (- (* x (- (* -1/16 (/ x (sqrt 2))) (* 1/8 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))
(* (sqrt x) (/ (sqrt -1) (sqrt 2)))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt 2)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (* (pow (sqrt -1) 3) (sqrt 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt 2))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (* (pow (sqrt -1) 3) (sqrt 2))))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (* (pow (sqrt -1) 5) (sqrt 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt 2)))))))
(* -1 (* (sqrt x) (/ (sqrt -1) (sqrt 2))))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt 2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (sqrt 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt 2))))))))
(asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))
(asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))
(asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))
(asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))
(asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))
(asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))
(asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))
(asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))
(asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x)))))
(asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x)))))
(asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x)))))
(asin (* (/ 1 (sqrt 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)))))
Outputs
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))
(+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))
(+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))
(+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))
(+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(+.f64 (PI.f64) (*.f64 (acos.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 (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -2 binary64)))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))
(*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))
(*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))
(*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))
(*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))
(*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))
(*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))
(*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x)))))
(*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))))
(* 2 (asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))))
(+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(/ 1 (sqrt 2))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/2 (/ x (sqrt 2))) (/ 1 (sqrt 2)))
(*.f64 (+.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+ (* x (- (* -1/8 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))
(+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (+.f64 (*.f64 x #s(literal -1/8 binary64)) #s(literal -1/2 binary64))))
(+ (* x (- (* x (- (* -1/16 (/ x (sqrt 2))) (* 1/8 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))
(+.f64 (*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64))))) (*.f64 (+.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* (sqrt x) (/ (sqrt -1) (sqrt 2)))
(/.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt 2)))))
(*.f64 x (+.f64 (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 #s(literal 2 binary64)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (* (pow (sqrt -1) 3) (sqrt 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt 2))))))
(*.f64 x (+.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 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))) (/ 1 (* (pow (sqrt -1) 3) (sqrt 2))))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (* (pow (sqrt -1) 5) (sqrt 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt 2)))))))
(*.f64 x (+.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 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 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))))))
(* -1 (* (sqrt x) (/ (sqrt -1) (sqrt 2))))
(/.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt 2))))))
(*.f64 (/.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (-.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 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt 2)))))))
(-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (sqrt 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt 2))))))))
(-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.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))))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))))))
(asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))
(asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
(asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))
(asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
(asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))
(asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
(asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))
(asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
(asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))
(asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
(asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))
(asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
(asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))
(asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
(asin (* (/ 1 (sqrt 2)) (sqrt (- 1 x))))
(asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
(asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x)))))
(asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
(asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x)))))
(asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
(asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x)))))
(asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
(asin (* (/ 1 (sqrt 2)) (sqrt (+ 1 (* -1 x)))))
(asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))
(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))))

eval799.0ms (4%)

Compiler

Compiled 53773 to 4117 computations (92.3% saved)

prune327.0ms (1.6%)

Pruning

19 alts after pruning (17 fresh and 2 done)

PrunedKeptTotal
New2356172373
Fresh101
Picked415
Done011
Total2361192380
Accuracy
9.1%
Counts
2380 → 19
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶6.0%
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)))
5.9%
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))) #s(literal -2 binary64)))
▶5.8%
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
5.9%
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
▶4.0%
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (*.f64 (asin.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -2 binary64)))
5.9%
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
4.0%
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (*.f64 (asin.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -2 binary64)))
4.0%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (*.f64 (asin.f64 (sqrt.f64 #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 (fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))) #s(literal -2 binary64)))
5.9%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))) #s(literal -2 binary64)))
5.8%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
5.9%
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (sqrt.f64 (PI.f64)) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)))
5.9%
(fma.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)))
5.8%
(fma.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
▶7.6%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))))
5.4%
(-.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))))
▶4.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
✓5.9%
(-.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))))))
✓4.0%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
Compiler

Compiled 686 to 544 computations (20.7% saved)

simplify158.0ms (0.8%)

Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64))
✓cost-diff0
(PI.f64)
✓cost-diff0
(pow.f64 (PI.f64) #s(literal 2/3 binary64))
✓cost-diff6272
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)))
✓cost-diff0
(/.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))))
✓cost-diff0
(PI.f64)
✓cost-diff0
(pow.f64 (PI.f64) #s(literal 1/4 binary64))
✓cost-diff6272
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (*.f64 (asin.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -2 binary64)))
✓cost-diff0
(/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))
✓cost-diff0
(PI.f64)
✓cost-diff0
(pow.f64 (PI.f64) #s(literal 2/3 binary64))
✓cost-diff6272
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #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 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
✓cost-diff0
(-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 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 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))))
Rules
1702×sum3-define
1448×fnmadd-define
1312×fmsub-define
1292×fnmsub-define
1214×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04817179869417
19417179869412
215417179869409
327217179869409
450817179869399
5103917179869399
6189817179869397
7272617179869397
8370117179869397
9711617179869397
08015259
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(- (/ (PI) 2) (- (PI) (* (acos (sqrt (/ (- 1 x) 2))) 2)))
(/ (PI) 2)
(PI)
2
(- (PI) (* (acos (sqrt (/ (- 1 x) 2))) 2))
(* (acos (sqrt (/ (- 1 x) 2))) 2)
(acos (sqrt (/ (- 1 x) 2)))
(sqrt (/ (- 1 x) 2))
(/ (- 1 x) 2)
(- 1 x)
1
x
(- (/ (PI) 2) (* 2 (asin (/ 1 (sqrt 2)))))
(/ (PI) 2)
(PI)
2
(* 2 (asin (/ 1 (sqrt 2))))
(asin (/ 1 (sqrt 2)))
(/ 1 (sqrt 2))
1
(sqrt 2)
(+ (* (pow (PI) 2/3) (/ (cbrt (PI)) 2)) (* (asin (sqrt (/ (- 1 x) 2))) -2))
(pow (PI) 2/3)
(PI)
2/3
(/ (cbrt (PI)) 2)
(cbrt (PI))
2
(* (asin (sqrt (/ (- 1 x) 2))) -2)
(asin (sqrt (/ (- 1 x) 2)))
(sqrt (/ (- 1 x) 2))
(/ (- 1 x) 2)
(- 1 x)
1
x
-2
(+ (* (pow (PI) 1/4) (/ (pow (PI) 1/4) (/ 2 (sqrt (PI))))) (* (asin (sqrt 1/2)) -2))
(pow (PI) 1/4)
(PI)
1/4
(/ (pow (PI) 1/4) (/ 2 (sqrt (PI))))
(/ 2 (sqrt (PI)))
2
(sqrt (PI))
(* (asin (sqrt 1/2)) -2)
(asin (sqrt 1/2))
(sqrt 1/2)
1/2
-2
(+ (* (pow (PI) 2/3) (/ (pow (pow (PI) 1/6) 2) 2)) (* (asin (pow (/ 2 (- 1 x)) -1/2)) -2))
(pow (PI) 2/3)
(PI)
2/3
(/ (pow (pow (PI) 1/6) 2) 2)
(pow (pow (PI) 1/6) 2)
(pow (PI) 1/6)
1/6
2
(* (asin (pow (/ 2 (- 1 x)) -1/2)) -2)
(asin (pow (/ 2 (- 1 x)) -1/2))
(pow (/ 2 (- 1 x)) -1/2)
(/ 2 (- 1 x))
(- 1 x)
1
x
-1/2
-2
Outputs
(- (/ (PI) 2) (- (PI) (* (acos (sqrt (/ (- 1 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 (PI.f64) #s(literal -2 binary64)))
(/ (PI) 2)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI)
(PI.f64)
2
#s(literal 2 binary64)
(- (PI) (* (acos (sqrt (/ (- 1 x) 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)))
(* (acos (sqrt (/ (- 1 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 x) 2)))
(acos.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
(- (/ (PI) 2) (* 2 (asin (/ 1 (sqrt 2)))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(/ (PI) 2)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI)
(PI.f64)
2
#s(literal 2 binary64)
(* 2 (asin (/ 1 (sqrt 2))))
(*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(asin (/ 1 (sqrt 2)))
(asin.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/ 1 (sqrt 2))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
1
#s(literal 1 binary64)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (* (pow (PI) 2/3) (/ (cbrt (PI)) 2)) (* (asin (sqrt (/ (- 1 x) 2))) -2))
(+.f64 (*.f64 (cbrt.f64 (PI.f64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #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)))
(pow (PI) 2/3)
(pow.f64 (PI.f64) #s(literal 2/3 binary64))
(PI)
(PI.f64)
2/3
#s(literal 2/3 binary64)
(/ (cbrt (PI)) 2)
(/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))
(cbrt (PI))
(cbrt.f64 (PI.f64))
2
#s(literal 2 binary64)
(* (asin (sqrt (/ (- 1 x) 2))) -2)
(*.f64 (asin.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 2 binary64))))) #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
-2
#s(literal -2 binary64)
(+ (* (pow (PI) 1/4) (/ (pow (PI) 1/4) (/ 2 (sqrt (PI))))) (* (asin (sqrt 1/2)) -2))
(+.f64 (/.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(pow (PI) 1/4)
(pow.f64 (PI.f64) #s(literal 1/4 binary64))
(PI)
(PI.f64)
1/4
#s(literal 1/4 binary64)
(/ (pow (PI) 1/4) (/ 2 (sqrt (PI))))
(/.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))))
(/ 2 (sqrt (PI)))
(/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))
2
#s(literal 2 binary64)
(sqrt (PI))
(sqrt.f64 (PI.f64))
(* (asin (sqrt 1/2)) -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)
-2
#s(literal -2 binary64)
(+ (* (pow (PI) 2/3) (/ (pow (pow (PI) 1/6) 2) 2)) (* (asin (pow (/ 2 (- 1 x)) -1/2)) -2))
(+.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))))
(pow (PI) 2/3)
(pow.f64 (PI.f64) #s(literal 2/3 binary64))
(PI)
(PI.f64)
2/3
#s(literal 2/3 binary64)
(/ (pow (pow (PI) 1/6) 2) 2)
(/.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64))
(pow (pow (PI) 1/6) 2)
(pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64))
(pow (PI) 1/6)
(pow.f64 (PI.f64) #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
2
#s(literal 2 binary64)
(* (asin (pow (/ 2 (- 1 x)) -1/2)) -2)
(*.f64 #s(literal -2 binary64) (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))
(asin (pow (/ 2 (- 1 x)) -1/2))
(asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
(pow (/ 2 (- 1 x)) -1/2)
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(/ 2 (- 1 x))
(/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
-1/2
#s(literal -1/2 binary64)
-2
#s(literal -2 binary64)

localize2.5s (12.6%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))
✓accuracy100.0%
(asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
✓accuracy99.8%
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)))
✓accuracy4.6%
(PI.f64)
✓accuracy100.0%
(sqrt.f64 (PI.f64))
✓accuracy100.0%
(asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))
✓accuracy98.5%
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (*.f64 (asin.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -2 binary64)))
✓accuracy4.6%
(PI.f64)
✓accuracy100.0%
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
✓accuracy100.0%
(cbrt.f64 (PI.f64))
✓accuracy99.8%
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
✓accuracy4.6%
(PI.f64)
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy100.0%
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy100.0%
(asin.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
✓accuracy4.6%
(PI.f64)
✓accuracy100.0%
(acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
✓accuracy100.0%
(-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)))
✓accuracy99.8%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))))
✓accuracy4.6%
(PI.f64)
Results
2.3s252×5exit
10.0ms4×2valid
Compiler

Compiled 291 to 46 computations (84.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.8s
ival-pow: 549.0ms (31.2% of total)
ival-asin: 474.0ms (27% of total)
backward-pass: 220.0ms (12.5% of total)
ival-div: 121.0ms (6.9% of total)
ival-acos: 86.0ms (4.9% of total)
ival-mult: 80.0ms (4.6% of total)
compiled-spec: 72.0ms (4.1% of total)
ival-sqrt: 65.0ms (3.7% of total)
ival-sub: 29.0ms (1.6% of total)
ival-pi: 17.0ms (1% of total)
...c/correct-round.rkt:119:19: 17.0ms (1% of total)
ival-cbrt: 13.0ms (0.7% of total)
ival-add: 11.0ms (0.6% of total)
const: 4.0ms (0.2% of total)

series4.0ms (0%)

Counts
24 → 96
Calls
Call 1
Inputs
#<alt (- (/ (PI) 2) (- (PI) (* (acos (sqrt (/ (- 1 x) 2))) 2)))>
#<alt (/ (PI) 2)>
#<alt (PI)>
#<alt (- (PI) (* (acos (sqrt (/ (- 1 x) 2))) 2))>
#<alt (- (/ (PI) 2) (* 2 (asin (/ 1 (sqrt 2)))))>
#<alt (* 2 (asin (/ 1 (sqrt 2))))>
#<alt (+ (* (pow (PI) 2/3) (/ (cbrt (PI)) 2)) (* (asin (sqrt (/ (- 1 x) 2))) -2))>
#<alt (pow (PI) 2/3)>
#<alt (/ (cbrt (PI)) 2)>
#<alt (+ (* (pow (PI) 1/4) (/ (pow (PI) 1/4) (/ 2 (sqrt (PI))))) (* (asin (sqrt 1/2)) -2))>
#<alt (pow (PI) 1/4)>
#<alt (/ (pow (PI) 1/4) (/ 2 (sqrt (PI))))>
#<alt (+ (* (pow (PI) 2/3) (/ (pow (pow (PI) 1/6) 2) 2)) (* (asin (pow (/ 2 (- 1 x)) -1/2)) -2))>
#<alt (/ (pow (pow (PI) 1/6) 2) 2)>
#<alt (acos (sqrt (/ (- 1 x) 2)))>
#<alt (asin (/ 1 (sqrt 2)))>
#<alt (/ 1 (sqrt 2))>
#<alt (sqrt 2)>
#<alt (cbrt (PI))>
#<alt (asin (sqrt (/ (- 1 x) 2)))>
#<alt (asin (sqrt 1/2))>
#<alt (sqrt (PI))>
#<alt (asin (pow (/ 2 (- 1 x)) -1/2))>
#<alt (/ 2 (- 1 x))>
Outputs
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))) (PI))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))) (PI))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))) (PI))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))) (PI))>
#<alt (- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))>
#<alt (- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))>
#<alt (- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))>
#<alt (- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))>
#<alt (- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (acos (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (acos (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (acos (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (acos (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (acos (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (acos (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (acos (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (acos (* (sqrt 1/2) (sqrt (- 1 x))))>
#<alt (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))>
#<alt (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))>
#<alt (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))>
#<alt (acos (* (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 (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 2>
#<alt (+ 2 (* 2 x))>
#<alt (+ 2 (* x (+ 2 (* 2 x))))>
#<alt (+ 2 (* x (+ 2 (* x (+ 2 (* 2 x))))))>
#<alt (/ -2 x)>
#<alt (* -1 (/ (+ 2 (* 2 (/ 1 x))) x))>
#<alt (/ (- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 2) x)>
#<alt (/ (- (* -1 (/ (+ 2 (* 2 (/ 1 x))) (pow x 2))) (+ 2 (* 2 (/ 1 x)))) x)>
#<alt (/ -2 x)>
#<alt (* -1 (/ (+ 2 (* 2 (/ 1 x))) x))>
#<alt (* -1 (/ (+ 2 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))) x))>
#<alt (* -1 (/ (+ 2 (* -1 (/ (- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 2) x))) x))>
Calls

24 calls:

TimeVariablePointExpression
0.0ms
x
@0
(- (/ (PI) 2) (- (PI) (* (acos (sqrt (/ (- 1 x) 2))) 2)))
0.0ms
x
@-inf
(- (/ (PI) 2) (- (PI) (* (acos (sqrt (/ (- 1 x) 2))) 2)))
0.0ms
x
@inf
(- (/ (PI) 2) (- (PI) (* (acos (sqrt (/ (- 1 x) 2))) 2)))
0.0ms
x
@0
(+ (* (pow (PI) 2/3) (/ (pow (pow (PI) 1/6) 2) 2)) (* (asin (pow (/ 2 (- 1 x)) -1/2)) -2))
0.0ms
x
@inf
(+ (* (pow (PI) 2/3) (/ (cbrt (PI)) 2)) (* (asin (sqrt (/ (- 1 x) 2))) -2))

rewrite249.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
2738×*-lowering-*.f32
2738×*-lowering-*.f64
1942×fnmadd-define
1398×fnmsub-define
990×sum3-define
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
048163
1179136
2766130
36350123
08701123
Stop Event
1×iter limit
1×node limit
Counts
24 → 817
Calls
Call 1
Inputs
(- (/ (PI) 2) (- (PI) (* (acos (sqrt (/ (- 1 x) 2))) 2)))
(/ (PI) 2)
(PI)
(- (PI) (* (acos (sqrt (/ (- 1 x) 2))) 2))
(- (/ (PI) 2) (* 2 (asin (/ 1 (sqrt 2)))))
(* 2 (asin (/ 1 (sqrt 2))))
(+ (* (pow (PI) 2/3) (/ (cbrt (PI)) 2)) (* (asin (sqrt (/ (- 1 x) 2))) -2))
(pow (PI) 2/3)
(/ (cbrt (PI)) 2)
(+ (* (pow (PI) 1/4) (/ (pow (PI) 1/4) (/ 2 (sqrt (PI))))) (* (asin (sqrt 1/2)) -2))
(pow (PI) 1/4)
(/ (pow (PI) 1/4) (/ 2 (sqrt (PI))))
(+ (* (pow (PI) 2/3) (/ (pow (pow (PI) 1/6) 2) 2)) (* (asin (pow (/ 2 (- 1 x)) -1/2)) -2))
(/ (pow (pow (PI) 1/6) 2) 2)
(acos (sqrt (/ (- 1 x) 2)))
(asin (/ 1 (sqrt 2)))
(/ 1 (sqrt 2))
(sqrt 2)
(cbrt (PI))
(asin (sqrt (/ (- 1 x) 2)))
(asin (sqrt 1/2))
(sqrt (PI))
(asin (pow (/ 2 (- 1 x)) -1/2))
(/ 2 (- 1 x))
Outputs
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.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)))) (PI.f64)))
(+.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 (PI.f64) #s(literal -2 binary64)))
(+.f64 (+.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 (PI.f64) #s(literal -2 binary64))) (+.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (PI.f64)))
(+.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (+.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 (PI.f64) #s(literal 2 binary64))))
(+.f64 (-.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)))) (PI.f64)) (/.f64 (PI.f64) #s(literal 2 binary64)))
(+.f64 (/.f64 (PI.f64) #s(literal -2 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 (PI.f64) #s(literal -2 binary64)) (+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (PI.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 (PI.f64) #s(literal -2 binary64)) (-.f64 (+.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (PI.f64)) (*.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 #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 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) #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)))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 (PI.f64) (*.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 #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) #s(literal -2 binary64)) (PI.f64)))
(-.f64 (+.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 (PI.f64) #s(literal -2 binary64))) (+.f64 (*.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 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 #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)))) (PI.f64)) (/.f64 (PI.f64) #s(literal -2 binary64)))
(-.f64 (-.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)))) (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal -2 binary64) (sqrt.f64 (PI.f64)))))
(-.f64 (-.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)))) (PI.f64)) (*.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal -2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(-.f64 (-.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)))) (PI.f64)) (*.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (PI.f64) #s(literal 3/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))))
(-.f64 (-.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)))) (PI.f64)) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal -2 binary64)) (sqrt.f64 (PI.f64))))
(-.f64 (-.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)))) (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 #s(literal -1/2 binary64) (pow.f64 (PI.f64) #s(literal 3/4 binary64)))))
(-.f64 (-.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)))) (PI.f64)) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (PI.f64))))
(-.f64 (-.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)))) (PI.f64)) (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))) (/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))))
(-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.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 0 binary64) (-.f64 (+.f64 (PI.f64) (*.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 (PI.f64) #s(literal 2 binary64))))
(-.f64 (+.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 (PI.f64) #s(literal 2 binary64))) (PI.f64))
(-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 0 binary64)) (+.f64 (PI.f64) (*.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 (PI.f64) #s(literal 2 binary64)) (*.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))) (PI.f64))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (-.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)))) (PI.f64)))
(fma.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 (PI.f64) #s(literal -2 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)) (-.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)))) (PI.f64)))
(fma.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 (PI.f64) #s(literal -2 binary64)))
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (-.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)))) (PI.f64)))
(fma.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (-.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)))) (PI.f64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 2 binary64)) (-.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)))) (PI.f64)))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (-.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)))) (PI.f64)))
(fma.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (-.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)))) (PI.f64)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (-.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)))) (PI.f64)))
(fma.f64 #s(literal -1 binary64) (+.f64 (PI.f64) (*.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 (PI.f64) #s(literal 2 binary64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (-.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)))) (PI.f64)))
(fma.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) #s(literal -1/2 binary64) (-.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)))) (PI.f64)))
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (-.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)))) (PI.f64)))
(fma.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 3/4 binary64)) (-.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)))) (PI.f64)))
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))) (-.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)))) (PI.f64)))
(neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (+.f64 (PI.f64) (*.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) (*.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 (PI.f64) #s(literal -2 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1 binary64)))
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(fma.f64 #s(literal 1 binary64) (/.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)))))
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 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)))))
(fma.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 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)))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #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)))))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.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)))))
(fma.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 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)))))
(fma.f64 #s(literal 1/2 binary64) (PI.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)))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.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)))))
(fma.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) #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)))))
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.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)))))
(fma.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 3/4 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)))))
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.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)))))
(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)))))
(asin.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (log.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))))
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))))
(neg.f64 (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))))
(neg.f64 (/.f64 (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
(/.f64 #s(literal 1 binary64) (exp.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(/.f64 #s(literal -2 binary64) (+.f64 x #s(literal -1 binary64)))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(/.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 x #s(literal 2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(/.f64 (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1/2 binary64))
(/.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (exp.f64 (log.f64 #s(literal -2 binary64))) (exp.f64 (log.f64 (+.f64 x #s(literal -1 binary64)))))
(pow.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 1 binary64) x)) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(*.f64 #s(literal -2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -2 binary64))
(*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))))

simplify272.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
1546×*-lowering-*.f32
1546×*-lowering-*.f64
1500×div-sub
1328×fmsub-define
1304×fnmadd-define
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0601034
11571012
2366981
3836977
42240977
57923977
08640977
Stop Event
1×iter limit
1×node limit
Counts
96 → 96
Calls
Call 1
Inputs
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))) (PI))
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))) (PI))
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))) (PI))
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))) (PI))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(+ (* -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)))))) (* 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)))))) (* 1/2 (PI)))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(acos (* (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)))))
(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)))))
2
(+ 2 (* 2 x))
(+ 2 (* x (+ 2 (* 2 x))))
(+ 2 (* x (+ 2 (* x (+ 2 (* 2 x))))))
(/ -2 x)
(* -1 (/ (+ 2 (* 2 (/ 1 x))) x))
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 2) x)
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 x))) (pow x 2))) (+ 2 (* 2 (/ 1 x)))) x)
(/ -2 x)
(* -1 (/ (+ 2 (* 2 (/ 1 x))) x))
(* -1 (/ (+ 2 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))) x))
(* -1 (/ (+ 2 (* -1 (/ (- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 2) x))) x))
Outputs
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #s(literal -2 binary64)))
(- (PI) (* 2 (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(+.f64 (PI.f64) (*.f64 (acos.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(acos.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))))
(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))))
2
#s(literal 2 binary64)
(+ 2 (* 2 x))
(+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x))
(+ 2 (* x (+ 2 (* 2 x))))
(+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))))
(+ 2 (* x (+ 2 (* x (+ 2 (* 2 x))))))
(*.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x x))))
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(* -1 (/ (+ 2 (* 2 (/ 1 x))) x))
(/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal -2 binary64) x)) x)
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 2) x)
(/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal -2 binary64) x)) x)) x)
(/ (- (* -1 (/ (+ 2 (* 2 (/ 1 x))) (pow x 2))) (+ 2 (* 2 (/ 1 x)))) x)
(*.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) x)) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x))
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(* -1 (/ (+ 2 (* 2 (/ 1 x))) x))
(/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal -2 binary64) x)) x)
(* -1 (/ (+ 2 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal -2 binary64) x)) x)) x)
(* -1 (/ (+ 2 (* -1 (/ (- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 2) x))) x))
(*.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) x)) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x))

eval282.0ms (1.4%)

Compiler

Compiled 34750 to 3836 computations (89% saved)

prune247.0ms (1.2%)

Pruning

19 alts after pruning (15 fresh and 4 done)

PrunedKeptTotal
New166281670
Fresh5712
Picked325
Done022
Total1670191689
Accuracy
9.1%
Counts
1689 → 19
Alt Table
Click to see full alt table
StatusAccuracyProgram
5.9%
(fma.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 4 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
6.0%
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 4/3 binary64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
6.1%
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)) #s(literal 2 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)))) #s(literal -2 binary64)))
✓5.8%
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
▶6.0%
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 2 binary64)) (-.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)))) (PI.f64)))
5.9%
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #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)))
4.0%
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -2 binary64)))
5.9%
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
4.0%
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (*.f64 (asin.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -2 binary64)))
5.9%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (-.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)))) (PI.f64)))
6.1%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 (fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))) #s(literal -2 binary64)))
5.8%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
▶5.9%
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (sqrt.f64 (PI.f64)) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)))
▶5.8%
(fma.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
▶5.4%
(-.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))))
✓4.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
✓5.9%
(-.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))))))
✓4.0%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
▶7.6%
(-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.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)))
Compiler

Compiled 652 to 517 computations (20.7% saved)

simplify177.0ms (0.9%)

Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(sqrt.f64 (PI.f64))
✓cost-diff0
(/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
✓cost-diff0
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64)))
✓cost-diff6272
(fma.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
✓cost-diff64
(acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))
✓cost-diff64
(*.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))))
✓cost-diff64
(-.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)))) (PI.f64))
✓cost-diff6336
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 2 binary64)) (-.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)))) (PI.f64)))
✓cost-diff0
(PI.f64)
✓cost-diff0
(pow.f64 (PI.f64) #s(literal -1/2 binary64))
✓cost-diff0
(/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64)))
✓cost-diff6272
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (sqrt.f64 (PI.f64)) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 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-diff256
(-.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
(pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))
✓cost-diff64
(acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))
✓cost-diff64
(*.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))
✓cost-diff64
(-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.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)))
Rules
2108×fnmadd-define
1992×fnmsub-define
1968×sum5-define
1950×fma-lowering-fma.f32
1950×fma-lowering-fma.f64
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
052311
1102309
2190305
3410305
4890289
51859289
63553287
75140287
86568287
08214287
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(- (/ (PI) -2) (* (acos (pow (+ 1/2 (/ x -2)) 1/2)) -2))
(/ (PI) -2)
(PI)
-2
(* (acos (pow (+ 1/2 (/ x -2)) 1/2)) -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
(- (/ (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
(+ (* (/ 1/2 (pow (PI) -1/2)) (sqrt (PI))) (* (asin (pow (/ 2 (- 1 x)) -1/2)) -2))
(/ 1/2 (pow (PI) -1/2))
1/2
(pow (PI) -1/2)
(PI)
-1/2
(sqrt (PI))
(* (asin (pow (/ 2 (- 1 x)) -1/2)) -2)
(asin (pow (/ 2 (- 1 x)) -1/2))
(pow (/ 2 (- 1 x)) -1/2)
(/ 2 (- 1 x))
2
(- 1 x)
1
x
-2
(+ (* (pow (PI) 1/4) (/ (pow (PI) 3/4) 2)) (- (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) (PI)))
(pow (PI) 1/4)
(PI)
1/4
(/ (pow (PI) 3/4) 2)
(pow (PI) 3/4)
3/4
2
(- (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) (PI))
(* 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
(+ (* (* (/ (sqrt (PI)) 2) (cbrt (PI))) (pow (PI) 1/6)) (* (asin (sqrt (/ (- 1 x) 2))) -2))
(* (/ (sqrt (PI)) 2) (cbrt (PI)))
(/ (sqrt (PI)) 2)
(sqrt (PI))
(PI)
2
(cbrt (PI))
(pow (PI) 1/6)
1/6
(* (asin (sqrt (/ (- 1 x) 2))) -2)
(asin (sqrt (/ (- 1 x) 2)))
(sqrt (/ (- 1 x) 2))
(/ (- 1 x) 2)
(- 1 x)
1
x
-2
Outputs
(- (/ (PI) -2) (* (acos (pow (+ 1/2 (/ x -2)) 1/2)) -2))
(+.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.f64 (acos.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)
(* (acos (pow (+ 1/2 (/ x -2)) 1/2)) -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
(- (/ (PI) 2) (+ (PI) (* (- 0 (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) (* (- 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)
(+ (* (/ 1/2 (pow (PI) -1/2)) (sqrt (PI))) (* (asin (pow (/ 2 (- 1 x)) -1/2)) -2))
(+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (*.f64 #s(literal -2 binary64) (asin.f64 (pow.f64 (/.f64 #s(literal -2 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1/2 binary64)))))
(/ 1/2 (pow (PI) -1/2))
(/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(pow (PI) -1/2)
(pow.f64 (PI.f64) #s(literal -1/2 binary64))
(PI)
(PI.f64)
-1/2
#s(literal -1/2 binary64)
(sqrt (PI))
(sqrt.f64 (PI.f64))
(* (asin (pow (/ 2 (- 1 x)) -1/2)) -2)
(*.f64 #s(literal -2 binary64) (asin.f64 (pow.f64 (/.f64 #s(literal -2 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1/2 binary64))))
(asin (pow (/ 2 (- 1 x)) -1/2))
(asin.f64 (pow.f64 (/.f64 #s(literal -2 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1/2 binary64)))
(pow (/ 2 (- 1 x)) -1/2)
(pow.f64 (/.f64 #s(literal -2 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1/2 binary64))
(/ 2 (- 1 x))
(/.f64 #s(literal -2 binary64) (+.f64 x #s(literal -1 binary64)))
2
#s(literal 2 binary64)
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
-2
#s(literal -2 binary64)
(+ (* (pow (PI) 1/4) (/ (pow (PI) 3/4) 2)) (- (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) (PI)))
(+.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 2 binary64))) (-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)) (PI.f64)))
(pow (PI) 1/4)
(pow.f64 (PI.f64) #s(literal 1/4 binary64))
(PI)
(PI.f64)
1/4
#s(literal 1/4 binary64)
(/ (pow (PI) 3/4) 2)
(/.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 2 binary64))
(pow (PI) 3/4)
(pow.f64 (PI.f64) #s(literal 3/4 binary64))
3/4
#s(literal 3/4 binary64)
2
#s(literal 2 binary64)
(- (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) (PI))
(-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)) (PI.f64))
(* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2)))
(*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #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)
(+ (* (* (/ (sqrt (PI)) 2) (cbrt (PI))) (pow (PI) 1/6)) (* (asin (sqrt (/ (- 1 x) 2))) -2))
(+.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/6 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) (cbrt (PI)))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (cbrt.f64 (PI.f64)) #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)
(cbrt (PI))
(cbrt.f64 (PI.f64))
(pow (PI) 1/6)
(pow.f64 (PI.f64) #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
(* (asin (sqrt (/ (- 1 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 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
-2
#s(literal -2 binary64)

localize3.6s (17.8%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(sqrt.f64 (PI.f64))
✓accuracy100.0%
(cbrt.f64 (PI.f64))
✓accuracy99.8%
(fma.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
✓accuracy4.6%
(PI.f64)
✓accuracy100.0%
(acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))
✓accuracy100.0%
(-.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)))) (PI.f64))
✓accuracy99.8%
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 2 binary64)) (-.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)))) (PI.f64)))
✓accuracy4.6%
(PI.f64)
✓accuracy100.0%
(asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
✓accuracy100.0%
(sqrt.f64 (PI.f64))
✓accuracy99.8%
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (sqrt.f64 (PI.f64)) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)))
✓accuracy4.6%
(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)))
✓accuracy4.6%
(PI.f64)
✓accuracy100.0%
(*.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))
✓accuracy100.0%
(acos.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))
✓accuracy99.8%
(-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.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)))
✓accuracy4.6%
(PI.f64)
Results
3.4s252×5exit
14.0ms4×2valid
Compiler

Compiled 328 to 50 computations (84.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.6s
ival-pow: 1.1s (43.7% of total)
ival-acos: 549.0ms (21% of total)
backward-pass: 301.0ms (11.5% of total)
ival-mult: 104.0ms (4% of total)
ival-div: 100.0ms (3.8% of total)
compiled-spec: 100.0ms (3.8% of total)
ival-sub: 98.0ms (3.8% of total)
ival-asin: 79.0ms (3% of total)
ival-sqrt: 44.0ms (1.7% of total)
ival-add: 38.0ms (1.5% of total)
...c/correct-round.rkt:119:19: 28.0ms (1.1% of total)
ival-cbrt: 13.0ms (0.5% of total)
ival-pi: 11.0ms (0.4% of total)
const: 5.0ms (0.2% of total)

series9.0ms (0%)

Counts
23 → 120
Calls
Call 1
Inputs
#<alt (- (/ (PI) -2) (* (acos (pow (+ 1/2 (/ x -2)) 1/2)) -2))>
#<alt (* (acos (pow (+ 1/2 (/ x -2)) 1/2)) -2)>
#<alt (acos (pow (+ 1/2 (/ x -2)) 1/2))>
#<alt (pow (+ 1/2 (/ x -2)) 1/2)>
#<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 (+ (* (/ 1/2 (pow (PI) -1/2)) (sqrt (PI))) (* (asin (pow (/ 2 (- 1 x)) -1/2)) -2))>
#<alt (/ 1/2 (pow (PI) -1/2))>
#<alt (pow (PI) -1/2)>
#<alt (PI)>
#<alt (+ (* (pow (PI) 1/4) (/ (pow (PI) 3/4) 2)) (- (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) (PI)))>
#<alt (- (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) (PI))>
#<alt (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2)))>
#<alt (+ (* (* (/ (sqrt (PI)) 2) (cbrt (PI))) (pow (PI) 1/6)) (* (asin (sqrt (/ (- 1 x) 2))) -2))>
#<alt (* (/ (sqrt (PI)) 2) (cbrt (PI)))>
#<alt (/ (sqrt (PI)) 2)>
#<alt (sqrt (PI))>
#<alt (acos (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (asin (pow (/ 2 (- 1 x)) -1/2))>
#<alt (cbrt (PI))>
Outputs
#<alt (- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))>
#<alt (- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))>
#<alt (- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))>
#<alt (- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))>
#<alt (- (* -1/2 (PI)) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))>
#<alt (- (* -1/2 (PI)) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))>
#<alt (- (* -1/2 (PI)) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))>
#<alt (- (* -1/2 (PI)) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))>
#<alt (- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))>
#<alt (- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))>
#<alt (- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))>
#<alt (- (* -1/2 (PI)) (* -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 (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 (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 (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))) (PI))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))) (PI))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))) (PI))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))) (PI))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))>
#<alt (- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))>
#<alt (- (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))) (PI))>
#<alt (- (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))) (PI))>
#<alt (- (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))) (PI))>
#<alt (- (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))) (PI))>
#<alt (- (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))) (PI))>
#<alt (- (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))) (PI))>
#<alt (- (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))) (PI))>
#<alt (- (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))) (PI))>
#<alt (- (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))) (PI))>
#<alt (- (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))) (PI))>
#<alt (- (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))) (PI))>
#<alt (- (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))) (PI))>
#<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) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))>
#<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)))))>
Calls

30 calls:

TimeVariablePointExpression
2.0ms
x
@0
(+ (* (* (/ (sqrt (PI)) 2) (cbrt (PI))) (pow (PI) 1/6)) (* (asin (sqrt (/ (- 1 x) 2))) -2))
1.0ms
x
@-inf
(pow (+ 1/2 (/ x -2)) 1/2)
1.0ms
x
@0
(+ (* (pow (PI) 1/4) (/ (pow (PI) 3/4) 2)) (- (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) (PI)))
1.0ms
x
@inf
(pow (+ 1/2 (/ x -2)) 1/2)
1.0ms
x
@0
(- (/ (PI) -2) (* (acos (pow (+ 1/2 (/ x -2)) 1/2)) -2))

rewrite293.0ms (1.5%)

Algorithm
1×batch-egg-rewrite
Rules
2970×*-lowering-*.f32
2970×*-lowering-*.f64
1986×pow-lowering-pow.f64
1986×pow-lowering-pow.f32
1084×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
052170
1188144
2788134
35691134
08085134
Stop Event
1×iter limit
1×node limit
Counts
23 → 855
Calls
Call 1
Inputs
(- (/ (PI) -2) (* (acos (pow (+ 1/2 (/ x -2)) 1/2)) -2))
(* (acos (pow (+ 1/2 (/ x -2)) 1/2)) -2)
(acos (pow (+ 1/2 (/ x -2)) 1/2))
(pow (+ 1/2 (/ x -2)) 1/2)
(- (/ (PI) 2) (+ (PI) (* (- 0 (acos (sqrt 1/2))) 2)))
(+ (PI) (* (- 0 (acos (sqrt 1/2))) 2))
(* (- 0 (acos (sqrt 1/2))) 2)
(/ (PI) 2)
(+ (* (/ 1/2 (pow (PI) -1/2)) (sqrt (PI))) (* (asin (pow (/ 2 (- 1 x)) -1/2)) -2))
(/ 1/2 (pow (PI) -1/2))
(pow (PI) -1/2)
(PI)
(+ (* (pow (PI) 1/4) (/ (pow (PI) 3/4) 2)) (- (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) (PI)))
(- (* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2))) (PI))
(* 2 (acos (pow (+ 1/2 (/ x -2)) 1/2)))
(+ (* (* (/ (sqrt (PI)) 2) (cbrt (PI))) (pow (PI) 1/6)) (* (asin (sqrt (/ (- 1 x) 2))) -2))
(* (/ (sqrt (PI)) 2) (cbrt (PI)))
(/ (sqrt (PI)) 2)
(sqrt (PI))
(acos (sqrt 1/2))
(sqrt 1/2)
(asin (pow (/ 2 (- 1 x)) -1/2))
(cbrt (PI))
Outputs
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)) (PI.f64)))
(+.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 (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 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #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 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)) (PI.f64)) (/.f64 (PI.f64) #s(literal 2 binary64)))
(+.f64 (-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)) (PI.f64)) (+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (PI.f64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.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)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(+.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.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 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)) (+.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 -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))))
(+.f64 (+.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 #s(literal 0 binary64) (PI.f64)) (PI.f64)))
(+.f64 (+.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 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #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 (*.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 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #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 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #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 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #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 (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 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.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 1 binary64))) #s(literal 1 binary64))
(-.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)))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 (PI.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) (+.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (/.f64 (PI.f64) #s(literal -2 binary64))))
(-.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 (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)) (PI.f64)))
(-.f64 (-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)) (PI.f64)) (/.f64 (PI.f64) #s(literal -2 binary64)))
(-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) (PI.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)))))))
(-.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)))))) (+.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 -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)) #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)))))))
(-.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))) #s(literal 0 binary64)) (PI.f64))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (-.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 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))
(fma.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 (PI.f64) #s(literal -2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (-.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 (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)))
(fma.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (-.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 (sqrt.f64 (PI.f64)) (/.f64 #s(literal -1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)) (-.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 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -3/4 binary64))) (-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)) (PI.f64)))
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(/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (fabs.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal -1/4 binary64))) (pow.f64 (PI.f64) #s(literal -1/4 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal -1/3 binary64))) (pow.f64 (PI.f64) #s(literal -1/6 binary64)))
(pow.f64 (PI.f64) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 3/4 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/6 binary64))
(pow.f64 (fabs.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (fabs.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64)))) #s(literal -1 binary64))
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)))))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (log.f64 (exp.f64 (cbrt.f64 (PI.f64)))))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/12 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/12 binary64)) (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/18 binary64)) (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64))))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal -1/4 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal -1/3 binary64))) (pow.f64 (pow.f64 (PI.f64) #s(literal -1/6 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/12 binary64))) (pow.f64 (PI.f64) #s(literal 1/12 binary64)))
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/18 binary64)))
(*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(+.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(+.f64 (acos.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 0 binary64))
(+.f64 (-.f64 #s(literal 0 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64)))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (-.f64 #s(literal 0 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -3/4 binary64))) (-.f64 #s(literal 0 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) (*.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (-.f64 #s(literal 0 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -3/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (sqrt.f64 (PI.f64)) (-.f64 #s(literal 0 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 (cbrt.f64 (PI.f64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 5/6 binary64)) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 5/6 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64)) (-.f64 #s(literal 0 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(neg.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(*.f64 #s(literal 1 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
(pow.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
(+.f64 (/.f64 (PI.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 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (/.f64 (PI.f64) #s(literal 2 binary64)))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.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 (PI.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)) #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)) (/.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 0 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) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (-.f64 #s(literal 0 binary64) (acos.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))) (-.f64 #s(literal 0 binary64) (acos.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)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -3/4 binary64))) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) (*.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (-.f64 #s(literal 0 binary64) (acos.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 -3/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (acos.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)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(fma.f64 (cbrt.f64 (PI.f64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #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)))))))
(fma.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 5/6 binary64)) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 5/6 binary64)) #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)))))))
(fma.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (acos.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)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(fma.f64 (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(neg.f64 (-.f64 #s(literal 0 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(neg.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(neg.f64 (asin.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 #s(literal 2 binary64)))))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(exp.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 2/3 binary64) (log.f64 (PI.f64))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) #s(literal 2/3 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) (log.f64 (PI.f64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (PI.f64))) #s(literal 1/6 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 3 binary64) (log.f64 (PI.f64))) #s(literal 1/9 binary64)))
(fabs.f64 (cbrt.f64 (PI.f64)))
(sqrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(cbrt.f64 (PI.f64))
(pow.f64 (PI.f64) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2/3 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/6 binary64))
(pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/9 binary64))
(*.f64 #s(literal 1 binary64) (cbrt.f64 (PI.f64)))
(*.f64 (cbrt.f64 (PI.f64)) #s(literal 1 binary64))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (pow.f64 (PI.f64) #s(literal 2/9 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 1/3 binary64)))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64))))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))

simplify235.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
4112×*-lowering-*.f32
4112×*-lowering-*.f64
1672×/-lowering-/.f32
1672×/-lowering-/.f64
1658×+-lowering-+.f64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01311396
13611315
210291306
333841298
081371298
Stop Event
1×iter limit
1×node limit
Counts
120 → 120
Calls
Call 1
Inputs
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(- (* -1/2 (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)))))
(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))))))))
(+ (* -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)))))) (* 1/2 (PI)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))) (PI))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))) (PI))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))) (PI))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))) (PI))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(- (+ (* 1/2 (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))))) (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 (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)))))) (* 1/2 (PI)))
(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)))))
Outputs
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))))
(* -2 (acos (sqrt (- 1/2 (* 1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))))
(* -2 (acos (sqrt (+ 1/2 (* -1/2 x)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(acos (sqrt (- 1/2 (* 1/2 x))))
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(acos (sqrt (- 1/2 (* 1/2 x))))
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(acos (sqrt (- 1/2 (* 1/2 x))))
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(acos (sqrt (- 1/2 (* 1/2 x))))
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(acos (sqrt (+ 1/2 (* -1/2 x))))
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/4 (/ x (sqrt 1/2))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 x #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (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 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal -1/4 binary64) (*.f64 x #s(literal -1/16 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 (*.f64 x (*.f64 #s(literal -1/128 binary64) (*.f64 x (/.f64 x (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64)))))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal -1/4 binary64) (*.f64 x #s(literal -1/16 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 #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1/2 binary64))) (+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (/.f64 (*.f64 #s(literal -1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) #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 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1/2 binary64))) (+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (/.f64 (*.f64 #s(literal -1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) #s(literal -1/2 binary64)))) (+.f64 (*.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)))) (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 1/2 binary64)) (*.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 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 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))))
(* -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 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (/.f64 (*.f64 #s(literal -1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) #s(literal 1/2 binary64))))))
(* -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 #s(literal -1/128 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64)))) (+.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (/.f64 (*.f64 #s(literal -1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) #s(literal 1/2 binary64)))))))
(+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))) (PI))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))) (PI))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))) (PI))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))) (PI))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(+.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (PI.f64)))
(- (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))) (PI))
(-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (PI.f64))
(- (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))) (PI))
(-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (PI.f64))
(- (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))) (PI))
(-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (PI.f64))
(- (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))) (PI))
(-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (PI.f64))
(- (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))) (PI))
(-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (PI.f64))
(- (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))) (PI))
(-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (PI.f64))
(- (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))) (PI))
(-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (PI.f64))
(- (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))) (PI))
(-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (PI.f64))
(- (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))) (PI))
(-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (PI.f64))
(- (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))) (PI))
(-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (PI.f64))
(- (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))) (PI))
(-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (PI.f64))
(- (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))) (PI))
(-.f64 (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)) (PI.f64))
(* 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)))))
(*.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)))))
(*.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)))))
(*.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)))))
(*.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)))))
(*.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)))))
(*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64))
(+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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)))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.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))))

eval465.0ms (2.3%)

Compiler

Compiled 52311 to 5589 computations (89.3% saved)

prune299.0ms (1.5%)

Pruning

21 alts after pruning (17 fresh and 4 done)

PrunedKeptTotal
New2230112241
Fresh4610
Picked505
Done044
Total2239212260
Accuracy
9.2%
Counts
2260 → 21
Alt Table
Click to see full alt table
StatusAccuracyProgram
5.9%
(fma.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 4 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
5.9%
(fma.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) (*.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
6.0%
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 4/3 binary64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
✓5.8%
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
6.0%
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal -2 binary64)) (*.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 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -2 binary64) (+.f64 x #s(literal -1 binary64))))))) (PI.f64)))
6.1%
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 2 binary64)) (+.f64 (-.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 1 binary64))) #s(literal 1 binary64)))
4.0%
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -2 binary64)))
5.9%
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 5/6 binary64)) #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)))))))
5.9%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (-.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)))) (PI.f64)))
6.1%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 (fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))) #s(literal -2 binary64)))
5.8%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
5.9%
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)))
4.1%
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (sqrt.f64 (PI.f64)) (-.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (PI.f64)))
5.9%
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/2 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 #s(literal -1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))
✓4.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
✓5.9%
(-.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))))))
✓4.0%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
7.6%
(-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
5.4%
(-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.f64 (acos.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -2 binary64)))
Compiler

Compiled 1145 to 468 computations (59.1% saved)

regimes84.0ms (0.4%)

Counts
43 → 1
Calls
Call 1
Inputs
(-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.f64 (acos.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)))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.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 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(-.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))))
(-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.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)) (*.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)))))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 #s(literal 1/2 binary64))) #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)) (-.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (PI.f64)))
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (*.f64 (asin.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #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))) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #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)) (*.f64 (asin.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 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal -2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #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)) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 5/6 binary64)) #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)))))))
(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 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) (*.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (*.f64 #s(literal -2 binary64) (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)) (sqrt.f64 (PI.f64)) (-.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)))) (PI.f64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #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)))
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))) #s(literal -2 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 2 binary64)) (-.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)))) (PI.f64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))) #s(literal -2 binary64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -2 binary64) (+.f64 x #s(literal -1 binary64))))))) (PI.f64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 2 binary64)) (+.f64 (-.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 1 binary64))) #s(literal 1 binary64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (*.f64 (asin.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (*.f64 (asin.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(fma.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 4 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
(fma.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 4/3 binary64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)) #s(literal 2 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)))) #s(literal -2 binary64)))
(fma.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)))) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) #s(literal -2 binary64)))
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 (fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))) #s(literal -2 binary64)))
Outputs
(-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
Calls

7 calls:

15.0ms
x
13.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
12.0ms
(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
10.0ms
(-.f64 #s(literal 1 binary64) x)
10.0ms
(-.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
AccuracySegmentsBranch
7.6%1x
7.6%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))))))
7.6%1(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
7.6%1(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
7.6%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
7.6%1(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
7.6%1(-.f64 #s(literal 1 binary64) x)
Compiler

Compiled 51 to 41 computations (19.6% saved)

regimes2.0ms (0%)

Accuracy

Total -2.0b remaining (-3.2%)

Threshold costs -2b (-3.2%)

Counts
3 → 1
Calls
Call 1
Inputs
(-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.f64 (acos.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)))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
Outputs
(-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.f64 (acos.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -2 binary64)))
Calls

1 calls:

2.0ms
x
Results
AccuracySegmentsBranch
5.4%1x
Compiler

Compiled 2 to 1 computations (50% saved)

simplify8.0ms (0%)

Algorithm
1×egg-herbie
Rules
16×+-commutative_binary64
14×*-commutative_binary64
14×sub-neg_binary64
10×neg-sub0_binary64
10×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01522
12822
24922
35922
46522
56622
Stop Event
1×saturated
Calls
Call 1
Inputs
(-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.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 (acos.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -2 binary64)))
Outputs
(-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.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 #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 (acos.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) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))))

soundness1.4s (7%)

Rules
4112×*-lowering-*.f32
4112×*-lowering-*.f64
2970×*-lowering-*.f32
2970×*-lowering-*.f64
2738×*-lowering-*.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01139
16038
226738
3148134
0844934
01311396
13611315
210291306
333841298
081371298
052170
1188144
2788134
35691134
08085134
036154
1135137
2580137
33312137
08200137
048163
1179136
2766130
36350123
08701123
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 89 to 65 computations (27% saved)

preprocess31.0ms (0.2%)

Compiler

Compiled 80 to 56 computations (30% saved)

end0.0ms (0%)

Profiling

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