Ian Simplification

Time bar (total: 17.7s)

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 (39.1% of total)
ival-asin: 1.0ms (39.1% of total)
ival-pi: 0.0ms (0% of total)
ival-sub: 0.0ms (0% of total)
ival-mult: 0.0ms (0% of total)
const: 0.0ms (0% of total)
ival-sqrt: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample3.6s (20.5%)

Results
1.8s3268×2valid
1.4s4800×1valid
26.0ms188×0valid
0.0ms5×0invalid
Precisions
Click to see histograms. Total time spent on operations: 2.6s
ival-asin: 1.2s (44.3% of total)
ival-sub: 323.0ms (12.5% of total)
ival-div: 322.0ms (12.4% of total)
ival-sqrt: 228.0ms (8.8% of total)
backward-pass: 228.0ms (8.8% of total)
ival-mult: 174.0ms (6.7% of total)
ival-pi: 138.0ms (5.3% of total)
const: 30.0ms (1.2% of total)
Bogosity

preprocess79.0ms (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))

explain368.0ms (2.1%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2550-1(0.02706781788494566)(-.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
176.0ms318×1valid
127.0ms184×2valid
1.0ms10×0valid
Compiler

Compiled 118 to 35 computations (70.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 158.0ms
ival-asin: 68.0ms (42.9% of total)
backward-pass: 24.0ms (15.1% of total)
ival-div: 19.0ms (12% of total)
ival-sub: 13.0ms (8.2% of total)
ival-sqrt: 12.0ms (7.6% of total)
ival-mult: 12.0ms (7.6% of total)
ival-pi: 8.0ms (5% of total)
const: 2.0ms (1.3% 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
▶7.8%
(-.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)

simplify34.0ms (0.2%)

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

localize151.0ms (0.9%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(PI.f64)
✓accuracy100.0%
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
✓accuracy98.5%
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
✓accuracy9.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
Results
67.0ms159×1valid
61.0ms92×2valid
1.0ms5×0valid
Compiler

Compiled 52 to 12 computations (76.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 75.0ms
ival-asin: 30.0ms (39.9% of total)
backward-pass: 12.0ms (16% of total)
ival-div: 9.0ms (12% of total)
ival-sub: 7.0ms (9.3% of total)
ival-mult: 7.0ms (9.3% of total)
ival-sqrt: 5.0ms (6.6% of total)
ival-pi: 3.0ms (4% of total)
const: 1.0ms (1.3% of total)

series5.0ms (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
1.0ms
x
@inf
(sqrt (/ (- 1 x) 2))
1.0ms
x
@-inf
(sqrt (/ (- 1 x) 2))
1.0ms
x
@0
(- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2)))))
0.0ms
x
@inf
(- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2)))))
0.0ms
x
@0
(sqrt (/ (- 1 x) 2))

rewrite265.0ms (1.5%)

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
3148634
0845834
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 (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 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 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)))))))))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 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))))))))))
(+.f64 #s(literal 0 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64))))
(+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))
(+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 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)))))))))
(+.f64 (+.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))) #s(literal 0 binary64))
(+.f64 (+.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))) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 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))))))))
(+.f64 (+.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))) (+.f64 (+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 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))))))) (+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 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)))))))))
(+.f64 (+.f64 (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 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))))))) (+.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))))
(+.f64 (fma.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)))))) (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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -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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(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64)))))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal 1/9 binary64))))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal 1/6 binary64))))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal 1/6 binary64))))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 5/6 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 4/3 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 7/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/9 binary64)))
(*.f64 (pow.f64 (E.f64) (*.f64 #s(literal 2/3 binary64) (log.f64 (PI.f64)))) (cbrt.f64 (PI.f64)))
(*.f64 (cbrt.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 8/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/9 binary64)))) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/9 binary64)) #s(literal 1/3 binary64)))
(*.f64 (cbrt.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 8/3 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 1/3 binary64)))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 17/6 binary64))) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 1/3 binary64)))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 11/4 binary64))) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 1/3 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 7/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/8 binary64)))
(*.f64 (sqrt.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 5/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/9 binary64)))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/6 binary64)))
(*.f64 (sqrt.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 5/3 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))) (pow.f64 (PI.f64) #s(literal 1/12 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 11/6 binary64))) (pow.f64 (PI.f64) #s(literal 1/12 binary64)))
(*.f64 (fabs.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (fabs.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 7/3 binary64))))
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(*.f64 (neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64)))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(*.f64 (neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(+.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))))
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(fma.f64 #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)) (*.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 (PI.f64) #s(literal 2 binary64)) #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)))))) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))
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(+.f64 #s(literal 0 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
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(-.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 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (asin.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)))
(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 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1 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 #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 (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 (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 #s(literal 1/2 binary64) (/.f64 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 #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 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.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 #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 #s(literal -1 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 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 (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 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 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 (-.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 #s(literal 1/2 binary64) (/.f64 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 #s(literal 1/2 binary64) (/.f64 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 #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 #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)))))))
(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 #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 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)))
(exp.f64 (+.f64 (*.f64 (log.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (*.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (+.f64 (*.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (*.f64 (log.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))
(exp.f64 (-.f64 (*.f64 (log.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(-.f64 #s(literal 0 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 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 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)))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
(neg.f64 (/.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) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))))))
(/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 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 (sqrt.f64 (+.f64 x #s(literal -1 binary64))) (sqrt.f64 #s(literal -2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -2 binary64) (-.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -2 binary64))))
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(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -2 binary64)))))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))
(pow.f64 (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) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))) #s(literal 1 binary64))
(*.f64 (pow.f64 (-.f64 #s(literal 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 (sqrt.f64 (+.f64 x #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 x #s(literal -1 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)) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -2 binary64) (-.f64 #s(literal 1 binary64) x)))))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -2 binary64)))))

simplify232.0ms (1.3%)

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)))))))

eval75.0ms (0.4%)

Compiler

Compiled 8529 to 1180 computations (86.2% saved)

prune55.0ms (0.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New3937400
Fresh000
Picked011
Done000
Total3938401
Accuracy
10.8%
Counts
401 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.6%
(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 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
7.8%
(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 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
▶9.0%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #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))))))))
▶7.8%
(-.f64 (/.f64 (PI.f64) #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)))))
▶7.9%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)))))))
▶6.7%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
✓7.8%
(-.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))))))
▶4.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
Compiler

Compiled 244 to 193 computations (20.9% saved)

simplify203.0ms (1.1%)

Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓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 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 x #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 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
✓cost-diff0
(*.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))))
✓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 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64))))
✓cost-diff0
(PI.f64)
✓cost-diff0
(/.f64 (PI.f64) #s(literal 2 binary64))
✓cost-diff0
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
✓cost-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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
✓cost-diff128
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #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))))))))
Rules
2234×+-lowering-+.f64
2234×+-lowering-+.f32
1802×fnmadd-define
1780×--lowering--.f32
1780×--lowering--.f64
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
036268
181263
2157258
3360254
4604251
51301245
63607244
08501244
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (+ 1/2 (/ x -2)))))))
(/ (PI) 2)
(PI)
2
(* 2 (- (/ (PI) 2) (acos (sqrt (+ 1/2 (/ x -2))))))
(- (/ (PI) 2) (acos (sqrt (+ 1/2 (/ x -2)))))
(acos (sqrt (+ 1/2 (/ x -2))))
(sqrt (+ 1/2 (/ x -2)))
(+ 1/2 (/ x -2))
1/2
(/ x -2)
x
-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 (pow (/ 2 (- 1 x)) -1/2))))
(/ (PI) 2)
(PI)
2
(* 2 (asin (pow (/ 2 (- 1 x)) -1/2)))
(asin (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) (+ 1 (* x -1/2))))))
(/ (PI) 2)
(PI)
2
(* 2 (asin (* (sqrt 1/2) (+ 1 (* x -1/2)))))
(asin (* (sqrt 1/2) (+ 1 (* x -1/2))))
(* (sqrt 1/2) (+ 1 (* x -1/2)))
(sqrt 1/2)
1/2
(+ 1 (* x -1/2))
1
(* x -1/2)
x
-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
Outputs
(- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (+ 1/2 (/ x -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)
(* 2 (- (/ (PI) 2) (acos (sqrt (+ 1/2 (/ x -2))))))
(+.f64 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (PI.f64))
(- (/ (PI) 2) (acos (sqrt (+ 1/2 (/ x -2)))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(acos (sqrt (+ 1/2 (/ x -2))))
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(sqrt (+ 1/2 (/ x -2)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
(+ 1/2 (/ x -2))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))
1/2
#s(literal 1/2 binary64)
(/ x -2)
(/.f64 x #s(literal -2 binary64))
x
-2
#s(literal -2 binary64)
(- (/ (PI) 2) (* 2 (asin (sqrt 1/2))))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) (asin.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)
(* 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 (pow (/ 2 (- 1 x)) -1/2))))
(+.f64 (/.f64 (PI.f64) #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)))))
(/ (PI) 2)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI)
(PI.f64)
2
#s(literal 2 binary64)
(* 2 (asin (pow (/ 2 (- 1 x)) -1/2)))
(*.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)
(- (/ (PI) 2) (* 2 (asin (* (sqrt 1/2) (+ 1 (* x -1/2))))))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 x #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) (+ 1 (* x -1/2)))))
(*.f64 #s(literal 2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 x #s(literal -2 binary64))))))
(asin (* (sqrt 1/2) (+ 1 (* x -1/2))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 x #s(literal -2 binary64)))))
(* (sqrt 1/2) (+ 1 (* x -1/2)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 x #s(literal -2 binary64))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1 (* x -1/2))
(+.f64 #s(literal 1 binary64) (/.f64 x #s(literal -2 binary64)))
1
#s(literal 1 binary64)
(* x -1/2)
(/.f64 x #s(literal -2 binary64))
x
-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 #s(literal -2 binary64) (asin.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)))))))
(/ (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

localize887.0ms (5%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)))
✓accuracy98.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))))
✓accuracy98.5%
(asin.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)))))
✓accuracy9.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)))))))
✓accuracy100.0%
(PI.f64)
✓accuracy100.0%
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64))))
✓accuracy98.5%
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))))
✓accuracy9.0%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
✓accuracy100.0%
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
✓accuracy100.0%
(/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))
✓accuracy98.5%
(asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
✓accuracy9.1%
(-.f64 (/.f64 (PI.f64) #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)))))
✓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%
(PI.f64)
✓accuracy98.4%
(asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
✓accuracy100.0%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
✓accuracy100.0%
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
✓accuracy9.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #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))))))))
Results
801.0ms256×2valid
Compiler

Compiled 278 to 37 computations (86.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 457.0ms
ival-asin: 146.0ms (31.9% of total)
backward-pass: 67.0ms (14.7% of total)
ival-pow: 55.0ms (12% of total)
ival-mult: 54.0ms (11.8% of total)
ival-acos: 43.0ms (9.4% of total)
ival-sub: 30.0ms (6.6% of total)
ival-div: 27.0ms (5.9% of total)
ival-sqrt: 20.0ms (4.4% of total)
ival-add: 8.0ms (1.8% of total)
ival-pi: 5.0ms (1.1% of total)
const: 2.0ms (0.4% of total)

series19.0ms (0.1%)

Counts
25 → 228
Calls
Call 1
Inputs
#<alt (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (+ 1/2 (/ x -2)))))))>
#<alt (* 2 (- (/ (PI) 2) (acos (sqrt (+ 1/2 (/ x -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 (pow (/ 2 (- 1 x)) -1/2))))>
#<alt (* 2 (asin (pow (/ 2 (- 1 x)) -1/2)))>
#<alt (- (/ (PI) 2) (* 2 (asin (* (sqrt 1/2) (+ 1 (* x -1/2))))))>
#<alt (* 2 (asin (* (sqrt 1/2) (+ 1 (* x -1/2)))))>
#<alt (- (/ (PI) 2) (* 2 (asin (/ 1 (sqrt (/ 2 (- 1 x)))))))>
#<alt (* 2 (asin (/ 1 (sqrt (/ 2 (- 1 x))))))>
#<alt (acos (sqrt (+ 1/2 (/ x -2))))>
#<alt (- (/ (PI) 2) (acos (sqrt (+ 1/2 (/ x -2)))))>
#<alt (sqrt (+ 1/2 (/ x -2)))>
#<alt (asin (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (asin (pow (/ 2 (- 1 x)) -1/2))>
#<alt (/ 2 (- 1 x))>
#<alt (pow (/ 2 (- 1 x)) -1/2)>
#<alt (asin (* (sqrt 1/2) (+ 1 (* x -1/2))))>
#<alt (* (sqrt 1/2) (+ 1 (* x -1/2)))>
#<alt (asin (/ 1 (sqrt (/ 2 (- 1 x)))))>
#<alt (/ 1 (sqrt (/ 2 (- 1 x))))>
#<alt (sqrt (/ 2 (- 1 x)))>
Outputs
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x))))))>
#<alt (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 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 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 (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))))>
#<alt (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x)))))>
#<alt (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x)))))>
#<alt (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x)))))>
#<alt (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x)))))>
#<alt (* 2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x)))))>
#<alt (* 2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x)))))>
#<alt (* 2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x)))))>
#<alt (* 2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x)))))>
#<alt (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x)))))>
#<alt (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x)))))>
#<alt (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x)))))>
#<alt (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 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 (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 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x)))))>
#<alt (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x)))))>
#<alt (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x)))))>
#<alt (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x)))))>
#<alt (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))>
#<alt (- (* 1/2 (PI)) (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 (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))>
#<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 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))>
#<alt (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))>
#<alt (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))>
#<alt (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))>
#<alt (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))>
#<alt (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))>
#<alt (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))>
#<alt (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))>
#<alt (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))>
#<alt (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))>
#<alt (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))>
#<alt (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))>
#<alt (* -1/2 (* x (sqrt 1/2)))>
#<alt (* x (+ (* -1/2 (sqrt 1/2)) (/ (sqrt 1/2) x)))>
#<alt (* x (+ (* -1/2 (sqrt 1/2)) (/ (sqrt 1/2) x)))>
#<alt (* x (+ (* -1/2 (sqrt 1/2)) (/ (sqrt 1/2) x)))>
#<alt (* -1/2 (* x (sqrt 1/2)))>
#<alt (* -1 (* x (+ (* -1 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2)))))>
#<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 (/ 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 (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (* x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 3/8 (* x (sqrt 2))) (* 1/2 (sqrt 2)))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (sqrt 2)) (* x (+ (* 5/16 (* x (sqrt 2))) (* 3/8 (sqrt 2)))))))>
#<alt (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2)))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2)))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (* (sqrt 2) (+ 1 (* 1/4 (/ x (pow (sqrt -1) 2))))) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2))))))>
#<alt (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2)))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2)))))>
#<alt (+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (* (sqrt -1) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 x)) (* (sqrt -1) (* (sqrt 2) (+ 1 (* -1/4 x))))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2)))))>
Calls

57 calls:

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

rewrite322.0ms (1.8%)

Algorithm
1×batch-egg-rewrite
Rules
1876×*-lowering-*.f32
1876×*-lowering-*.f64
1608×fnmadd-define
1356×fmsub-define
1320×fmm-def
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
036225
1145167
2553166
32967166
08373166
Stop Event
1×iter limit
1×node limit
Counts
25 → 996
Calls
Call 1
Inputs
(- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (+ 1/2 (/ x -2)))))))
(* 2 (- (/ (PI) 2) (acos (sqrt (+ 1/2 (/ x -2))))))
(/ (PI) 2)
(PI)
(- (/ (PI) 2) (* 2 (asin (sqrt 1/2))))
(* 2 (asin (sqrt 1/2)))
(- (/ (PI) 2) (* 2 (asin (pow (/ 2 (- 1 x)) -1/2))))
(* 2 (asin (pow (/ 2 (- 1 x)) -1/2)))
(- (/ (PI) 2) (* 2 (asin (* (sqrt 1/2) (+ 1 (* x -1/2))))))
(* 2 (asin (* (sqrt 1/2) (+ 1 (* x -1/2)))))
(- (/ (PI) 2) (* 2 (asin (/ 1 (sqrt (/ 2 (- 1 x)))))))
(* 2 (asin (/ 1 (sqrt (/ 2 (- 1 x))))))
(acos (sqrt (+ 1/2 (/ x -2))))
(- (/ (PI) 2) (acos (sqrt (+ 1/2 (/ x -2)))))
(sqrt (+ 1/2 (/ x -2)))
(asin (sqrt 1/2))
(sqrt 1/2)
(asin (pow (/ 2 (- 1 x)) -1/2))
(/ 2 (- 1 x))
(pow (/ 2 (- 1 x)) -1/2)
(asin (* (sqrt 1/2) (+ 1 (* x -1/2))))
(* (sqrt 1/2) (+ 1 (* x -1/2)))
(asin (/ 1 (sqrt (/ 2 (- 1 x)))))
(/ 1 (sqrt (/ 2 (- 1 x))))
(sqrt (/ 2 (- 1 x)))
Outputs
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (+.f64 (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))))
(+.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (+.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 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (/.f64 (PI.f64) #s(literal 2 binary64)))
(+.f64 (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))))
(+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) (+.f64 (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))))
(+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) (+.f64 (+.f64 (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) (+.f64 (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))))
(+.f64 (+.f64 (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))))
(+.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 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (+.f64 (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (*.f64 #s(literal 2 binary64) (asin.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) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(-.f64 (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (/.f64 (PI.f64) #s(literal -2 binary64)))
(-.f64 (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (PI.f64))))
(-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 0 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(-.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal -2 binary64) (acos.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 -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (+.f64 (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))))))
(fma.f64 #s(literal 2 binary64) (asin.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 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 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
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(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 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 #s(literal 1/2 binary64) (/.f64 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 -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 (-.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 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(fma.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.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 (-.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 #s(literal 1/2 binary64) (/.f64 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 #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 #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 2/3 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)))))))
(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 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(neg.f64 (asin.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(neg.f64 (+.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #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)))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal -1/2 binary64))) (log.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)))))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
(neg.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))) #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 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64))) (sqrt.f64 #s(literal -2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 0 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 (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 #s(literal -2 binary64))) (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 (+.f64 x #s(literal -1 binary64)))))
(/.f64 (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 #s(literal -1 binary64))) (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))) #s(literal 1 binary64))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))))
(pow.f64 (exp.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1/2 binary64)) #s(literal -1 binary64)) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -1 binary64))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 (pow.f64 #s(literal -2 binary64) #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))
(*.f64 (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64))))))
(*.f64 (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 #s(literal -2 binary64))) (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))))
(*.f64 (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal -1 binary64))))) (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 #s(literal 2 binary64))))
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)))
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))
(/.f64 (sqrt.f64 #s(literal -2 binary64)) (*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (sqrt.f64 #s(literal -2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))) #s(literal -1 binary64))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)))
(pow.f64 (exp.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -1/2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x))) #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 2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))

simplify311.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
4408×*-lowering-*.f32
4408×*-lowering-*.f64
2990×+-lowering-+.f64
2990×+-lowering-+.f32
1778×/-lowering-/.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02993043
19582862
230542812
371732806
087472806
Stop Event
1×iter limit
1×node limit
Counts
228 → 228
Calls
Call 1
Inputs
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x)))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x)))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x)))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x)))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x))))))
(* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x))))))
(* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x))))))
(* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x))))))
(* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x))))))
(* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x))))))
(* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x))))))
(* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x))))))
(* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x))))))
(* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x))))))
(* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x))))))
(* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 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)))))))
(* 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))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))))
(* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x)))))
(* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x)))))
(* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x)))))
(* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x)))))
(* 2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x)))))
(* 2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x)))))
(* 2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x)))))
(* 2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x)))))
(* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x)))))
(* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x)))))
(* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x)))))
(* 2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 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))))))
(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))))
(- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))
(- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))
(- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))
(- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))
(- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x)))))
(- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x)))))
(- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x)))))
(- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x)))))
(- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))
(- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))
(- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))
(- (* 1/2 (PI)) (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))))))))
(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))
(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))))))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin (* (sqrt 1/2) (- 1 (* 1/2 x))))
(asin (* (sqrt 1/2) (- 1 (* 1/2 x))))
(asin (* (sqrt 1/2) (- 1 (* 1/2 x))))
(asin (* (sqrt 1/2) (- 1 (* 1/2 x))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))
(+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))
(+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))
(* -1/2 (* x (sqrt 1/2)))
(* x (+ (* -1/2 (sqrt 1/2)) (/ (sqrt 1/2) x)))
(* x (+ (* -1/2 (sqrt 1/2)) (/ (sqrt 1/2) x)))
(* x (+ (* -1/2 (sqrt 1/2)) (/ (sqrt 1/2) x)))
(* -1/2 (* x (sqrt 1/2)))
(* -1 (* x (+ (* -1 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2)))))
(* -1 (* x (+ (* -1 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2)))))
(* -1 (* x (+ (* -1 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2)))))
(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)))))
(/ 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))))))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (* x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/8 (* x (sqrt 2))) (* 1/2 (sqrt 2)))))
(+ (sqrt 2) (* x (+ (* 1/2 (sqrt 2)) (* x (+ (* 5/16 (* x (sqrt 2))) (* 3/8 (sqrt 2)))))))
(* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2)))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2)))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (* (sqrt 2) (+ 1 (* 1/4 (/ x (pow (sqrt -1) 2))))) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2))))))
(* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2)))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2)))))
(+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (* (sqrt -1) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 x)) (* (sqrt -1) (* (sqrt 2) (+ 1 (* -1/4 x))))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2)))))
Outputs
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) #s(literal -2 binary64)))
(* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x))))))
(*.f64 #s(literal 2 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x))))))
(*.f64 #s(literal 2 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x))))))
(*.f64 #s(literal 2 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x))))))
(*.f64 #s(literal 2 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x))))))
(*.f64 #s(literal 2 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x))))))
(*.f64 #s(literal 2 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x))))))
(*.f64 #s(literal 2 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(* 2 (- (* 1/2 (PI)) (acos (sqrt (- 1/2 (* 1/2 x))))))
(*.f64 #s(literal 2 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x))))))
(*.f64 #s(literal 2 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(* 2 (- (* 1/2 (PI)) (acos (sqrt (+ 1/2 (* -1/2 x))))))
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(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 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 #s(literal 1/2 binary64) x)))
(+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(* -1/2 (* x (sqrt 1/2)))
(*.f64 #s(literal -1/2 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* x (+ (* -1/2 (sqrt 1/2)) (/ (sqrt 1/2) x)))
(*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(* x (+ (* -1/2 (sqrt 1/2)) (/ (sqrt 1/2) x)))
(*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(* x (+ (* -1/2 (sqrt 1/2)) (/ (sqrt 1/2) x)))
(*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(* -1/2 (* x (sqrt 1/2)))
(*.f64 #s(literal -1/2 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (* -1 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2)))))
(*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(* -1 (* x (+ (* -1 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2)))))
(*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(* -1 (* x (+ (* -1 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2)))))
(*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(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))))
(/ 1 (sqrt 2))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/2 (/ x (sqrt 2))) (/ 1 (sqrt 2)))
(+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal -1/2 binary64) x) (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 x (+.f64 (/.f64 (*.f64 x #s(literal -1/8 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(+ (* x (- (* x (- (* -1/16 (/ x (sqrt 2))) (* 1/8 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))
(+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal -1/2 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 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (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 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #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 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))) (+.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 2 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 x (*.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) 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 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 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 (-.f64 #s(literal 0 binary64) 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 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64))))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (* x (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)))
(+ (sqrt 2) (* x (+ (* 3/8 (* x (sqrt 2))) (* 1/2 (sqrt 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 x (*.f64 x #s(literal 3/8 binary64))) (+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))))
(+ (sqrt 2) (* x (+ (* 1/2 (sqrt 2)) (* x (+ (* 5/16 (* x (sqrt 2))) (* 3/8 (sqrt 2)))))))
(+.f64 (*.f64 x (*.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 3/8 binary64) (*.f64 x #s(literal 5/16 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))))
(* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2))))
(+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2)))))
(+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (* (sqrt 2) (+ 1 (* 1/4 (/ x (pow (sqrt -1) 2))))) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2))))))
(+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (/.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/4 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal -1 binary64))))))
(* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2))))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2)))))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal -1/2 binary64) (+.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))
(+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (* (sqrt -1) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 x)) (* (sqrt -1) (* (sqrt 2) (+ 1 (* -1/4 x))))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 2)))))
(-.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))))) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (sqrt.f64 x) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 x x)))))

eval553.0ms (3.1%)

Compiler

Compiled 40180 to 3815 computations (90.5% saved)

prune243.0ms (1.4%)

Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New194671953
Fresh022
Picked325
Done011
Total1949121961
Accuracy
10.8%
Counts
1961 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.6%
(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 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
6.5%
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))))
7.8%
(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 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
▶4.1%
(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 -2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
▶6.5%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 #s(literal -2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))))
▶9.0%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))))
5.1%
(-.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))))
✓7.8%
(-.f64 (/.f64 (PI.f64) #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)))))
▶6.7%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64)))))
▶4.5%
(-.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))))))
✓7.8%
(-.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))))))
✓4.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
Compiler

Compiled 347 to 278 computations (19.9% saved)

simplify218.0ms (1.2%)

Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))
✓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 (sqrt.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
(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 #s(literal -2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) #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 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) #s(literal -1/2 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 #s(literal 1/2 binary64) (/.f64 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 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))))
Rules
4928×sum4-define
1302×fnmadd-define
1140×*-lowering-*.f32
1140×*-lowering-*.f64
1130×sum3-define
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
042262
194250
2167246
3316246
4589246
51243235
62452233
74341233
86635233
97499233
107766233
117927233
127965233
137973233
09577233
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(- (/ (PI) 2) (- (PI) (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)))
(/ (PI) 2)
(PI)
2
(- (PI) (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))
(* (acos (sqrt (+ 1/2 (/ x -2)))) 2)
(acos (sqrt (+ 1/2 (/ x -2))))
(sqrt (+ 1/2 (/ x -2)))
(+ 1/2 (/ x -2))
1/2
(/ x -2)
x
-2
(- (/ (PI) 2) (* 2 (asin (/ 1 (sqrt 2)))))
(/ (PI) 2)
(PI)
2
(* 2 (asin (/ 1 (sqrt 2))))
(asin (/ 1 (sqrt 2)))
(/ 1 (sqrt 2))
1
(sqrt 2)
(- (/ (PI) 2) (* 2 (asin (pow (+ 2 (* 2 x)) -1/2))))
(/ (PI) 2)
(PI)
2
(* 2 (asin (pow (+ 2 (* 2 x)) -1/2)))
(asin (pow (+ 2 (* 2 x)) -1/2))
(pow (+ 2 (* 2 x)) -1/2)
(+ 2 (* 2 x))
(* 2 x)
x
-1/2
(+ (* (/ (sqrt (PI)) 2) (sqrt (PI))) (* -2 (asin (* (sqrt 1/2) (+ (/ x -2) 1)))))
(/ (sqrt (PI)) 2)
(sqrt (PI))
(PI)
2
(* -2 (asin (* (sqrt 1/2) (+ (/ x -2) 1))))
-2
(asin (* (sqrt 1/2) (+ (/ x -2) 1)))
(* (sqrt 1/2) (+ (/ x -2) 1))
(sqrt 1/2)
1/2
(+ (/ x -2) 1)
(/ x -2)
x
1
(+ (* (pow (PI) 1/4) (* (pow (PI) 1/4) (/ (sqrt (PI)) 2))) (* -2 (asin (sqrt 1/2))))
(pow (PI) 1/4)
(PI)
1/4
(* (pow (PI) 1/4) (/ (sqrt (PI)) 2))
(/ (sqrt (PI)) 2)
(sqrt (PI))
2
(* -2 (asin (sqrt 1/2)))
-2
(asin (sqrt 1/2))
(sqrt 1/2)
1/2
Outputs
(- (/ (PI) 2) (- (PI) (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (/.f64 (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 (+ 1/2 (/ x -2)))) 2))
(+.f64 (PI.f64) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(* (acos (sqrt (+ 1/2 (/ x -2)))) 2)
(*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(acos (sqrt (+ 1/2 (/ x -2))))
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(sqrt (+ 1/2 (/ x -2)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
(+ 1/2 (/ x -2))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))
1/2
#s(literal 1/2 binary64)
(/ x -2)
(/.f64 x #s(literal -2 binary64))
x
-2
#s(literal -2 binary64)
(- (/ (PI) 2) (* 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))
(- (/ (PI) 2) (* 2 (asin (pow (+ 2 (* 2 x)) -1/2))))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64)))))
(/ (PI) 2)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI)
(PI.f64)
2
#s(literal 2 binary64)
(* 2 (asin (pow (+ 2 (* 2 x)) -1/2)))
(*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64))))
(asin (pow (+ 2 (* 2 x)) -1/2))
(asin.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64)))
(pow (+ 2 (* 2 x)) -1/2)
(pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64))
(+ 2 (* 2 x))
(+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
x
-1/2
#s(literal -1/2 binary64)
(+ (* (/ (sqrt (PI)) 2) (sqrt (PI))) (* -2 (asin (* (sqrt 1/2) (+ (/ x -2) 1)))))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 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)
(* -2 (asin (* (sqrt 1/2) (+ (/ x -2) 1))))
(*.f64 #s(literal -2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)))))
-2
#s(literal -2 binary64)
(asin (* (sqrt 1/2) (+ (/ x -2) 1)))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))
(* (sqrt 1/2) (+ (/ x -2) 1))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(+ (/ x -2) 1)
(+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))
(/ x -2)
(/.f64 x #s(literal -2 binary64))
x
1
#s(literal 1 binary64)
(+ (* (pow (PI) 1/4) (* (pow (PI) 1/4) (/ (sqrt (PI)) 2))) (* -2 (asin (sqrt 1/2))))
(+.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))) (*.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) (/ (sqrt (PI)) 2))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(/ (sqrt (PI)) 2)
(/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
(sqrt (PI))
(sqrt.f64 (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))))
-2
#s(literal -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)

localize2.9s (16.2%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(sqrt.f64 (PI.f64))
✓accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
✓accuracy100.0%
(asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))
✓accuracy3.1%
(PI.f64)
✓accuracy100.0%
(sqrt.f64 (PI.f64))
✓accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
✓accuracy100.0%
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))
✓accuracy3.1%
(PI.f64)
✓accuracy100.0%
(*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64))))
✓accuracy100.0%
(*.f64 #s(literal 2 binary64) x)
✓accuracy100.0%
(asin.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64)))
✓accuracy3.1%
(PI.f64)
✓accuracy100.0%
(*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy100.0%
(asin.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
✓accuracy3.1%
(PI.f64)
✓accuracy100.0%
(*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal 2 binary64))
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
✓accuracy100.0%
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
✓accuracy3.1%
(PI.f64)
Results
2.7s256×5exit
Compiler

Compiled 272 to 41 computations (84.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.1s
ival-asin: 707.0ms (33% of total)
ival-pow: 582.0ms (27.1% of total)
backward-pass: 191.0ms (8.9% of total)
ival-acos: 163.0ms (7.6% of total)
ival-mult: 140.0ms (6.5% of total)
ival-div: 130.0ms (6.1% of total)
compiled-spec: 80.0ms (3.7% of total)
ival-sqrt: 61.0ms (2.8% of total)
ival-add: 43.0ms (2% of total)
ival-sub: 33.0ms (1.5% of total)
ival-pi: 11.0ms (0.5% of total)
const: 4.0ms (0.2% of total)

series9.0ms (0%)

Counts
24 → 132
Calls
Call 1
Inputs
#<alt (- (/ (PI) 2) (- (PI) (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)))>
#<alt (/ (PI) 2)>
#<alt (PI)>
#<alt (- (PI) (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))>
#<alt (- (/ (PI) 2) (* 2 (asin (/ 1 (sqrt 2)))))>
#<alt (* 2 (asin (/ 1 (sqrt 2))))>
#<alt (- (/ (PI) 2) (* 2 (asin (pow (+ 2 (* 2 x)) -1/2))))>
#<alt (* 2 (asin (pow (+ 2 (* 2 x)) -1/2)))>
#<alt (+ (* (/ (sqrt (PI)) 2) (sqrt (PI))) (* -2 (asin (* (sqrt 1/2) (+ (/ x -2) 1)))))>
#<alt (/ (sqrt (PI)) 2)>
#<alt (sqrt (PI))>
#<alt (+ (* (pow (PI) 1/4) (* (pow (PI) 1/4) (/ (sqrt (PI)) 2))) (* -2 (asin (sqrt 1/2))))>
#<alt (pow (PI) 1/4)>
#<alt (* (pow (PI) 1/4) (/ (sqrt (PI)) 2))>
#<alt (acos (sqrt (+ 1/2 (/ x -2))))>
#<alt (sqrt (+ 1/2 (/ x -2)))>
#<alt (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)>
#<alt (asin (/ 1 (sqrt 2)))>
#<alt (sqrt 2)>
#<alt (asin (pow (+ 2 (* 2 x)) -1/2))>
#<alt (* 2 x)>
#<alt (asin (* (sqrt 1/2) (+ (/ x -2) 1)))>
#<alt (sqrt 1/2)>
#<alt (asin (sqrt 1/2))>
Outputs
#<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 (- (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))>
#<alt (- (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))>
#<alt (- (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))>
#<alt (- (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))>
#<alt (- (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))>
#<alt (- (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))>
#<alt (- (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))>
#<alt (- (PI) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))>
#<alt (- (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))>
#<alt (- (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))>
#<alt (- (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))>
#<alt (- (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (- 2 (* -2 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (- 2 (* -2 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (- 2 (* -2 x)))))))>
#<alt (- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (- 2 (* -2 x)))))))>
#<alt (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x))))))>
#<alt (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x))))))>
#<alt (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x))))))>
#<alt (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x))))))>
#<alt (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x))))))>
#<alt (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x))))))>
#<alt (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x))))))>
#<alt (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x))))))>
#<alt (* 2 (asin (sqrt (/ 1 (- 2 (* -2 x))))))>
#<alt (* 2 (asin (sqrt (/ 1 (- 2 (* -2 x))))))>
#<alt (* 2 (asin (sqrt (/ 1 (- 2 (* -2 x))))))>
#<alt (* 2 (asin (sqrt (/ 1 (- 2 (* -2 x))))))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))) (* 1/2 (PI)))>
#<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 (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 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))>
#<alt (asin (sqrt (/ 1 (+ 2 (* 2 x)))))>
#<alt (asin (sqrt (/ 1 (+ 2 (* 2 x)))))>
#<alt (asin (sqrt (/ 1 (+ 2 (* 2 x)))))>
#<alt (asin (sqrt (/ 1 (+ 2 (* 2 x)))))>
#<alt (asin (sqrt (/ 1 (+ 2 (* 2 x)))))>
#<alt (asin (sqrt (/ 1 (+ 2 (* 2 x)))))>
#<alt (asin (sqrt (/ 1 (+ 2 (* 2 x)))))>
#<alt (asin (sqrt (/ 1 (- 2 (* -2 x)))))>
#<alt (asin (sqrt (/ 1 (- 2 (* -2 x)))))>
#<alt (asin (sqrt (/ 1 (- 2 (* -2 x)))))>
#<alt (asin (sqrt (/ 1 (- 2 (* -2 x)))))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))>
#<alt (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))>
#<alt (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))>
#<alt (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))>
#<alt (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))>
#<alt (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))>
#<alt (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))>
#<alt (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))>
#<alt (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))>
#<alt (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))>
#<alt (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))>
#<alt (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))>
Calls

33 calls:

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

rewrite350.0ms (2%)

Algorithm
1×batch-egg-rewrite
Rules
2242×*-lowering-*.f32
2242×*-lowering-*.f64
1902×sum4-define
1556×fnmadd-define
1394×pow-lowering-pow.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
042169
1155143
2626140
33156140
08280140
Stop Event
1×iter limit
1×node limit
Counts
24 → 600
Calls
Call 1
Inputs
(- (/ (PI) 2) (- (PI) (* (acos (sqrt (+ 1/2 (/ x -2)))) 2)))
(/ (PI) 2)
(PI)
(- (PI) (* (acos (sqrt (+ 1/2 (/ x -2)))) 2))
(- (/ (PI) 2) (* 2 (asin (/ 1 (sqrt 2)))))
(* 2 (asin (/ 1 (sqrt 2))))
(- (/ (PI) 2) (* 2 (asin (pow (+ 2 (* 2 x)) -1/2))))
(* 2 (asin (pow (+ 2 (* 2 x)) -1/2)))
(+ (* (/ (sqrt (PI)) 2) (sqrt (PI))) (* -2 (asin (* (sqrt 1/2) (+ (/ x -2) 1)))))
(/ (sqrt (PI)) 2)
(sqrt (PI))
(+ (* (pow (PI) 1/4) (* (pow (PI) 1/4) (/ (sqrt (PI)) 2))) (* -2 (asin (sqrt 1/2))))
(pow (PI) 1/4)
(* (pow (PI) 1/4) (/ (sqrt (PI)) 2))
(acos (sqrt (+ 1/2 (/ x -2))))
(sqrt (+ 1/2 (/ x -2)))
(* (acos (sqrt (+ 1/2 (/ x -2)))) 2)
(asin (/ 1 (sqrt 2)))
(sqrt 2)
(asin (pow (+ 2 (* 2 x)) -1/2))
(* 2 x)
(asin (* (sqrt 1/2) (+ (/ x -2) 1)))
(sqrt 1/2)
(asin (sqrt 1/2))
Outputs
(+.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 #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 #s(literal 0 binary64) (PI.f64)) (+.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 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))))
(+.f64 (+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (/.f64 (PI.f64) #s(literal -2 binary64))) (+.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (PI.f64)))
(+.f64 (+.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 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))))
(+.f64 (+.f64 (*.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 (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) #s(literal -1 binary64)) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))))
(+.f64 (+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (/.f64 (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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(-.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 (*.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)) (PI.f64)))
(-.f64 #s(literal 0 binary64) (-.f64 (+.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 (PI.f64) #s(literal 2 binary64))))
(-.f64 (-.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (PI.f64)) (/.f64 (PI.f64) #s(literal -2 binary64)))
(-.f64 (-.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (PI.f64)) (/.f64 #s(literal -1 binary64) (/.f64 #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 (*.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 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))))
(-.f64 (+.f64 (*.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.f64))
(-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 0 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 (-.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))))))) (PI.f64))
(fma.f64 (PI.f64) #s(literal 1/2 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)))
(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 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #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 1 binary64) (/.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)))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.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)))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.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)))))))
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (-.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (PI.f64)))
(fma.f64 #s(literal -1 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 (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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (PI.f64)))
(neg.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)))))))))
(neg.f64 (+.f64 (+.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 (PI.f64) #s(literal -2 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
(-.f64 (/.f64 (+.f64 (PI.f64) #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(neg.f64 (/.f64 (PI.f64) #s(literal -2 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (PI.f64))))
(/.f64 (PI.f64) #s(literal 2 binary64))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (PI.f64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (PI.f64)))
(/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))))
(/.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 3/4 binary64))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) (PI.f64)))
(/.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))) (/.f64 #s(literal -2 binary64) (sqrt.f64 (PI.f64))))
(pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) #s(literal -1 binary64))
(*.f64 (PI.f64) #s(literal 1/2 binary64))
(*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) (PI.f64))
(*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal -1/2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (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 (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 -1 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/2 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))))
(*.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 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (cbrt.f64 (PI.f64))) #s(literal -1/2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) #s(literal -1/2 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal -2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (PI.f64))))
(*.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 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/12 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/8 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/8 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 2 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal -1/2 binary64)))
(*.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 (/.f64 (sqrt.f64 (PI.f64)) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))))
(*.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)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (pow.f64 (PI.f64) #s(literal -1/2 binary64))))
(*.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 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
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(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (-.f64 #s(literal 0 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 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 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 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 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 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 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))))
(fma.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))))
(neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 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 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(+.f64 (-.f64 #s(literal 0 binary64) (acos.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))) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (-.f64 #s(literal 0 binary64) (acos.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) (acos.f64 (sqrt.f64 #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 (sqrt.f64 #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 (sqrt.f64 #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 (sqrt.f64 #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 (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) (acos.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) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))

simplify338.0ms (1.9%)

Algorithm
1×egg-herbie
Rules
4318×*-lowering-*.f32
4318×*-lowering-*.f64
1850×/-lowering-/.f32
1850×/-lowering-/.f64
1478×+-lowering-+.f64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01371456
13841327
210871294
335971286
084661286
Stop Event
1×iter limit
1×node limit
Counts
132 → 132
Calls
Call 1
Inputs
(- (+ (* 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))
(- (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))))))
(- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))))
(- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))))
(- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))))
(- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))))
(- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))))
(- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))))
(- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))))
(- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))))
(- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (- 2 (* -2 x)))))))
(- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (- 2 (* -2 x)))))))
(- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (- 2 (* -2 x)))))))
(- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (- 2 (* -2 x)))))))
(* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x))))))
(* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x))))))
(* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x))))))
(* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x))))))
(* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x))))))
(* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x))))))
(* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x))))))
(* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x))))))
(* 2 (asin (sqrt (/ 1 (- 2 (* -2 x))))))
(* 2 (asin (sqrt (/ 1 (- 2 (* -2 x))))))
(* 2 (asin (sqrt (/ 1 (- 2 (* -2 x))))))
(* 2 (asin (sqrt (/ 1 (- 2 (* -2 x))))))
(+ (* -2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (* (sqrt 1/2) (- 1 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))) (* 1/2 (PI)))
(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 (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)))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin (sqrt (/ 1 (- 2 (* -2 x)))))
(asin (sqrt (/ 1 (- 2 (* -2 x)))))
(asin (sqrt (/ 1 (- 2 (* -2 x)))))
(asin (sqrt (/ 1 (- 2 (* -2 x)))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin (* (sqrt 1/2) (- 1 (* 1/2 x))))
(asin (* (sqrt 1/2) (- 1 (* 1/2 x))))
(asin (* (sqrt 1/2) (- 1 (* 1/2 x))))
(asin (* (sqrt 1/2) (- 1 (* 1/2 x))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
Outputs
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (- 1/2 (* 1/2 x)))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (+ (* 1/2 (PI)) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x)))))) (PI))
(+.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))) (*.f64 (PI.f64) #s(literal -1/2 binary64)))
(- (PI) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (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) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (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) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (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) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (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) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+.f64 (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) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+.f64 (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) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+.f64 (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) (* 2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+.f64 (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) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (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) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (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) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (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) (* 2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal -2 binary64)))
(- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)))))))
(- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)))))))
(- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)))))))
(- (* 1/2 (PI)) (* 2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))))
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(asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)))))
(asin (sqrt (/ 1 (- 2 (* -2 x)))))
(asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)))))
(asin (sqrt (/ 1 (- 2 (* -2 x)))))
(asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)))))
(asin (sqrt (/ 1 (- 2 (* -2 x)))))
(asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)))))
(asin (sqrt (/ 1 (- 2 (* -2 x)))))
(asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)))))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))
(asin (* (sqrt 1/2) (- 1 (* 1/2 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))
(asin (* (sqrt 1/2) (- 1 (* 1/2 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))
(asin (* (sqrt 1/2) (- 1 (* 1/2 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))
(asin (* (sqrt 1/2) (- 1 (* 1/2 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))
(asin (* (sqrt 1/2) (+ 1 (* -1/2 x))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))

eval398.0ms (2.2%)

Compiler

Compiled 35751 to 3555 computations (90.1% saved)

prune222.0ms (1.3%)

Pruning

20 alts after pruning (16 fresh and 4 done)

PrunedKeptTotal
New1720141734
Fresh224
Picked415
Done033
Total1726201746
Accuracy
11.0%
Counts
1746 → 20
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.7%
(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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (PI.f64)))
▶7.6%
(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 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
6.5%
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64)))))
7.8%
(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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (PI.f64)))
▶6.6%
(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 -2 binary64) (asin.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64)))))
4.1%
(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 #s(literal -2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
▶7.8%
(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 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
7.7%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (-.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (PI.f64)))
6.9%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.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 #s(literal 0 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))))))
6.7%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 #s(literal -2 binary64) (fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (-.f64 #s(literal 0 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))))))
6.5%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 #s(literal -2 binary64) (asin.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64)))))
6.7%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (*.f64 #s(literal -2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))))
6.7%
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (sqrt.f64 (PI.f64)) (*.f64 #s(literal -2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))))
7.7%
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.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)))))))
▶5.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 2 binary64))))
✓7.8%
(-.f64 (/.f64 (PI.f64) #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)))))
✓4.5%
(-.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))))))
✓7.8%
(-.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))))))
✓4.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
▶9.0%
(-.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)))))))
Compiler

Compiled 677 to 530 computations (21.7% saved)

simplify165.0ms (0.9%)

Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓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 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
✓cost-diff0
(/.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 2 binary64))
✓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 3/4 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) #s(literal -1/2 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 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
✓cost-diff0
(-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 2 binary64)))
✓cost-diff0
(PI.f64)
✓cost-diff0
(/.f64 (PI.f64) #s(literal 2 binary64))
✓cost-diff128
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 2 binary64))))
✓cost-diff0
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 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) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
Rules
1632×sum3-define
1510×fnmadd-define
1268×fmsub-define
1266×fnmsub-define
1264×sum5-define
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0448589934860
1828589934852
21398589934849
32438589934849
44538589934849
59978589934849
617728589934847
725698589934847
836258589934847
969458589934847
1079808589934847
08052277
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(- (/ (PI) -2) (* -2 (acos (sqrt (+ 1/2 (/ x -2))))))
(/ (PI) -2)
(PI)
-2
(* -2 (acos (sqrt (+ 1/2 (/ x -2)))))
(acos (sqrt (+ 1/2 (/ x -2))))
(sqrt (+ 1/2 (/ x -2)))
(+ 1/2 (/ x -2))
1/2
(/ x -2)
x
(- (/ (PI) 2) (- (PI) (* (acos (sqrt 1/2)) 2)))
(/ (PI) 2)
(PI)
2
(- (PI) (* (acos (sqrt 1/2)) 2))
(* (acos (sqrt 1/2)) 2)
(acos (sqrt 1/2))
(sqrt 1/2)
1/2
(+ (* (pow (PI) 2/3) (/ (cbrt (PI)) 2)) (* (asin (sqrt (+ 1/2 (/ x -2)))) -2))
(pow (PI) 2/3)
(PI)
2/3
(/ (cbrt (PI)) 2)
(cbrt (PI))
2
(* (asin (sqrt (+ 1/2 (/ x -2)))) -2)
(asin (sqrt (+ 1/2 (/ x -2))))
(sqrt (+ 1/2 (/ x -2)))
(+ 1/2 (/ x -2))
1/2
(/ x -2)
x
-2
(+ (* (pow (PI) 1/4) (/ (pow (PI) 3/4) 2)) (* -2 (asin (pow (+ 2 (* 2 x)) -1/2))))
(pow (PI) 1/4)
(PI)
1/4
(/ (pow (PI) 3/4) 2)
(pow (PI) 3/4)
3/4
2
(* -2 (asin (pow (+ 2 (* 2 x)) -1/2)))
-2
(asin (pow (+ 2 (* 2 x)) -1/2))
(pow (+ 2 (* 2 x)) -1/2)
(+ 2 (* 2 x))
(* 2 x)
x
-1/2
(+ (* (pow (PI) 1/4) (/ (pow (PI) 1/4) (/ 2 (sqrt (PI))))) (* (asin (sqrt (+ 1/2 (/ x -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 (/ x -2)))) -2)
(asin (sqrt (+ 1/2 (/ x -2))))
(sqrt (+ 1/2 (/ x -2)))
(+ 1/2 (/ x -2))
1/2
(/ x -2)
x
-2
Outputs
(- (/ (PI) -2) (* -2 (acos (sqrt (+ 1/2 (/ x -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)
(* -2 (acos (sqrt (+ 1/2 (/ x -2)))))
(*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(acos (sqrt (+ 1/2 (/ x -2))))
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(sqrt (+ 1/2 (/ x -2)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
(+ 1/2 (/ x -2))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))
1/2
#s(literal 1/2 binary64)
(/ x -2)
(/.f64 x #s(literal -2 binary64))
x
(- (/ (PI) 2) (- (PI) (* (acos (sqrt 1/2)) 2)))
(+.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(/ (PI) 2)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI)
(PI.f64)
2
#s(literal 2 binary64)
(- (PI) (* (acos (sqrt 1/2)) 2))
(+.f64 (PI.f64) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(* (acos (sqrt 1/2)) 2)
(*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(acos (sqrt 1/2))
(acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(+ (* (pow (PI) 2/3) (/ (cbrt (PI)) 2)) (* (asin (sqrt (+ 1/2 (/ x -2)))) -2))
(+.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(pow (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 (+ 1/2 (/ x -2)))) -2)
(*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(asin (sqrt (+ 1/2 (/ x -2))))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(sqrt (+ 1/2 (/ x -2)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
(+ 1/2 (/ x -2))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))
1/2
#s(literal 1/2 binary64)
(/ x -2)
(/.f64 x #s(literal -2 binary64))
x
-2
#s(literal -2 binary64)
(+ (* (pow (PI) 1/4) (/ (pow (PI) 3/4) 2)) (* -2 (asin (pow (+ 2 (* 2 x)) -1/2))))
(+.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 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)))))
(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 (asin (pow (+ 2 (* 2 x)) -1/2)))
(*.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))))
-2
#s(literal -2 binary64)
(asin (pow (+ 2 (* 2 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 (* 2 x)) -1/2)
(pow.f64 (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal -1/2 binary64))
(+ 2 (* 2 x))
(*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
x
-1/2
#s(literal -1/2 binary64)
(+ (* (pow (PI) 1/4) (/ (pow (PI) 1/4) (/ 2 (sqrt (PI))))) (* (asin (sqrt (+ 1/2 (/ x -2)))) -2))
(+.f64 (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (/.f64 (*.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)))))
(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 (/ x -2)))) -2)
(*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(asin (sqrt (+ 1/2 (/ x -2))))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(sqrt (+ 1/2 (/ x -2)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
(+ 1/2 (/ x -2))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))
1/2
#s(literal 1/2 binary64)
(/ x -2)
(/.f64 x #s(literal -2 binary64))
x
-2
#s(literal -2 binary64)

localize2.4s (13.6%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
✓accuracy100.0%
(sqrt.f64 (PI.f64))
✓accuracy99.7%
(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 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
✓accuracy5.4%
(PI.f64)
✓accuracy100.0%
(pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64))
✓accuracy100.0%
(asin.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) #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 3/4 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64)))))
✓accuracy5.4%
(PI.f64)
✓accuracy100.0%
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
✓accuracy100.0%
(cbrt.f64 (PI.f64))
✓accuracy99.7%
(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 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
✓accuracy5.4%
(PI.f64)
✓accuracy100.0%
(*.f64 (acos.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 2 binary64))
✓accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
✓accuracy100.0%
(acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))
✓accuracy5.4%
(PI.f64)
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))
✓accuracy100.0%
(acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
✓accuracy99.7%
(-.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)))))))
✓accuracy5.4%
(PI.f64)
Results
2.2s250×5exit
15.0ms6×2valid
Compiler

Compiled 292 to 42 computations (85.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.7s
ival-pow: 545.0ms (31.5% of total)
ival-acos: 523.0ms (30.2% of total)
backward-pass: 223.0ms (12.9% of total)
compiled-spec: 93.0ms (5.4% of total)
ival-div: 84.0ms (4.9% of total)
ival-mult: 82.0ms (4.7% of total)
ival-sqrt: 42.0ms (2.4% of total)
ival-asin: 41.0ms (2.4% of total)
ival-add: 33.0ms (1.9% of total)
ival-sub: 26.0ms (1.5% of total)
ival-cbrt: 14.0ms (0.8% of total)
ival-pi: 11.0ms (0.6% of total)
...c/correct-round.rkt:119:19: 11.0ms (0.6% of total)
const: 4.0ms (0.2% of total)

series8.0ms (0%)

Counts
25 → 120
Calls
Call 1
Inputs
#<alt (- (/ (PI) -2) (* -2 (acos (sqrt (+ 1/2 (/ x -2))))))>
#<alt (/ (PI) -2)>
#<alt (PI)>
#<alt (* -2 (acos (sqrt (+ 1/2 (/ x -2)))))>
#<alt (- (/ (PI) 2) (- (PI) (* (acos (sqrt 1/2)) 2)))>
#<alt (/ (PI) 2)>
#<alt (- (PI) (* (acos (sqrt 1/2)) 2))>
#<alt (+ (* (pow (PI) 2/3) (/ (cbrt (PI)) 2)) (* (asin (sqrt (+ 1/2 (/ x -2)))) -2))>
#<alt (pow (PI) 2/3)>
#<alt (/ (cbrt (PI)) 2)>
#<alt (+ (* (pow (PI) 1/4) (/ (pow (PI) 3/4) 2)) (* -2 (asin (pow (+ 2 (* 2 x)) -1/2))))>
#<alt (pow (PI) 1/4)>
#<alt (/ (pow (PI) 3/4) 2)>
#<alt (+ (* (pow (PI) 1/4) (/ (pow (PI) 1/4) (/ 2 (sqrt (PI))))) (* (asin (sqrt (+ 1/2 (/ x -2)))) -2))>
#<alt (/ (pow (PI) 1/4) (/ 2 (sqrt (PI))))>
#<alt (acos (sqrt (+ 1/2 (/ x -2))))>
#<alt (sqrt (+ 1/2 (/ x -2)))>
#<alt (acos (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (* (acos (sqrt 1/2)) 2)>
#<alt (cbrt (PI))>
#<alt (asin (sqrt (+ 1/2 (/ x -2))))>
#<alt (asin (pow (+ 2 (* 2 x)) -1/2))>
#<alt (pow (+ 2 (* 2 x)) -1/2)>
#<alt (sqrt (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 (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (/ 1 (- 2 (* -2 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (/ 1 (- 2 (* -2 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (/ 1 (- 2 (* -2 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (/ 1 (- 2 (* -2 x)))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))>
#<alt (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 (asin (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (asin (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (asin (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (asin (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (asin (sqrt (- 1/2 (* 1/2 x))))>
#<alt (asin (sqrt (- 1/2 (* 1/2 x))))>
#<alt (asin (sqrt (- 1/2 (* 1/2 x))))>
#<alt (asin (sqrt (- 1/2 (* 1/2 x))))>
#<alt (asin (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (asin (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (asin (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (asin (sqrt (+ 1/2 (* -1/2 x))))>
#<alt (asin (sqrt (/ 1 (+ 2 (* 2 x)))))>
#<alt (asin (sqrt (/ 1 (+ 2 (* 2 x)))))>
#<alt (asin (sqrt (/ 1 (+ 2 (* 2 x)))))>
#<alt (asin (sqrt (/ 1 (+ 2 (* 2 x)))))>
#<alt (asin (sqrt (/ 1 (+ 2 (* 2 x)))))>
#<alt (asin (sqrt (/ 1 (+ 2 (* 2 x)))))>
#<alt (asin (sqrt (/ 1 (+ 2 (* 2 x)))))>
#<alt (asin (sqrt (/ 1 (+ 2 (* 2 x)))))>
#<alt (asin (sqrt (/ 1 (- 2 (* -2 x)))))>
#<alt (asin (sqrt (/ 1 (- 2 (* -2 x)))))>
#<alt (asin (sqrt (/ 1 (- 2 (* -2 x)))))>
#<alt (asin (sqrt (/ 1 (- 2 (* -2 x)))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/4 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* 1/2 (/ (* x (- 1/2 (* 1/16 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (+ (* -1/2 (/ (* x (+ 1/2 (* -1/4 (/ (- 1/2 (* 1/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 1/2 (* 1/16 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 1/4 (/ 1 (sqrt 1/2))))))>
#<alt (* (sqrt (/ 1 x)) (sqrt 1/2))>
#<alt (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/2)))) (* (sqrt (/ 1 x)) (sqrt 1/2)))>
#<alt (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/2)))) (* (sqrt (/ 1 x)) (sqrt 1/2))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 1/2 (* 1/16 (/ x (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/2)))) (* (sqrt (/ 1 x)) (sqrt 1/2)))))>
#<alt (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/2)))>
#<alt (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/2))))>
#<alt (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/2)))))>
#<alt (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (sqrt -1) (sqrt -1/2)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (+ 1/2 (* -1/16 (/ x (pow (sqrt -1/2) 2))))) (sqrt -1/2))))) (pow x 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/2)))))>
Calls

30 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(pow (+ 2 (* 2 x)) -1/2)
1.0ms
x
@0
(+ (* (pow (PI) 1/4) (/ (pow (PI) 3/4) 2)) (* -2 (asin (pow (+ 2 (* 2 x)) -1/2))))
1.0ms
x
@-inf
(pow (+ 2 (* 2 x)) -1/2)
0.0ms
x
@0
(- (/ (PI) -2) (* -2 (acos (sqrt (+ 1/2 (/ x -2))))))
0.0ms
x
@0
(pow (+ 2 (* 2 x)) -1/2)

rewrite452.0ms (2.6%)

Algorithm
1×batch-egg-rewrite
Rules
2540×*-lowering-*.f32
2540×*-lowering-*.f64
1174×prod-diff
1154×sum3-define
998×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
044175
1159141
2682138
36663138
08017138
Stop Event
1×iter limit
1×node limit
Counts
25 → 826
Calls
Call 1
Inputs
(- (/ (PI) -2) (* -2 (acos (sqrt (+ 1/2 (/ x -2))))))
(/ (PI) -2)
(PI)
(* -2 (acos (sqrt (+ 1/2 (/ x -2)))))
(- (/ (PI) 2) (- (PI) (* (acos (sqrt 1/2)) 2)))
(/ (PI) 2)
(- (PI) (* (acos (sqrt 1/2)) 2))
(+ (* (pow (PI) 2/3) (/ (cbrt (PI)) 2)) (* (asin (sqrt (+ 1/2 (/ x -2)))) -2))
(pow (PI) 2/3)
(/ (cbrt (PI)) 2)
(+ (* (pow (PI) 1/4) (/ (pow (PI) 3/4) 2)) (* -2 (asin (pow (+ 2 (* 2 x)) -1/2))))
(pow (PI) 1/4)
(/ (pow (PI) 3/4) 2)
(+ (* (pow (PI) 1/4) (/ (pow (PI) 1/4) (/ 2 (sqrt (PI))))) (* (asin (sqrt (+ 1/2 (/ x -2)))) -2))
(/ (pow (PI) 1/4) (/ 2 (sqrt (PI))))
(acos (sqrt (+ 1/2 (/ x -2))))
(sqrt (+ 1/2 (/ x -2)))
(acos (sqrt 1/2))
(sqrt 1/2)
(* (acos (sqrt 1/2)) 2)
(cbrt (PI))
(asin (sqrt (+ 1/2 (/ x -2))))
(asin (pow (+ 2 (* 2 x)) -1/2))
(pow (+ 2 (* 2 x)) -1/2)
(sqrt (PI))
Outputs
(+.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 (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 (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))))))))
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(-.f64 (+.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))
(-.f64 (-.f64 (/.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))))))
(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 (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 #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 -1/3 binary64))) (pow.f64 (PI.f64) #s(literal 2/3 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 (pow.f64 (PI.f64) #s(literal 3/4 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 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/4 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 (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 (/.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 (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 2/3 binary64)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/3 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 (/.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 (/.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 (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))) (-.f64 #s(literal 0 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)))))))
(neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 2 binary64))) #s(literal -1/2 binary64)))))
(+.f64 (-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 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) (asin.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 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 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 2 binary64) (*.f64 x #s(literal 2 binary64))) #s(literal -1/2 binary64)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/3 binary64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 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 2 binary64) (*.f64 x #s(literal 2 binary64))) #s(literal -1/2 binary64)))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 2 binary64))) #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) (acos.f64 (pow.f64 (+.f64 #s(literal 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 2 binary64) (*.f64 x #s(literal 2 binary64))) #s(literal -1/2 binary64)))))
(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 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 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/3 binary64))) (-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 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 2 binary64) (*.f64 x #s(literal 2 binary64))) #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) (acos.f64 (pow.f64 (+.f64 #s(literal 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 2 binary64) (*.f64 x #s(literal 2 binary64))) #s(literal -1/2 binary64)))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))) (-.f64 #s(literal 0 binary64) (acos.f64 (pow.f64 (+.f64 #s(literal 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 2 binary64) (*.f64 x #s(literal 2 binary64))) #s(literal -1/2 binary64)))))
(asin.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 2 binary64))))))
(pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 2 binary64))) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 (+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 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)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))))
(exp.f64 (*.f64 (*.f64 #s(literal 2/3 binary64) (log.f64 (PI.f64))) #s(literal 3/4 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (PI.f64))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 (PI.f64))) #s(literal 2 binary64)))
(fabs.f64 (sqrt.f64 (PI.f64)))
(fabs.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))))
(sqrt.f64 (PI.f64))
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))))
(/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))) #s(literal -1 binary64))
(pow.f64 (PI.f64) #s(literal 1/2 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1 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))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 1 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/12 binary64)) #s(literal 2 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/12 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/8 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/8 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/8 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/8 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 4/9 binary64)) #s(literal 3/4 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64)) #s(literal 3/4 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (PI.f64) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/3 binary64)) #s(literal 1/4 binary64)) (pow.f64 (PI.f64) #s(literal 1/12 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 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (PI.f64) #s(literal 1/8 binary64))) (pow.f64 (PI.f64) #s(literal 1/8 binary64)))
(*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) (pow.f64 (PI.f64) #s(literal 1/12 binary64)))

simplify328.0ms (1.9%)

Algorithm
1×egg-herbie
Rules
4474×*-lowering-*.f32
4474×*-lowering-*.f64
1730×fma-lowering-fma.f32
1730×fma-lowering-fma.f64
1428×fma-define
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01941544
15621387
217371368
351111364
081121364
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)))))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (/ 1 (- 2 (* -2 x)))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (/ 1 (- 2 (* -2 x)))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (/ 1 (- 2 (* -2 x)))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (/ 1 (- 2 (* -2 x)))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(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))))))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin (sqrt (- 1/2 (* 1/2 x))))
(asin (sqrt (- 1/2 (* 1/2 x))))
(asin (sqrt (- 1/2 (* 1/2 x))))
(asin (sqrt (- 1/2 (* 1/2 x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin (sqrt (/ 1 (- 2 (* -2 x)))))
(asin (sqrt (/ 1 (- 2 (* -2 x)))))
(asin (sqrt (/ 1 (- 2 (* -2 x)))))
(asin (sqrt (/ 1 (- 2 (* -2 x)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/4 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* 1/2 (/ (* x (- 1/2 (* 1/16 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (+ (* -1/2 (/ (* x (+ 1/2 (* -1/4 (/ (- 1/2 (* 1/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 1/2 (* 1/16 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 1/4 (/ 1 (sqrt 1/2))))))
(* (sqrt (/ 1 x)) (sqrt 1/2))
(+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/2)))) (* (sqrt (/ 1 x)) (sqrt 1/2)))
(+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/2)))) (* (sqrt (/ 1 x)) (sqrt 1/2))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 1/2 (* 1/16 (/ x (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/2)))) (* (sqrt (/ 1 x)) (sqrt 1/2)))))
(* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/2)))
(+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/2))))
(+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/2)))))
(+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (sqrt -1) (sqrt -1/2)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (+ 1/2 (* -1/16 (/ x (pow (sqrt -1/2) 2))))) (sqrt -1/2))))) (pow x 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/2)))))
Outputs
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (- 1/2 (* 1/2 x))))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)) (*.f64 (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64)))
(- (* -1/2 (PI)) (* -2 (acos (sqrt (+ 1/2 (* -1/2 x))))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)) (*.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 #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)))))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))))
(+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))))
(+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))))
(+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))))
(+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))))
(+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))))
(+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))))
(+ (* -2 (asin (sqrt (/ 1 (+ 2 (* 2 x)))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))))
(+ (* -2 (asin (sqrt (/ 1 (- 2 (* -2 x)))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))))
(+ (* -2 (asin (sqrt (/ 1 (- 2 (* -2 x)))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))))
(+ (* -2 (asin (sqrt (/ 1 (- 2 (* -2 x)))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))))
(+ (* -2 (asin (sqrt (/ 1 (- 2 (* -2 x)))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (- 1/2 (* 1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))))
(+ (* -2 (asin (sqrt (+ 1/2 (* -1/2 x))))) (* 1/2 (PI)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (asin.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 x (/.f64 #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 x (+.f64 (*.f64 x (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(+ (sqrt 1/2) (* x (- (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 5))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/4 (/ 1 (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (*.f64 x (+.f64 (/.f64 (*.f64 x #s(literal -1/128 binary64)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(* (sqrt x) (sqrt -1/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1/2 binary64)))
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2))))
(*.f64 x (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1/2 binary64)))) (*.f64 (sqrt.f64 #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2)))))
(*.f64 x (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1/2 binary64)))) (+.f64 (*.f64 (sqrt.f64 #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal -1/2 binary64)))))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/2) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/2) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 x)) (sqrt -1/2))))))
(*.f64 x (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1/2 binary64)))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/128 binary64) (pow.f64 (sqrt.f64 #s(literal -1/2 binary64)) #s(literal 5 binary64)))) (+.f64 (*.f64 (sqrt.f64 #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal -1/2 binary64))))))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(* -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 #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 (*.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 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #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 1/16 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (*.f64 #s(literal 1/128 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))))))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(asin (sqrt (- 1/2 (* 1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(asin (sqrt (- 1/2 (* 1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(asin (sqrt (- 1/2 (* 1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(asin (sqrt (- 1/2 (* 1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(asin (sqrt (+ 1/2 (* -1/2 x))))
(asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))
(asin (sqrt (/ 1 (+ 2 (* 2 x)))))
(asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))
(asin (sqrt (/ 1 (- 2 (* -2 x)))))
(asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))
(asin (sqrt (/ 1 (- 2 (* -2 x)))))
(asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))
(asin (sqrt (/ 1 (- 2 (* -2 x)))))
(asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))
(asin (sqrt (/ 1 (- 2 (* -2 x)))))
(asin.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (+.f64 x #s(literal 1 binary64))))))
(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 x (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (sqrt 1/2) (* x (- (* 1/2 (/ (* x (- 1/2 (* 1/16 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))))
(+ (sqrt 1/2) (* x (- (* x (+ (* -1/2 (/ (* x (+ 1/2 (* -1/4 (/ (- 1/2 (* 1/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 1/2 (* 1/16 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 1/4 (/ 1 (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 #s(literal -5/32 binary64) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(* (sqrt (/ 1 x)) (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/2)))) (* (sqrt (/ 1 x)) (sqrt 1/2)))
(+.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/2)))) (* (sqrt (/ 1 x)) (sqrt 1/2))))
(+.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 1/2 (* 1/16 (/ x (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/2)))) (* (sqrt (/ 1 x)) (sqrt 1/2)))))
(+.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (sqrt.f64 #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/2)))
(*.f64 (sqrt.f64 #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))
(+ (* -1/4 (* (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 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))) (*.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))))))
(+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 5))) (/ (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 (/.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) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))))
(+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (sqrt -1) (sqrt -1/2)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (+ 1/2 (* -1/16 (/ x (pow (sqrt -1/2) 2))))) (sqrt -1/2))))) (pow x 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/2)))))
(+.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 (*.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 (*.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/2 binary64))))) (*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (sqrt.f64 #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (*.f64 x (*.f64 x x)))))

eval353.0ms (2%)

Compiler

Compiled 37384 to 3992 computations (89.3% saved)

prune520.0ms (2.9%)

Pruning

26 alts after pruning (20 fresh and 6 done)

PrunedKeptTotal
New1703121715
Fresh3811
Picked325
Done044
Total1709261735
Accuracy
11.2%
Counts
1735 → 26
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.6%
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3/4 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 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
7.8%
(fma.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/4 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)))))))
7.8%
(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 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
7.7%
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 1/4 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)))
7.7%
(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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (PI.f64)))
7.8%
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) #s(literal -2 binary64)))
✓7.6%
(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 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
6.5%
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) (asin.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64)))))
7.7%
(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)))
7.8%
(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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (PI.f64)))
4.1%
(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 #s(literal -2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
7.7%
(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 (fma.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/4 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))))))) #s(literal -2 binary64)))
7.7%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (-.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (PI.f64)))
6.9%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.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 #s(literal 0 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))))))
6.7%
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (*.f64 #s(literal -2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))))
4.5%
(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)))
7.8%
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (sqrt.f64 (PI.f64)) (*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
7.8%
(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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
7.7%
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.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)))))))
7.9%
(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)))
✓7.8%
(-.f64 (/.f64 (PI.f64) #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)))))
✓4.5%
(-.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))))))
✓7.8%
(-.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))))))
✓4.1%
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
✓9.0%
(-.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)))))))
5.1%
(-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
Compiler

Compiled 1224 to 553 computations (54.8% saved)

regimes76.0ms (0.4%)

Counts
41 → 1
Calls
Call 1
Inputs
(-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 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 (PI.f64) (*.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 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.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 #s(literal 2 binary64) (asin.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 x #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 (/.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 #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) (-.f64 (/.f64 (PI.f64) #s(literal 2 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 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal -2 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 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (PI.f64)))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.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)))))))
(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 #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 #s(literal -2 binary64) (asin.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) #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 (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 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 #s(literal -2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))))
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (-.f64 (*.f64 #s(literal 2 binary64) (acos.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -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 #s(literal -2 binary64) (asin.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64)))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/4 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 (/.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))) (sqrt.f64 (PI.f64)) (*.f64 #s(literal -2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 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 -2 binary64) (asin.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) #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 -2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64)))))) (PI.f64)))
(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 -2 binary64) (asin.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (*.f64 #s(literal -2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 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 #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 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (*.f64 (asin.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
(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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))) #s(literal -2 binary64)))
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3/4 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 #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 (*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 1/4 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)))
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 #s(literal -2 binary64) (fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (-.f64 #s(literal 0 binary64) (acos.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))))))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (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 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -2 binary64))))))) #s(literal -2 binary64)))
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (*.f64 #s(literal -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 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 x #s(literal -2 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 (fma.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) (/.f64 (pow.f64 (PI.f64) #s(literal 1/4 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))))))) #s(literal -2 binary64)))
Outputs
(-.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)))))))
Calls

7 calls:

12.0ms
x
11.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
11.0ms
(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
10.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
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
9.0%1x
9.0%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))))))
9.0%1(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
9.0%1(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
9.0%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
9.0%1(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
9.0%1(-.f64 #s(literal 1 binary64) x)
Compiler

Compiled 51 to 41 computations (19.6% saved)

regimes2.0ms (0%)

Accuracy

Total -1.8b remaining (-3%)

Threshold costs -1.8b (-3%)

Counts
4 → 1
Calls
Call 1
Inputs
(-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 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 (PI.f64) (*.f64 (acos.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 2 binary64))))
Outputs
(-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (*.f64 #s(literal -2 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
Calls

1 calls:

2.0ms
x
Results
AccuracySegmentsBranch
5.1%1x
Compiler

Compiled 2 to 1 computations (50% saved)

simplify10.0ms (0.1%)

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
12722
24722
35722
46422
56622
Stop Event
1×saturated
Calls
Call 1
Inputs
(-.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 #s(literal -2 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
Outputs
(-.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 #s(literal -2 binary64) (acos.f64 (sqrt.f64 #s(literal 1/2 binary64)))))

soundness1.5s (8.4%)

Rules
4318×*-lowering-*.f32
4318×*-lowering-*.f64
2540×*-lowering-*.f32
2540×*-lowering-*.f64
2242×*-lowering-*.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01139
16038
226738
3148634
0845834
044175
1159141
2682138
36663138
08017138
036225
1145167
2553166
32967166
08373166
01371456
13841327
210871294
335971286
084661286
042169
1155143
2626140
33156140
08280140
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 97 to 73 computations (24.7% saved)

preprocess39.0ms (0.2%)

Compiler

Compiled 80 to 56 computations (30% saved)

end0.0ms (0%)

Profiling

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