bug323 (missed optimization)

Time bar (total: 5.5s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%25%75%0%0%0%0
100%25%0%75%0%0%0%1
Compiler

Compiled 12 to 10 computations (16.7% saved)

sample1.2s (21.4%)

Memory
6.8MiB live, 1 715.2MiB allocated
Samples
896.0ms7 945×1valid
15.0ms311×0valid
Precisions
Click to see histograms. Total time spent on operations: 673.0ms
ival-acos: 303.0ms (45% of total)
ival-sub: 151.0ms (22.4% of total)
adjust: 120.0ms (17.8% of total)
ival-<=: 73.0ms (10.9% of total)
exact: 12.0ms (1.8% of total)
ival-and: 11.0ms (1.6% of total)
ival-assert: 3.0ms (0.4% of total)
Bogosity

preprocess14.0ms (0.3%)

Memory
11.2MiB live, 11.2MiB allocated
Algorithm
egg-herbie
Rules
24×lower-+.f64
24×lower-+.f32
20×sub-neg
18×lower--.f32
16×sub-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0611
1159
2279
3499
4679
5899
61029
044
064
1104
2144
3194
4264
5344
6444
7554
8584
0584
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(acos.f64 (-.f64 #s(literal 1 binary64) x))
Outputs
(acos.f64 (-.f64 #s(literal 1 binary64) x))

explain87.0ms (1.6%)

Memory
-11.3MiB live, 73.6MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2550-0-(acos.f64 (-.f64 #s(literal 1 binary64) x))
00-0-(-.f64 #s(literal 1 binary64) x)
00-0-#s(literal 1 binary64)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
acos.f64(acos.f64 (-.f64 #s(literal 1 binary64) x))sensitivity2551
Confusion
Predicted +Predicted -
+2550
-01
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+25500
-010
Precision?
0.99609375
Recall?
1.0
Freqs
test
numberfreq
01
1255
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
53.0ms492×1valid
1.0ms20×0valid
Compiler

Compiled 32 to 20 computations (37.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 32.0ms
ival-acos: 18.0ms (56.6% of total)
adjust: 7.0ms (22% of total)
ival-sub: 6.0ms (18.9% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.0%
(acos.f64 (-.f64 #s(literal 1 binary64) x))
Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Memory
4.8MiB live, 4.8MiB allocated
Algorithm
egg-herbie
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
cost-diff0
(-.f64 #s(literal 1 binary64) x)
cost-diff0
(acos.f64 (-.f64 #s(literal 1 binary64) x))
Rules
24×lower-+.f64
24×lower-+.f32
18×lower--.f32
16×sub-neg
16×lower--.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
049
069
1109
2149
3199
4269
5349
6449
7559
8589
0589
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
Outputs
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x

localize49.0ms (0.9%)

Memory
-25.1MiB live, 13.7MiB allocated
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(-.f64 #s(literal 1 binary64) x)
accuracy7.0%
(acos.f64 (-.f64 #s(literal 1 binary64) x))
Samples
42.0ms246×1valid
0.0ms10×0valid
Compiler

Compiled 11 to 6 computations (45.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 15.0ms
ival-acos: 9.0ms (59.2% of total)
adjust: 3.0ms (19.7% of total)
ival-sub: 3.0ms (19.7% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series1.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Counts
2 → 24
Calls
Call 1
Inputs
#<alt (acos.f64 (-.f64 #s(literal 1 binary64) x))>
#<alt (-.f64 #s(literal 1 binary64) x)>
Outputs
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
Calls

6 calls:

TimeVariablePointExpression
0.0ms
x
@inf
(- 1 x)
0.0ms
x
@-inf
(- 1 x)
0.0ms
x
@0
(acos (- 1 x))
0.0ms
x
@-inf
(acos (- 1 x))
0.0ms
x
@inf
(acos (- 1 x))

simplify9.0ms (0.2%)

Memory
2.6MiB live, 2.6MiB allocated
Algorithm
egg-herbie
Rules
112×lower-fma.f64
112×lower-fma.f32
80×lower-*.f64
80×lower-*.f32
48×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01480
12980
26280
311380
417180
523980
625980
025980
Stop Event
iter limit
saturated
Counts
24 → 24
Calls
Call 1
Inputs
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
Outputs
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)

rewrite286.0ms (5.2%)

Memory
-6.2MiB live, 291.2MiB allocated
Algorithm
batch-egg-rewrite
Rules
4 910×lower-fma.f64
4 910×lower-fma.f32
4 364×lower-*.f64
4 364×lower-*.f32
4 164×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
047
067
1287
21717
313857
093867
Stop Event
iter limit
node limit
iter limit
Counts
2 → 339
Calls
Call 1
Inputs
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
Outputs
(acos.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))
(+.f64 (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(+.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (acos.f64 (+.f64 #s(literal 1 binary64) x)))
(-.f64 (PI.f64) (acos.f64 (+.f64 (neg.f64 x) #s(literal -1 binary64))))
(-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (asin.f64 (+.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (fma.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))) (/.f64 (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (fma.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))))
(-.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x)))))
(-.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))) (/.f64 (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))))
(fma.f64 #s(literal 1 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 (neg.f64 (PI.f64)) #s(literal -1/2 binary64) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal -1 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 #s(literal -1 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))) (-.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (acos.f64 (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (-.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))) (fma.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))))
(/.f64 (-.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64) (-.f64 (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (*.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))) (-.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (acos.f64 (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (acos.f64 (+.f64 #s(literal 1 binary64) x))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (acos.f64 (+.f64 #s(literal 1 binary64) x))) (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64) (-.f64 (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (*.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (acos.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (acos.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))))) (*.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 (*.f64 #s(literal 1 binary64) (fma.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))) (*.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))))))) (*.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 (asin.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))))) (*.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 (*.f64 #s(literal 1 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x)))) (*.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))) (acos.f64 (+.f64 #s(literal 1 binary64) x))))))) (*.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (+.f64 #s(literal 1 binary64) x))))))
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(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (*.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (+.f64 (neg.f64 x) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (*.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (+.f64 (neg.f64 x) #s(literal -1 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (*.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x)))

eval68.0ms (1.2%)

Memory
6.6MiB live, 42.9MiB allocated
Compiler

Compiled 12 893 to 1 318 computations (89.8% saved)

prune39.0ms (0.7%)

Memory
-10.7MiB live, 66.0MiB allocated
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New3612363
Fresh000
Picked011
Done000
Total3613364
Accuracy
9.5%
Counts
364 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.0%
(acos.f64 (-.f64 #s(literal 1 binary64) x))
6.9%
(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
3.8%
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify5.0ms (0.1%)

Memory
4.9MiB live, 4.9MiB allocated
Algorithm
egg-herbie
Localize:

Found 5 expressions of interest:

NewMetricScoreProgram
cost-diff0
(neg.f64 x)
cost-diff0
#s(approx (- 1 x) (neg.f64 x))
cost-diff0
(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
cost-diff0
#s(approx (- 1 x) #s(literal 1 binary64))
cost-diff0
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
Rules
24×lower-+.f64
24×lower-+.f32
18×lower--.f64
18×lower--.f32
16×sub-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0828
01128
11728
22128
32628
43428
54428
65928
76228
06228
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
#s(approx (- 1 x) #s(literal 1 binary64))
#s(literal 1 binary64)
(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
#s(approx (- 1 x) (neg.f64 x))
(neg.f64 x)
x
Outputs
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
#s(approx (- 1 x) #s(literal 1 binary64))
#s(literal 1 binary64)
(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
#s(approx (- 1 x) (neg.f64 x))
(neg.f64 x)
x

localize37.0ms (0.7%)

Memory
-11.0MiB live, 32.5MiB allocated
Localize:

Found 5 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(neg.f64 x)
accuracy7.0%
(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
accuracy2.3%
#s(approx (- 1 x) (neg.f64 x))
accuracy100.0%
#s(approx (- 1 x) #s(literal 1 binary64))
accuracy7.0%
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
Samples
28.0ms246×1valid
1.0ms10×0valid
Compiler

Compiled 20 to 7 computations (65% saved)

Precisions
Click to see histograms. Total time spent on operations: 17.0ms
ival-acos: 9.0ms (52.5% of total)
adjust: 4.0ms (23.3% of total)
ival-sub: 3.0ms (17.5% of total)
ival-neg: 1.0ms (5.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series2.0ms (0%)

Memory
1.2MiB live, 1.2MiB allocated
Counts
5 → 60
Calls
Call 1
Inputs
#<alt (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))>
#<alt #s(approx (- 1 x) #s(literal 1 binary64))>
#<alt (acos.f64 #s(approx (- 1 x) (neg.f64 x)))>
#<alt #s(approx (- 1 x) (neg.f64 x))>
#<alt (neg.f64 x)>
Outputs
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
Calls

15 calls:

TimeVariablePointExpression
0.0ms
x
@inf
(neg x)
0.0ms
x
@-inf
(neg x)
0.0ms
x
@inf
(- 1 x)
0.0ms
x
@inf
(- 1 x)
0.0ms
x
@-inf
(- 1 x)

simplify10.0ms (0.2%)

Memory
9.5MiB live, 9.5MiB allocated
Algorithm
egg-herbie
Rules
112×lower-fma.f64
112×lower-fma.f32
80×lower-*.f64
80×lower-*.f32
48×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
014184
129184
262184
3113184
4171184
5239184
6259184
0259184
Stop Event
iter limit
saturated
Counts
60 → 60
Calls
Call 1
Inputs
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
Outputs
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)

rewrite205.0ms (3.7%)

Memory
8.1MiB live, 242.2MiB allocated
Algorithm
batch-egg-rewrite
Rules
4 396×lower-*.f64
4 396×lower-*.f32
2 938×lower-/.f64
2 938×lower-/.f32
1 988×frac-sub
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0826
01126
13726
220326
3173223
0915423
Stop Event
iter limit
node limit
iter limit
Counts
5 → 205
Calls
Call 1
Inputs
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
#s(approx (- 1 x) #s(literal 1 binary64))
(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
#s(approx (- 1 x) (neg.f64 x))
(neg.f64 x)
Outputs
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))
(+.f64 (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(+.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))))
(-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))))
(-.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (fma.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))) (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #s(literal 3 binary64)) (fma.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))))
(-.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))))) (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #s(literal 2 binary64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))))))
(fma.f64 #s(literal 1 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))
(fma.f64 #s(literal -1 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))
(fma.f64 (neg.f64 (PI.f64)) #s(literal -1/2 binary64) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))
(fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal -1 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))) (-.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))) (-.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64))) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) #s(literal 1 binary64)))) (acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))))))
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#s(approx (- 1 x) x)
x
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(+.f64 #s(literal 0 binary64) x)
(exp.f64 (log.f64 x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) x)
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(-.f64 (/.f64 #s(literal 0 binary64) x) x)
(fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))
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(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) x #s(literal 0 binary64))
(neg.f64 x)
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(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 x x)))
(/.f64 (*.f64 x (*.f64 x x)) (*.f64 x x))
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(*.f64 #s(literal 1 binary64) x)
(*.f64 x #s(literal 1 binary64))
(*.f64 x #s(literal -1 binary64))
(*.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal -1 binary64) x)

eval31.0ms (0.6%)

Memory
12.3MiB live, 48.5MiB allocated
Compiler

Compiled 8 006 to 767 computations (90.4% saved)

prune31.0ms (0.6%)

Memory
-5.1MiB live, 43.0MiB allocated
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2632265
Fresh000
Picked202
Done011
Total2653268
Accuracy
9.5%
Counts
268 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
6.9%
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))
7.0%
(acos.f64 (-.f64 #s(literal 1 binary64) x))
6.9%
(acos.f64 #s(approx (- 1 x) x))
Compiler

Compiled 21 to 14 computations (33.3% saved)

simplify20.0ms (0.4%)

Memory
-19.1MiB live, 18.3MiB allocated
Algorithm
egg-herbie
Localize:

Found 6 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
cost-diff0
(PI.f64)
cost-diff0
(sqrt.f64 (PI.f64))
cost-diff1600
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))
cost-diff0
#s(approx (- 1 x) x)
cost-diff0
(acos.f64 #s(approx (- 1 x) x))
Rules
228×lower-fma.f32
226×lower-fma.f64
160×lower-*.f32
158×lower-*.f64
80×lower-+.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01253
02053
13349
24449
37149
410849
517949
626749
735049
837349
938149
038149
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(acos.f64 #s(approx (- 1 x) x))
#s(approx (- 1 x) x)
x
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))
(sqrt.f64 (PI.f64))
(PI.f64)
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(neg.f64 (asin.f64 #s(approx (- 1 x) x)))
(asin.f64 #s(approx (- 1 x) x))
#s(approx (- 1 x) x)
x
Outputs
(acos.f64 #s(approx (- 1 x) x))
#s(approx (- 1 x) x)
x
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))
(-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (asin.f64 #s(approx (- 1 x) x)))
(sqrt.f64 (PI.f64))
(PI.f64)
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(neg.f64 (asin.f64 #s(approx (- 1 x) x)))
(asin.f64 #s(approx (- 1 x) x))
#s(approx (- 1 x) x)
x

localize78.0ms (1.4%)

Memory
8.9MiB live, 81.3MiB allocated
Localize:

Found 6 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
#s(approx (- 1 x) x)
accuracy98.7%
(asin.f64 #s(approx (- 1 x) x))
accuracy98.4%
(sqrt.f64 (PI.f64))
accuracy11.9%
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))
accuracy100.0%
#s(approx (- 1 x) x)
accuracy7.0%
(acos.f64 #s(approx (- 1 x) x))
Samples
59.0ms245×1valid
1.0ms11×0valid
Compiler

Compiled 44 to 14 computations (68.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 43.0ms
ival-acos: 10.0ms (23.3% of total)
ival-asin: 8.0ms (18.6% of total)
adjust: 6.0ms (14% of total)
ival-mult: 6.0ms (14% of total)
ival-sub: 3.0ms (7% of total)
ival-sqrt: 3.0ms (7% of total)
ival-pi: 2.0ms (4.7% of total)
ival-neg: 2.0ms (4.7% of total)
ival-add: 2.0ms (4.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series2.0ms (0%)

Memory
6.1MiB live, 6.1MiB allocated
Counts
7 → 48
Calls
Call 1
Inputs
#<alt (acos.f64 #s(approx (- 1 x) x))>
#<alt #s(approx (- 1 x) x)>
#<alt (fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))>
#<alt (sqrt.f64 (PI.f64))>
#<alt (PI.f64)>
#<alt (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))>
#<alt (asin.f64 #s(approx (- 1 x) x))>
Outputs
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
Calls

12 calls:

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

simplify31.0ms (0.6%)

Memory
-9.1MiB live, 31.9MiB allocated
Algorithm
egg-herbie
Rules
240×lower-fma.f64
240×lower-fma.f32
160×lower-*.f64
160×lower-*.f32
88×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
021224
141224
277224
3134224
4206224
5292224
6353224
7387224
8438224
9455224
10463224
0463224
Stop Event
iter limit
saturated
Counts
48 → 48
Calls
Call 1
Inputs
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
Outputs
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (- 1 x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(acos (+ 1 (* -1 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (- 1 x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (+ 1 (* -1 x)))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (+ 1 (* -1 x)))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (+ 1 (* -1 x)))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(asin (+ 1 (* -1 x)))
(asin.f64 (-.f64 #s(literal 1 binary64) x))

rewrite309.0ms (5.6%)

Memory
15.3MiB live, 335.5MiB allocated
Algorithm
batch-egg-rewrite
Rules
6 028×lower-fma.f32
6 026×lower-fma.f64
3 660×lower-*.f32
3 658×lower-*.f64
1 574×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01238
02030
17530
250930
3591930
0875930
Stop Event
iter limit
node limit
iter limit
Counts
7 → 659
Calls
Call 1
Inputs
(acos.f64 #s(approx (- 1 x) x))
#s(approx (- 1 x) x)
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))
(sqrt.f64 (PI.f64))
(PI.f64)
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
(asin.f64 #s(approx (- 1 x) x))
Outputs
(acos.f64 #s(approx (- 1 x) x))
(+.f64 (asin.f64 #s(approx (- 1 x) x)) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (asin.f64 #s(approx (- 1 x) x)))
(+.f64 #s(literal 0 binary64) (acos.f64 #s(approx (- 1 x) x)))
(+.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 0 binary64))
(+.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))) (acos.f64 #s(approx (- 1 x) x))) (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (acos.f64 #s(approx (- 1 x) x))))
(+.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (neg.f64 (acos.f64 #s(approx (- 1 x) x))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (acos.f64 #s(approx (- 1 x) x)))) #s(literal -1 binary64)))
(-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (asin.f64 #s(approx (- 1 x) x)))
(-.f64 #s(literal 0 binary64) (neg.f64 (acos.f64 #s(approx (- 1 x) x))))
(-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))) (acos.f64 #s(approx (- 1 x) x))) (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (acos.f64 #s(approx (- 1 x) x))))
(-.f64 (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (acos.f64 #s(approx (- 1 x) x))) (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))))
(-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/8 binary64))) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (acos.f64 #s(approx (- 1 x) x)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))))) (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (acos.f64 #s(approx (- 1 x) x)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))))))
(-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (acos.f64 #s(approx (- 1 x) x)))
(-.f64 (+.f64 #s(literal 0 binary64) (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))) (acos.f64 #s(approx (- 1 x) x)))) (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (acos.f64 #s(approx (- 1 x) x))))
(-.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (*.f64 (PI.f64) #s(literal -1/2 binary64))) (acos.f64 #s(approx (- 1 x) x)))
(fma.f64 #s(literal 1 binary64) (asin.f64 #s(approx (- 1 x) x)) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 #s(literal 1 binary64) (acos.f64 #s(approx (- 1 x) x)) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 (PI.f64) #s(literal -1/2 binary64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 (PI.f64) #s(literal -1/2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (PI.f64) (/.f64 (*.f64 (PI.f64) #s(literal 1/4 binary64)) (acos.f64 #s(approx (- 1 x) x))) (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 (sqrt.f64 (PI.f64)) (neg.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (PI.f64) #s(literal 1/4 binary64))) (acos.f64 #s(approx (- 1 x) x))) (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 #s(literal 1/2 binary64) (neg.f64 (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
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(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))) (*.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (neg.f64 (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))))) (*.f64 (/.f64 #s(literal 2 binary64) (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))))
(/.f64 (-.f64 (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) (acos.f64 #s(approx (- 1 x) x)))) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (acos.f64 #s(approx (- 1 x) x)))))
(/.f64 (-.f64 (*.f64 (PI.f64) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (acos.f64 #s(approx (- 1 x) x)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))))) (*.f64 #s(literal 2 binary64) (fma.f64 (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))))) (*.f64 #s(literal 2 binary64) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (acos.f64 #s(approx (- 1 x) x)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))))))
(/.f64 (-.f64 (*.f64 (PI.f64) (acos.f64 #s(approx (- 1 x) x))) (*.f64 #s(literal 2 binary64) (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)))) (*.f64 #s(literal 2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(/.f64 (-.f64 (*.f64 (PI.f64) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (acos.f64 #s(approx (- 1 x) x)) (neg.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))))) (*.f64 #s(literal 2 binary64) (neg.f64 (fma.f64 (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)))))) (*.f64 #s(literal 2 binary64) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (acos.f64 #s(approx (- 1 x) x)) (neg.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))))))
(/.f64 (-.f64 (*.f64 (PI.f64) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))) (*.f64 #s(literal 2 binary64) (neg.f64 (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))))) (*.f64 #s(literal 2 binary64) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))))
(/.f64 (-.f64 (*.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal 1 binary64) (acos.f64 #s(approx (- 1 x) x)))) #s(literal -2 binary64)) (*.f64 #s(literal -2 binary64) (/.f64 #s(literal 1 binary64) (acos.f64 #s(approx (- 1 x) x)))))
(/.f64 (-.f64 (*.f64 (neg.f64 (PI.f64)) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (acos.f64 #s(approx (- 1 x) x)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))))) (*.f64 #s(literal -2 binary64) (fma.f64 (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))))) (*.f64 #s(literal -2 binary64) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (acos.f64 #s(approx (- 1 x) x)) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))))))
(/.f64 (-.f64 (*.f64 (neg.f64 (PI.f64)) (acos.f64 #s(approx (- 1 x) x))) (*.f64 #s(literal -2 binary64) (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(/.f64 (-.f64 (*.f64 (neg.f64 (PI.f64)) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (acos.f64 #s(approx (- 1 x) x)) (neg.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))))) (*.f64 #s(literal -2 binary64) (neg.f64 (fma.f64 (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/8 binary64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)))))) (*.f64 #s(literal -2 binary64) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (acos.f64 #s(approx (- 1 x) x)) (neg.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))))))
(/.f64 (-.f64 (*.f64 (neg.f64 (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))) (*.f64 #s(literal -2 binary64) (neg.f64 (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))))) (*.f64 #s(literal -2 binary64) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (*.f64 (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/8 binary64))) (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)))) (fma.f64 (acos.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x)))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(/.f64 (neg.f64 (-.f64 (*.f64 (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/8 binary64))) (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)))) (fma.f64 (acos.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (-.f64 (*.f64 (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/8 binary64))) (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (acos.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x)))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x)))) (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x)))))
(/.f64 (+.f64 (pow.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (PI.f64) #s(literal -1/2 binary64)) (-.f64 (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (*.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (acos.f64 #s(approx (- 1 x) x))))))
(/.f64 (fma.f64 (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/8 binary64)) (pow.f64 (neg.f64 (acos.f64 #s(approx (- 1 x) x))) #s(literal 3 binary64))) (fma.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)) (-.f64 (*.f64 (neg.f64 (acos.f64 #s(approx (- 1 x) x))) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))) (*.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))))))
(/.f64 (-.f64 (*.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (PI.f64) #s(literal -1/2 binary64))) (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))) (-.f64 (*.f64 (PI.f64) #s(literal -1/2 binary64)) (acos.f64 #s(approx (- 1 x) x))))
(/.f64 (-.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))) (*.f64 (neg.f64 (acos.f64 #s(approx (- 1 x) x))) (neg.f64 (acos.f64 #s(approx (- 1 x) x))))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(/.f64 (*.f64 #s(literal -1 binary64) (-.f64 (*.f64 (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/8 binary64))) (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)))) (fma.f64 (acos.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))))
(/.f64 (*.f64 #s(literal -1 binary64) (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x)))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(/.f64 (*.f64 (-.f64 (*.f64 (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/8 binary64))) (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))) #s(literal -1 binary64)) (fma.f64 (acos.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))))
(/.f64 (*.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x))) #s(literal -1 binary64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(asin.f64 #s(approx (- 1 x) x))
(pow.f64 (/.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (asin.f64 #s(approx (- 1 x) x)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (acos.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64)))) (-.f64 (*.f64 (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/8 binary64))) (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x)))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (asin.f64 #s(approx (- 1 x) x)))
(*.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 1 binary64))
(*.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal -1 binary64))
(*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (asin.f64 #s(approx (- 1 x) x))))
(*.f64 #s(literal -1 binary64) (asin.f64 #s(approx (- 1 x) x)))
(*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))))
(*.f64 (-.f64 (*.f64 (PI.f64) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/8 binary64))) (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (acos.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (*.f64 (PI.f64) (*.f64 (PI.f64) #s(literal 1/4 binary64))))))
(*.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x))) (/.f64 #s(literal 1 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 #s(approx (- 1 x) x)))))

eval104.0ms (1.9%)

Memory
5.4MiB live, 115.5MiB allocated
Compiler

Compiled 16 417 to 1 672 computations (89.8% saved)

prune74.0ms (1.4%)

Memory
-13.2MiB live, 119.9MiB allocated
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New8025807
Fresh000
Picked112
Done011
Total8037810
Accuracy
9.5%
Counts
810 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
6.9%
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
6.9%
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))))
5.2%
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
4.3%
(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))) (*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64))))
7.0%
(acos.f64 (-.f64 #s(literal 1 binary64) x))
6.9%
(acos.f64 #s(approx (- 1 x) x))
7.0%
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
Compiler

Compiled 169 to 98 computations (42% saved)

simplify184.0ms (3.4%)

Memory
1.5MiB live, 198.2MiB allocated
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(asin.f64 #s(approx (- 1 x) x))
cost-diff0
(pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))
cost-diff6144
(fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)))
cost-diff27136
(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))) (*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64))))
cost-diff0
(PI.f64)
cost-diff0
(sqrt.f64 (PI.f64))
cost-diff1728
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))
cost-diff2304
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))))
cost-diff0
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
cost-diff0
(PI.f64)
cost-diff0
(sqrt.f64 (PI.f64))
cost-diff1600
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
cost-diff0
(PI.f64)
cost-diff0
(sqrt.f64 (PI.f64))
cost-diff0
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
cost-diff1600
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
cost-diff0
(PI.f64)
cost-diff0
(*.f64 #s(literal 1/2 binary64) (PI.f64))
cost-diff0
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
cost-diff0
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
Rules
4 524×lower-fma.f32
4 514×lower-fma.f64
3 372×lower-*.f32
3 366×lower-*.f64
3 120×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
039303
068306
1117274
2216270
3522268
41256251
54154251
08411248
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 1/2 binary64) (PI.f64))
#s(literal 1/2 binary64)
(PI.f64)
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
(sqrt.f64 (PI.f64))
(PI.f64)
#s(literal 1/2 binary64)
(asin.f64 #s(approx (- 1 x) x))
#s(approx (- 1 x) x)
x
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
(sqrt.f64 (PI.f64))
(PI.f64)
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))))
(asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))
#s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))))
(sqrt.f64 (PI.f64))
(PI.f64)
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(neg.f64 (fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x))))
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))
(neg.f64 (sqrt.f64 (PI.f64)))
(acos.f64 #s(approx (- 1 x) x))
#s(approx (- 1 x) x)
x
(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))) (*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64))))
(fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)))
(pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))
(asin.f64 #s(approx (- 1 x) x))
#s(approx (- 1 x) x)
x
#s(literal 3 binary64)
(/.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))
(*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)))
Outputs
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 1/2 binary64) (PI.f64))
#s(literal 1/2 binary64)
(PI.f64)
(asin.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 #s(approx (- 1 x) x)))
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64)))
(sqrt.f64 (PI.f64))
(PI.f64)
#s(literal 1/2 binary64)
(asin.f64 #s(approx (- 1 x) x))
#s(approx (- 1 x) x)
x
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (PI.f64))
(PI.f64)
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64)))
#s(literal 1/2 binary64)
(neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))))
(asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))
#s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))))
(-.f64 (PI.f64) (acos.f64 #s(approx (- 1 x) x)))
(sqrt.f64 (PI.f64))
(PI.f64)
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64)))
#s(literal 1/2 binary64)
(neg.f64 (fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 #s(approx (- 1 x) x)))
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))
(fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x)))
(neg.f64 (sqrt.f64 (PI.f64)))
(acos.f64 #s(approx (- 1 x) x))
#s(approx (- 1 x) x)
x
(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))) (*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64))))
(*.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (/.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1 binary64)))
(fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (/.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1 binary64)))
(pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))
(asin.f64 #s(approx (- 1 x) x))
#s(approx (- 1 x) x)
x
#s(literal 3 binary64)
(/.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
(pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))
(*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))) (PI.f64))

localize187.0ms (3.4%)

Memory
15.9MiB live, 136.4MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy99.9%
(pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))
accuracy99.9%
(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))) (*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64))))
accuracy98.4%
(pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))
accuracy5.3%
(asin.f64 #s(approx (- 1 x) x))
accuracy100.0%
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))))
accuracy98.5%
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))
accuracy98.4%
(sqrt.f64 (PI.f64))
accuracy6.9%
(acos.f64 #s(approx (- 1 x) x))
accuracy100.0%
#s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))
accuracy98.7%
(asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))
accuracy98.4%
(sqrt.f64 (PI.f64))
accuracy11.9%
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
accuracy100.0%
#s(approx (- 1 x) x)
accuracy100.0%
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
accuracy98.4%
(sqrt.f64 (PI.f64))
accuracy5.3%
(asin.f64 #s(approx (- 1 x) x))
accuracy100.0%
(PI.f64)
accuracy98.7%
(asin.f64 (-.f64 #s(literal 1 binary64) x))
accuracy9.0%
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
accuracy9.0%
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
Samples
133.0ms243×1valid
3.0ms13×0valid
Compiler

Compiled 252 to 32 computations (87.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 104.0ms
ival-mult: 28.0ms (26.9% of total)
adjust: 14.0ms (13.5% of total)
ival-add: 12.0ms (11.5% of total)
ival-asin: 10.0ms (9.6% of total)
ival-acos: 9.0ms (8.7% of total)
ival-div: 6.0ms (5.8% of total)
ival-neg: 6.0ms (5.8% of total)
ival-pow: 5.0ms (4.8% of total)
ival-sub: 4.0ms (3.8% of total)
ival-pow2: 4.0ms (3.8% of total)
ival-sqrt: 4.0ms (3.8% of total)
ival-pi: 2.0ms (1.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series24.0ms (0.4%)

Memory
-11.1MiB live, 24.8MiB allocated
Counts
20 → 192
Calls
Call 1
Inputs
#<alt #s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))>
#<alt (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))>
#<alt (*.f64 #s(literal 1/2 binary64) (PI.f64))>
#<alt (PI.f64)>
#<alt (fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))>
#<alt (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))>
#<alt (sqrt.f64 (PI.f64))>
#<alt (fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))>
#<alt (fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))))>
#<alt (fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))>
#<alt (/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))) (*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64))))>
#<alt (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)))>
#<alt (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))>
#<alt (asin.f64 #s(approx (- 1 x) x))>
#<alt (asin.f64 (-.f64 #s(literal 1 binary64) x))>
#<alt #s(approx (- 1 x) x)>
#<alt (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))>
#<alt #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))>
#<alt (acos.f64 #s(approx (- 1 x) x))>
#<alt (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))>
Outputs
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (+ (asin (- 1 x)) (* 1/2 (PI)))>
#<alt (+ (asin (- 1 x)) (* 1/2 (PI)))>
#<alt (+ (asin (- 1 x)) (* 1/2 (PI)))>
#<alt (+ (asin (- 1 x)) (* 1/2 (PI)))>
#<alt (+ (asin (- 1 x)) (* 1/2 (PI)))>
#<alt (+ (asin (- 1 x)) (* 1/2 (PI)))>
#<alt (+ (asin (- 1 x)) (* 1/2 (PI)))>
#<alt (+ (asin (- 1 x)) (* 1/2 (PI)))>
#<alt (+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))>
#<alt (+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))>
#<alt (+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))>
#<alt (+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (- 1 x)))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))>
#<alt (- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))>
#<alt (- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))>
#<alt (- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))>
#<alt (- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))>
#<alt (- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))>
#<alt (- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))>
#<alt (- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))>
#<alt (- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))>
#<alt (- (* 1/2 (PI)) (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI))))>
#<alt (- (* 1/2 (PI)) (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI))))>
#<alt (- (* 1/2 (PI)) (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI))))>
#<alt (- (* 1/2 (PI)) (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI))))>
#<alt (+ (acos (- 1 x)) (* -1/2 (PI)))>
#<alt (+ (acos (- 1 x)) (* -1/2 (PI)))>
#<alt (+ (acos (- 1 x)) (* -1/2 (PI)))>
#<alt (+ (acos (- 1 x)) (* -1/2 (PI)))>
#<alt (+ (acos (- 1 x)) (* -1/2 (PI)))>
#<alt (+ (acos (- 1 x)) (* -1/2 (PI)))>
#<alt (+ (acos (- 1 x)) (* -1/2 (PI)))>
#<alt (+ (acos (- 1 x)) (* -1/2 (PI)))>
#<alt (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI)))>
#<alt (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI)))>
#<alt (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI)))>
#<alt (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI)))>
#<alt (* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))>
#<alt (* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))>
#<alt (* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))>
#<alt (* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))>
#<alt (* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))>
#<alt (* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))>
#<alt (* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))>
#<alt (* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))>
#<alt (* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (+ 1 (* -1 x))) 3) (PI))) (pow (asin (+ 1 (* -1 x))) 2))) (pow (asin (+ 1 (* -1 x))) 2)))>
#<alt (* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (+ 1 (* -1 x))) 3) (PI))) (pow (asin (+ 1 (* -1 x))) 2))) (pow (asin (+ 1 (* -1 x))) 2)))>
#<alt (* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (+ 1 (* -1 x))) 3) (PI))) (pow (asin (+ 1 (* -1 x))) 2))) (pow (asin (+ 1 (* -1 x))) 2)))>
#<alt (* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (+ 1 (* -1 x))) 3) (PI))) (pow (asin (+ 1 (* -1 x))) 2))) (pow (asin (+ 1 (* -1 x))) 2)))>
#<alt (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))>
#<alt (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))>
#<alt (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))>
#<alt (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))>
#<alt (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))>
#<alt (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))>
#<alt (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))>
#<alt (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))>
#<alt (+ (* 2 (/ (pow (asin (+ 1 (* -1 x))) 3) (PI))) (pow (asin (+ 1 (* -1 x))) 2))>
#<alt (+ (* 2 (/ (pow (asin (+ 1 (* -1 x))) 3) (PI))) (pow (asin (+ 1 (* -1 x))) 2))>
#<alt (+ (* 2 (/ (pow (asin (+ 1 (* -1 x))) 3) (PI))) (pow (asin (+ 1 (* -1 x))) 2))>
#<alt (+ (* 2 (/ (pow (asin (+ 1 (* -1 x))) 3) (PI))) (pow (asin (+ 1 (* -1 x))) 2))>
#<alt (pow (asin (- 1 x)) 3)>
#<alt (pow (asin (- 1 x)) 3)>
#<alt (pow (asin (- 1 x)) 3)>
#<alt (pow (asin (- 1 x)) 3)>
#<alt (pow (asin (- 1 x)) 3)>
#<alt (pow (asin (- 1 x)) 3)>
#<alt (pow (asin (- 1 x)) 3)>
#<alt (pow (asin (- 1 x)) 3)>
#<alt (pow (asin (+ 1 (* -1 x))) 3)>
#<alt (pow (asin (+ 1 (* -1 x))) 3)>
#<alt (pow (asin (+ 1 (* -1 x))) 3)>
#<alt (pow (asin (+ 1 (* -1 x))) 3)>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (- 1 x))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt (asin (+ 1 (* -1 x)))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (- 1 x))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (acos (+ 1 (* -1 x)))>
#<alt (pow (asin (- 1 x)) 2)>
#<alt (pow (asin (- 1 x)) 2)>
#<alt (pow (asin (- 1 x)) 2)>
#<alt (pow (asin (- 1 x)) 2)>
#<alt (pow (asin (- 1 x)) 2)>
#<alt (pow (asin (- 1 x)) 2)>
#<alt (pow (asin (- 1 x)) 2)>
#<alt (pow (asin (- 1 x)) 2)>
#<alt (pow (asin (+ 1 (* -1 x))) 2)>
#<alt (pow (asin (+ 1 (* -1 x))) 2)>
#<alt (pow (asin (+ 1 (* -1 x))) 2)>
#<alt (pow (asin (+ 1 (* -1 x))) 2)>
Calls

48 calls:

TimeVariablePointExpression
7.0ms
x
@-inf
(/ (+ (* (pow (asin (- 1 x)) 3) (/ 2 (PI))) (pow (asin (- 1 x)) 2)) (* (pow (asin (- 1 x)) 2) (/ 2 (PI))))
3.0ms
x
@inf
(/ (+ (* (pow (asin (- 1 x)) 3) (/ 2 (PI))) (pow (asin (- 1 x)) 2)) (* (pow (asin (- 1 x)) 2) (/ 2 (PI))))
3.0ms
x
@0
(/ (+ (* (pow (asin (- 1 x)) 3) (/ 2 (PI))) (pow (asin (- 1 x)) 2)) (* (pow (asin (- 1 x)) 2) (/ 2 (PI))))
1.0ms
x
@-inf
(+ (* (pow (asin (- 1 x)) 3) (/ 2 (PI))) (pow (asin (- 1 x)) 2))
1.0ms
x
@inf
(+ (* (pow (asin (- 1 x)) 3) (/ 2 (PI))) (pow (asin (- 1 x)) 2))

simplify332.0ms (6.1%)

Memory
-14.8MiB live, 312.2MiB allocated
Algorithm
egg-herbie
Rules
15 504×lower-fma.f64
15 504×lower-fma.f32
3 832×lower-*.f64
3 832×lower-*.f32
2 472×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0471564
11251564
22441516
34961468
411621420
529701420
084331372
Stop Event
iter limit
node limit
Counts
192 → 192
Calls
Call 1
Inputs
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))
(+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))
(+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))
(+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(- (* 1/2 (PI)) (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI))))
(- (* 1/2 (PI)) (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI))))
(- (* 1/2 (PI)) (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI))))
(- (* 1/2 (PI)) (+ (acos (+ 1 (* -1 x))) (* -1/2 (PI))))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(+ (acos (- 1 x)) (* -1/2 (PI)))
(+ (acos (+ 1 (* -1 x))) (* -1/2 (PI)))
(+ (acos (+ 1 (* -1 x))) (* -1/2 (PI)))
(+ (acos (+ 1 (* -1 x))) (* -1/2 (PI)))
(+ (acos (+ 1 (* -1 x))) (* -1/2 (PI)))
(* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))) (pow (asin (- 1 x)) 2)))
(* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (+ 1 (* -1 x))) 3) (PI))) (pow (asin (+ 1 (* -1 x))) 2))) (pow (asin (+ 1 (* -1 x))) 2)))
(* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (+ 1 (* -1 x))) 3) (PI))) (pow (asin (+ 1 (* -1 x))) 2))) (pow (asin (+ 1 (* -1 x))) 2)))
(* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (+ 1 (* -1 x))) 3) (PI))) (pow (asin (+ 1 (* -1 x))) 2))) (pow (asin (+ 1 (* -1 x))) 2)))
(* 1/2 (/ (* (PI) (+ (* 2 (/ (pow (asin (+ 1 (* -1 x))) 3) (PI))) (pow (asin (+ 1 (* -1 x))) 2))) (pow (asin (+ 1 (* -1 x))) 2)))
(+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))
(+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))
(+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))
(+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))
(+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))
(+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))
(+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))
(+ (* 2 (/ (pow (asin (- 1 x)) 3) (PI))) (pow (asin (- 1 x)) 2))
(+ (* 2 (/ (pow (asin (+ 1 (* -1 x))) 3) (PI))) (pow (asin (+ 1 (* -1 x))) 2))
(+ (* 2 (/ (pow (asin (+ 1 (* -1 x))) 3) (PI))) (pow (asin (+ 1 (* -1 x))) 2))
(+ (* 2 (/ (pow (asin (+ 1 (* -1 x))) 3) (PI))) (pow (asin (+ 1 (* -1 x))) 2))
(+ (* 2 (/ (pow (asin (+ 1 (* -1 x))) 3) (PI))) (pow (asin (+ 1 (* -1 x))) 2))
(pow (asin (- 1 x)) 3)
(pow (asin (- 1 x)) 3)
(pow (asin (- 1 x)) 3)
(pow (asin (- 1 x)) 3)
(pow (asin (- 1 x)) 3)
(pow (asin (- 1 x)) 3)
(pow (asin (- 1 x)) 3)
(pow (asin (- 1 x)) 3)
(pow (asin (+ 1 (* -1 x))) 3)
(pow (asin (+ 1 (* -1 x))) 3)
(pow (asin (+ 1 (* -1 x))) 3)
(pow (asin (+ 1 (* -1 x))) 3)
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (- 1 x))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
(asin (+ 1 (* -1 x)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (- 1 x))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
(acos (+ 1 (* -1 x)))
(pow (asin (- 1 x)) 2)
(pow (asin (- 1 x)) 2)
(pow (asin (- 1 x)) 2)
(pow (asin (- 1 x)) 2)
(pow (asin (- 1 x)) 2)
(pow (asin (- 1 x)) 2)
(pow (asin (- 1 x)) 2)
(pow (asin (- 1 x)) 2)
(pow (asin (+ 1 (* -1 x))) 2)
(pow (asin (+ 1 (* -1 x))) 2)
(pow (asin (+ 1 (* -1 x))) 2)
(pow (asin (+ 1 (* -1 x))) 2)
Outputs
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (- 1 x)) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(+ (asin (+ 1 (* -1 x))) (* 1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (- 1 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (asin (+ 1 (* -1 x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
(-.f64 (PI.f64) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(- (* 1/2 (PI)) (+ (acos (- 1 x)) (* -1/2 (PI))))
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(pow (asin (+ 1 (* -1 x))) 2)
(pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))
(pow (asin (+ 1 (* -1 x))) 2)
(pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))
(pow (asin (+ 1 (* -1 x))) 2)
(pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))

rewrite512.0ms (9.3%)

Memory
26.7MiB live, 422.9MiB allocated
Algorithm
batch-egg-rewrite
Rules
10 972×lower-fma.f32
10 962×lower-fma.f64
5 414×lower-*.f32
5 408×lower-*.f64
4 302×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
039210
068183
1264166
21898166
09204163
Stop Event
iter limit
node limit
iter limit
Counts
20 → 1 219
Calls
Call 1
Inputs
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 1/2 binary64) (PI.f64))
(PI.f64)
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
(*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64))
(sqrt.f64 (PI.f64))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))))
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))
(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))) (*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64))))
(fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)))
(pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))
(asin.f64 #s(approx (- 1 x) x))
(asin.f64 (-.f64 #s(literal 1 binary64) x))
#s(approx (- 1 x) x)
(asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))
#s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))
(acos.f64 #s(approx (- 1 x) x))
(pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))
Outputs
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
(+.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/2 binary64) (PI.f64)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) (PI.f64))) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(-.f64 #s(literal 0 binary64) (-.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (PI.f64))))
(-.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))) (/.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))))
(-.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))) (/.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))))
(-.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) #s(literal 0 binary64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (fma.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))) (/.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (fma.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))))
(-.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64)) (+.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (neg.f64 (*.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (PI.f64))))))) (/.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)) (+.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (neg.f64 (*.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (PI.f64))))))))
(-.f64 (/.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (-.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/2 binary64) (PI.f64)))) (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (-.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/2 binary64) (PI.f64)))))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64)) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64)))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (neg.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (PI.f64)))) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (neg.f64 (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (PI.f64))) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 #s(literal -1 binary64) (asin.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (PI.f64)))
(fma.f64 #s(literal -1 binary64) (*.f64 (PI.f64) #s(literal -1/2 binary64)) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (neg.f64 (neg.f64 (sqrt.f64 (PI.f64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)) (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))) (fma.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))) (fma.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))))
(/.f64 (fma.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))) (fma.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))))
(/.f64 (fma.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))) (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))))
(/.f64 (fma.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (neg.f64 (*.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (PI.f64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))) (fma.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))) (fma.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))))))
(/.f64 (-.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (fma.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (fma.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (fma.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (neg.f64 (*.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (PI.f64))))))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (-.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))) (-.f64 (neg.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/2 binary64) (PI.f64))))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))) (/.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (asin.f64 (-.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) (*.f64 (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (asin.f64 (-.f64 #s(literal 1 binary64) x))))) (/.f64 #s(literal 2 binary64) (PI.f64))))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))) #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (asin.f64 (-.f64 #s(literal 1 binary64) x))))) (PI.f64))) (*.f64 (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (asin.f64 (-.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))) #s(literal -2 binary64) (*.f64 (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (asin.f64 (-.f64 #s(literal 1 binary64) x))))) (neg.f64 (PI.f64)))) (*.f64 (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (asin.f64 (-.f64 #s(literal 1 binary64) x))))) #s(literal -2 binary64)))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))) (/.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (+.f64 #s(literal 0 binary64) (asin.f64 (-.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (*.f64 (+.f64 #s(literal 0 binary64) (asin.f64 (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 2 binary64) (PI.f64))))
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(/.f64 (+.f64 (pow.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 3 binary64)) (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64))) (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) (PI.f64))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) (PI.f64))) (-.f64 (pow.f64 (acos.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (*.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 #s(literal 1/2 binary64) (PI.f64))) (acos.f64 #s(approx (- 1 x) x))))))
(/.f64 (+.f64 (pow.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) #s(literal 3 binary64))) (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal 0 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal 0 binary64)) (-.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (*.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal 0 binary64)) (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x)))))))
(*.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 #s(approx (- 1 x) x))) (fma.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/8 binary64) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)))) (/.f64 (acos.f64 #s(approx (- 1 x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (asin.f64 #s(approx (- 1 x) x)) (-.f64 (asin.f64 #s(approx (- 1 x) x)) (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64))))))
(*.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 #s(approx (- 1 x) x))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 #s(approx (- 1 x) x))) (acos.f64 #s(approx (- 1 x) x)))) (/.f64 (acos.f64 #s(approx (- 1 x) x)) (/.f64 #s(literal 1 binary64) (acos.f64 #s(approx (- 1 x) x)))))
(+.f64 (*.f64 (asin.f64 #s(approx (- 1 x) x)) (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 (asin.f64 #s(approx (- 1 x) x)) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))))
(+.f64 (*.f64 (asin.f64 #s(approx (- 1 x) x)) (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 (neg.f64 (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (asin.f64 #s(approx (- 1 x) x)))))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (asin.f64 #s(approx (- 1 x) x)))) #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) (asin.f64 #s(approx (- 1 x) x))) (*.f64 (asin.f64 #s(approx (- 1 x) x)) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) (asin.f64 #s(approx (- 1 x) x))) (*.f64 (neg.f64 (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x))))
(fma.f64 (PI.f64) (*.f64 #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (*.f64 (asin.f64 #s(approx (- 1 x) x)) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))))
(fma.f64 (PI.f64) (*.f64 #s(literal 1/2 binary64) (asin.f64 #s(approx (- 1 x) x))) (*.f64 (neg.f64 (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (asin.f64 #s(approx (- 1 x) x))) (*.f64 (asin.f64 #s(approx (- 1 x) x)) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (asin.f64 #s(approx (- 1 x) x))) (*.f64 (neg.f64 (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x))) (*.f64 (asin.f64 #s(approx (- 1 x) x)) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x))) (*.f64 (neg.f64 (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x))))
(fma.f64 (asin.f64 #s(approx (- 1 x) x)) (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (asin.f64 #s(approx (- 1 x) x)) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))))
(fma.f64 (asin.f64 #s(approx (- 1 x) x)) (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (neg.f64 (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 #s(approx (- 1 x) x)) (*.f64 (asin.f64 #s(approx (- 1 x) x)) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 #s(approx (- 1 x) x)) (*.f64 (neg.f64 (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x))))
(fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal -1 binary64)) (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (*.f64 (asin.f64 #s(approx (- 1 x) x)) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))))
(fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal -1 binary64)) (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (*.f64 (neg.f64 (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x))))
(neg.f64 (*.f64 (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x))))
(neg.f64 (*.f64 (asin.f64 #s(approx (- 1 x) x)) (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x)))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (PI.f64) (asin.f64 #s(approx (- 1 x) x))) #s(literal 3 binary64)) (pow.f64 (*.f64 (asin.f64 #s(approx (- 1 x) x)) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (asin.f64 #s(approx (- 1 x) x)) (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 (asin.f64 #s(approx (- 1 x) x)) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))) (*.f64 (asin.f64 #s(approx (- 1 x) x)) (neg.f64 (acos.f64 #s(approx (- 1 x) x))))) (*.f64 (*.f64 (asin.f64 #s(approx (- 1 x) x)) (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 (asin.f64 #s(approx (- 1 x) x)) (neg.f64 (acos.f64 #s(approx (- 1 x) x))))))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (PI.f64) (asin.f64 #s(approx (- 1 x) x))) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x))) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (asin.f64 #s(approx (- 1 x) x)) (*.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 (neg.f64 (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x))) (*.f64 (neg.f64 (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x)))) (*.f64 (*.f64 (asin.f64 #s(approx (- 1 x) x)) (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 (neg.f64 (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x)))))))
(pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))
(pow.f64 (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (asin.f64 #s(approx (- 1 x) x))))
(*.f64 #s(literal 1 binary64) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)))
(*.f64 (asin.f64 #s(approx (- 1 x) x)) (asin.f64 #s(approx (- 1 x) x)))
(*.f64 (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x))))
(*.f64 #s(literal -1 binary64) (pow.f64 (*.f64 (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) (asin.f64 #s(approx (- 1 x) x))) #s(literal 1 binary64)))
(*.f64 (*.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal -1 binary64)) (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x))))
(*.f64 (pow.f64 (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (*.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 (PI.f64) #s(literal -1/2 binary64) (acos.f64 #s(approx (- 1 x) x))) #s(literal 1 binary64)))

eval481.0ms (8.8%)

Memory
19.0MiB live, 241.3MiB allocated
Compiler

Compiled 72 425 to 5 428 computations (92.5% saved)

prune522.0ms (9.5%)

Memory
-143.8MiB live, 391.8MiB allocated
Pruning

16 alts after pruning (12 fresh and 4 done)

PrunedKeptTotal
New2 373122 385
Fresh000
Picked325
Done022
Total2 376162 392
Accuracy
10.7%
Counts
2 392 → 16
Alt Table
Click to see full alt table
StatusAccuracyProgram
10.5%
(fma.f64 (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
6.9%
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
5.2%
(fma.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (sqrt.f64 (PI.f64))) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))))) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
10.4%
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))))
5.7%
(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))) (*.f64 (pow.f64 (fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))) #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64))))
5.7%
(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))) (*.f64 (pow.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))) #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64))))
10.5%
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64))) (/.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64))) (*.f64 (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))) (/.f64 #s(literal 2 binary64) (PI.f64))))
7.0%
(/.f64 (-.f64 (*.f64 (PI.f64) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))))) (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))))) (*.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))))))
7.0%
(acos.f64 (-.f64 #s(literal 1 binary64) x))
6.9%
(acos.f64 #s(approx (- 1 x) x))
5.2%
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
5.2%
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (sqrt.f64 (PI.f64))) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))))) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
5.1%
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)))) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
10.3%
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
7.0%
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
7.0%
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
Compiler

Compiled 745 to 292 computations (60.8% saved)

regimes20.0ms (0.4%)

Memory
-7.7MiB live, 31.6MiB allocated
Counts
22 → 1
Calls
Call 1
Inputs
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
(acos.f64 #s(approx (- 1 x) x))
(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))))
(fma.f64 (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (sqrt.f64 (PI.f64))) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))))) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (sqrt.f64 (PI.f64))) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))))) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (-.f64 (*.f64 (PI.f64) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))))) (*.f64 #s(literal 2 binary64) (-.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (pow.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))))) (*.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)))) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))) (*.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64))))
(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))) (*.f64 (pow.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))) #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64))))
(/.f64 (fma.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 3 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64)) (pow.f64 (asin.f64 #s(approx (- 1 x) x)) #s(literal 2 binary64))) (*.f64 (pow.f64 (fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (acos.f64 #s(approx (- 1 x) x)))) #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (PI.f64))))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64))) (/.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64))) (*.f64 (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))) (/.f64 #s(literal 2 binary64) (PI.f64))))
Outputs
(fma.f64 (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
Calls

3 calls:

7.0ms
x
6.0ms
(acos.f64 (-.f64 #s(literal 1 binary64) x))
6.0ms
(-.f64 #s(literal 1 binary64) x)
Results
AccuracySegmentsBranch
10.5%1x
10.5%1(acos.f64 (-.f64 #s(literal 1 binary64) x))
10.5%1(-.f64 #s(literal 1 binary64) x)
Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes12.0ms (0.2%)

Memory
19.7MiB live, 19.7MiB allocated
Counts
13 → 1
Calls
Call 1
Inputs
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
(acos.f64 #s(approx (- 1 x) x))
(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))))
Outputs
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))))
Calls

3 calls:

4.0ms
x
3.0ms
(-.f64 #s(literal 1 binary64) x)
3.0ms
(acos.f64 (-.f64 #s(literal 1 binary64) x))
Results
AccuracySegmentsBranch
10.4%1x
10.4%1(acos.f64 (-.f64 #s(literal 1 binary64) x))
10.4%1(-.f64 #s(literal 1 binary64) x)
Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes12.0ms (0.2%)

Memory
-18.0MiB live, 21.7MiB allocated
Counts
12 → 1
Calls
Call 1
Inputs
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
(acos.f64 #s(approx (- 1 x) x))
(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 (PI.f64))) (acos.f64 #s(approx (- 1 x) x)))))
Outputs
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
Calls

3 calls:

5.0ms
x
3.0ms
(-.f64 #s(literal 1 binary64) x)
3.0ms
(acos.f64 (-.f64 #s(literal 1 binary64) x))
Results
AccuracySegmentsBranch
10.3%1(-.f64 #s(literal 1 binary64) x)
10.3%1x
10.3%1(acos.f64 (-.f64 #s(literal 1 binary64) x))
Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes10.0ms (0.2%)

Memory
18.8MiB live, 18.8MiB allocated
Counts
10 → 2
Calls
Call 1
Inputs
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
(acos.f64 #s(approx (- 1 x) x))
(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 #s(approx (- 1 x) x)))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) x))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
Outputs
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x))))
(acos.f64 #s(approx (- 1 x) x))
Calls

3 calls:

3.0ms
x
3.0ms
(-.f64 #s(literal 1 binary64) x)
3.0ms
(acos.f64 (-.f64 #s(literal 1 binary64) x))
Results
AccuracySegmentsBranch
9.5%2(acos.f64 (-.f64 #s(literal 1 binary64) x))
9.5%2(-.f64 #s(literal 1 binary64) x)
9.5%2x
Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes7.0ms (0.1%)

Memory
-42.2MiB live, 12.1MiB allocated
Counts
4 → 2
Calls
Call 1
Inputs
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
(acos.f64 #s(approx (- 1 x) x))
(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
Outputs
(acos.f64 #s(approx (- 1 x) x))
(acos.f64 (-.f64 #s(literal 1 binary64) x))
Calls

3 calls:

4.0ms
x
2.0ms
(acos.f64 (-.f64 #s(literal 1 binary64) x))
2.0ms
(-.f64 #s(literal 1 binary64) x)
Results
AccuracySegmentsBranch
9.5%2x
9.5%2(acos.f64 (-.f64 #s(literal 1 binary64) x))
9.5%2(-.f64 #s(literal 1 binary64) x)
Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes5.0ms (0.1%)

Memory
9.0MiB live, 9.0MiB allocated
Counts
3 → 1
Calls
Call 1
Inputs
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
(acos.f64 #s(approx (- 1 x) x))
(acos.f64 #s(approx (- 1 x) (neg.f64 x)))
Outputs
(acos.f64 #s(approx (- 1 x) x))
Calls

3 calls:

2.0ms
x
1.0ms
(acos.f64 (-.f64 #s(literal 1 binary64) x))
1.0ms
(-.f64 #s(literal 1 binary64) x)
Results
AccuracySegmentsBranch
6.9%1x
6.9%1(-.f64 #s(literal 1 binary64) x)
6.9%1(acos.f64 (-.f64 #s(literal 1 binary64) x))
Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes3.0ms (0.1%)

Memory
6.5MiB live, 6.5MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
Outputs
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
Calls

3 calls:

1.0ms
x
1.0ms
(acos.f64 (-.f64 #s(literal 1 binary64) x))
1.0ms
(-.f64 #s(literal 1 binary64) x)
Results
AccuracySegmentsBranch
3.8%1x
3.8%1(acos.f64 (-.f64 #s(literal 1 binary64) x))
3.8%1(-.f64 #s(literal 1 binary64) x)
Compiler

Compiled 11 to 8 computations (27.3% saved)

bsearch0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
0.9999999999999999
1.0
Compiler

Compiled 8 to 8 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
0.0
1.4901161193847656e-8
Compiler

Compiled 8 to 8 computations (0% saved)

simplify10.0ms (0.2%)

Memory
16.1MiB live, 16.1MiB allocated
Algorithm
egg-herbie
Rules
20×+-commutative_binary64
20×sub-neg_binary64
18×*-commutative_binary64
14×neg-sub0_binary64
14×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
046138
166138
283138
393138
496138
Stop Event
saturated
Calls
Call 1
Inputs
(fma.f64 (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
(if (<=.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 9007199254740991/9007199254740992 binary64)) #s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))) (acos.f64 #s(approx (- 1 x) x)))
(if (<=.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 0 binary64)) (acos.f64 #s(approx (- 1 x) x)) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(acos.f64 #s(approx (- 1 x) x))
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))
Outputs
(fma.f64 (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (asin.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 #s(approx (- 1 x) (-.f64 #s(literal 1 binary64) x)))))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
#s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (fma.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x))))))
(if (<=.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 9007199254740991/9007199254740992 binary64)) #s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))) (acos.f64 #s(approx (- 1 x) x)))
(if (<=.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 9007199254740991/9007199254740992 binary64)) #s(approx (+ (* (sqrt (PI)) (* (sqrt (PI)) 1/2)) (neg (asin (- 1 x)))) (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (asin.f64 (-.f64 #s(literal 1 binary64) x)))) (acos.f64 #s(approx (- 1 x) x)))
(if (<=.f64 (acos.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 0 binary64)) (acos.f64 #s(approx (- 1 x) x)) (acos.f64 (-.f64 #s(literal 1 binary64) x)))
(acos.f64 #s(approx (- 1 x) x))
(acos.f64 #s(approx (- 1 x) #s(literal 1 binary64)))

soundness425.0ms (7.8%)

Memory
-16.5MiB live, 258.4MiB allocated
Rules
10 972×lower-fma.f32
10 962×lower-fma.f64
5 414×lower-*.f32
5 408×lower-*.f64
4 396×lower-*.f64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0826
01126
13726
220326
3173223
0915423
021224
141224
277224
3134224
4206224
5292224
6353224
7387224
8438224
9455224
10463224
0463224
01480
12980
26280
311380
417180
523980
625980
025980
039210
068183
1264166
21898166
09204163
Stop Event
fuel
iter limit
node limit
iter limit
iter limit
saturated
iter limit
saturated
iter limit
node limit
iter limit
Compiler

Compiled 330 to 174 computations (47.3% saved)

preprocess64.0ms (1.2%)

Memory
15.0MiB live, 97.2MiB allocated
Compiler

Compiled 216 to 76 computations (64.8% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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