Hyperbolic arc-(co)secant

Time bar (total: 5.7s)

start0.0ms (0%)

Memory
0.0MiB live, 0.1MiB allocated

analyze40.0ms (0.7%)

Memory
-32.5MiB live, 6.0MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
0%0%50%0%0%50%0%3
33.3%12.5%25%0%0%62.5%0%4
60%18.7%12.5%0%0%68.7%0%5
77.8%21.9%6.2%0%0%71.8%0%6
88.2%23.4%3.1%0%0%73.4%0%7
93.9%24.2%1.6%0%0%74.2%0%8
96.9%24.6%0.8%0%0%74.6%0%9
98.4%24.8%0.4%0%0%74.8%0%10
99.2%24.9%0.2%0%0%74.9%0%11
99.6%24.9%0.1%0%0%74.9%0%12
Compiler

Compiled 15 to 11 computations (26.7% saved)

sample958.0ms (16.9%)

Memory
12.4MiB live, 1 449.5MiB allocated
Samples
678.0ms8 256×0valid
1.0ms18×0invalid
Precisions
Click to see histograms. Total time spent on operations: 522.0ms
ival-div: 114.0ms (21.8% of total)
ival-log: 102.0ms (19.5% of total)
ival-sqrt: 95.0ms (18.2% of total)
ival-mult: 84.0ms (16.1% of total)
ival-add: 57.0ms (10.9% of total)
ival-sub: 56.0ms (10.7% of total)
ival-true: 6.0ms (1.1% of total)
exact: 4.0ms (0.8% of total)
ival-assert: 3.0ms (0.6% of total)
Bogosity

explain243.0ms (4.3%)

Memory
-10.8MiB live, 189.2MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
00-0-#s(literal 1 binary64)
00-0-(/.f64 #s(literal 1 binary64) x)
00-0-(*.f64 x x)
00-0-(-.f64 #s(literal 1 binary64) (*.f64 x x))
00-0-(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
00-0-(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)
00-0-x
00-0-(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
Confusion
Predicted +Predicted -
+00
-0256
Precision
0/0
Recall
0/0
Confusion?
Predicted +Predicted MaybePredicted -
+000
-00256
Precision?
0/0
Recall?
0/0
Freqs
test
numberfreq
0256
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-001
Precision?
0/0
Recall?
0/0
Samples
38.0ms512×0valid
Compiler

Compiled 122 to 31 computations (74.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 25.0ms
ival-div: 7.0ms (27.8% of total)
ival-log: 6.0ms (23.9% of total)
ival-sqrt: 4.0ms (15.9% of total)
ival-mult: 3.0ms (11.9% of total)
ival-add: 2.0ms (8% of total)
ival-sub: 2.0ms (8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

preprocess349.0ms (6.2%)

Memory
13.0MiB live, 211.2MiB allocated
Algorithm
1×egg-herbie
Rules
28 400×lower-fma.f64
28 400×lower-fma.f32
3 690×lower-*.f32
3 688×lower-*.f64
2 256×lower-+.f32
Iterations

Useful iterations: 14 (0.0ms)

IterNodesCost
01131
13427
27127
315327
426127
540927
663323
7100823
8142423
9199523
10439123
11587223
12690123
13731123
14767923
15783523
0913
01613
12413
23113
33913
45413
57413
611713
731513
859713
9116713
10209913
11383413
12482613
13518313
14551811
15577711
16585811
17606911
18698911
0804511
Stop Event
1×iter limit
1×node limit
1×iter limit
1×node limit
Calls
Call 1
Inputs
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
Outputs
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
(log.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64)) x))
Compiler

Compiled 14 to 9 computations (35.7% saved)

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
▶100.0%
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify286.0ms (5.1%)

Memory
9.9MiB live, 161.7MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)
cost-diff0
(/.f64 #s(literal 1 binary64) x)
cost-diff0
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
cost-diff704
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
Rules
28 400×lower-fma.f64
28 400×lower-fma.f32
3 690×lower-*.f32
3 688×lower-*.f64
2 256×lower-+.f32
Iterations

Useful iterations: 14 (0.0ms)

IterNodesCost
0952
01652
12452
23152
33952
45452
57452
611752
731552
859752
9116752
10209952
11383452
12482652
13518352
14551848
15577748
16585848
17606948
18698948
0804548
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)
Outputs
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
(log.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64)) x))
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
(/.f64 (-.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64)) x)
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)

localize78.0ms (1.4%)

Memory
13.9MiB live, 63.3MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 x x)
accuracy0
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
accuracy0.00390625
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
accuracy0.0078125
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
Samples
71.0ms256×0valid
Compiler

Compiled 54 to 11 computations (79.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 30.0ms
ival-log: 21.0ms (69.2% of total)
ival-div: 3.0ms (9.9% of total)
ival-sqrt: 2.0ms (6.6% of total)
ival-add: 1.0ms (3.3% of total)
ival-mult: 1.0ms (3.3% of total)
ival-sub: 1.0ms (3.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series21.0ms (0.4%)

Memory
-27.3MiB live, 8.8MiB allocated
Counts
6 → 72
Calls
Call 1
Inputs
#s(alt (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) (patch (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) #<representation binary64>) () ())
#s(alt (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) (patch (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) (patch (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) #<representation binary64>) () ())
#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
Outputs
#s(alt (/ 2 x) (taylor 0 x) (#s(alt (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) (patch (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* -1/2 (pow x 2))) x) (taylor 0 x) (#s(alt (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) (patch (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x) (taylor 0 x) (#s(alt (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) (patch (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x) (taylor 0 x) (#s(alt (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) (patch (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (* -1 (log x))) (taylor 0 x) (#s(alt (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) (patch (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2)))) (taylor 0 x) (#s(alt (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) (patch (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4)))) (taylor 0 x) (#s(alt (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) (patch (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4)))) (taylor 0 x) (#s(alt (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) (patch (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) (patch (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1/2 (pow x 2))) x) (taylor 0 x) (#s(alt (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) (patch (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x) (taylor 0 x) (#s(alt (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) (patch (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x) (taylor 0 x) (#s(alt (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) (patch (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor inf x) (#s(alt (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) (patch (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (/ 1 x)) (taylor inf x) (#s(alt (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) (patch (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x))) (taylor inf x) (#s(alt (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) (patch (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) #<representation binary64>) () ())) ())
#s(alt (- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))) (taylor inf x) (#s(alt (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) (patch (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) #<representation binary64>) () ())) ())
#s(alt (log (sqrt -1)) (taylor inf x) (#s(alt (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) (patch (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) #<representation binary64>) () ())) ())
#s(alt (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (taylor inf x) (#s(alt (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) (patch (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) #<representation binary64>) () ())) ())
#s(alt (- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3)))) (taylor inf x) (#s(alt (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) (patch (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) #<representation binary64>) () ())) ())
#s(alt (- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))) (taylor inf x) (#s(alt (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) (patch (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor inf x) (#s(alt (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) (patch (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))) (taylor inf x) (#s(alt (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) (patch (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) #<representation binary64>) () ())) ())
#s(alt (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))) (taylor inf x) (#s(alt (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) (patch (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) #<representation binary64>) () ())) ())
#s(alt (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))) (taylor inf x) (#s(alt (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) (patch (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt -1)) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt -1)) (taylor -inf x) (#s(alt (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) (patch (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (sqrt -1)) (/ 1 x)) (taylor -inf x) (#s(alt (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) (patch (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x))) (taylor -inf x) (#s(alt (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) (patch (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x))) (taylor -inf x) (#s(alt (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) (patch (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)) #<representation binary64>) () ())) ())
#s(alt (log (* -1 (sqrt -1))) (taylor -inf x) (#s(alt (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) (patch (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) #<representation binary64>) () ())) ())
#s(alt (- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1)))) (taylor -inf x) (#s(alt (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) (patch (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) #<representation binary64>) () ())) ())
#s(alt (+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x))) (taylor -inf x) (#s(alt (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) (patch (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) #<representation binary64>) () ())) ())
#s(alt (+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x))) (taylor -inf x) (#s(alt (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) (patch (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt -1)) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) (patch (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (sqrt -1)) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) (patch (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (sqrt -1)) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))) (/ 1/2 (* (pow x 2) (sqrt -1)))) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) (patch (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (sqrt -1)) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) (patch (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
16.0ms
x
@inf
((+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (/ 1 x) (/ (sqrt (- 1 (* x x))) x) (sqrt (- 1 (* x x))) (* x x))
2.0ms
x
@-inf
((+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (/ 1 x) (/ (sqrt (- 1 (* x x))) x) (sqrt (- 1 (* x x))) (* x x))
2.0ms
x
@0
((+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (/ 1 x) (/ (sqrt (- 1 (* x x))) x) (sqrt (- 1 (* x x))) (* x x))

simplify187.0ms (3.3%)

Memory
18.1MiB live, 136.9MiB allocated
Algorithm
1×egg-herbie
Rules
17 138×lower-fma.f64
17 138×lower-fma.f32
3 282×lower-*.f64
3 282×lower-*.f32
2 100×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0155803
1409778
21098758
33208745
47995745
08477716
Stop Event
1×iter limit
1×node limit
Counts
72 → 72
Calls
Call 1
Inputs
(/ 2 x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
(+ (log 2) (* -1 (log x)))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ (+ 1 (* -1/2 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(sqrt -1)
(+ (sqrt -1) (/ 1 x))
(+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))
(- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(log (sqrt -1))
(+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))
(- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
(- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))
(- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (sqrt -1))
(+ (* -1 (sqrt -1)) (/ 1 x))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))
(log (* -1 (sqrt -1)))
(- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(* -1 (sqrt -1))
(- (* -1 (sqrt -1)) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
(- (+ (* -1 (sqrt -1)) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))) (/ 1/2 (* (pow x 2) (sqrt -1))))
(- (+ (* -1 (sqrt -1)) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5))))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
Outputs
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64)) x)
(+ (log 2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(fma.f64 (*.f64 #s(literal -1/4 binary64) x) x (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))
(fma.f64 (*.f64 (fma.f64 #s(literal -3/32 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x) x (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))
(fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -5/96 binary64) (*.f64 x x) #s(literal -3/32 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) x) x (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 x))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))
(+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))
(- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(+.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x x))) (sqrt.f64 #s(literal -1 binary64)))
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))
(-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (log.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (*.f64 x x) x) (sqrt.f64 #s(literal -1 binary64)))))
(- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
(-.f64 (+.f64 (+.f64 (/.f64 #s(literal 3/40 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (*.f64 x x) x) (sqrt.f64 #s(literal -1 binary64)))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
(+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (sqrt.f64 #s(literal -1 binary64)))
(- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x x)))
(- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(-.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x x))) (/.f64 #s(literal -1/16 binary64) (*.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))))
(* x (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(fma.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* -1 (sqrt -1))
(neg.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (/ 1 x))
(-.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))
(-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))
(-.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 x x) x) (sqrt.f64 #s(literal -1 binary64)))) (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal 1 binary64))) x) (sqrt.f64 #s(literal -1 binary64)))
(log (* -1 (sqrt -1)))
(log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))
(-.f64 (-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 (*.f64 x x) x) (sqrt.f64 #s(literal -1 binary64)))))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))
(-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 3/40 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x))) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (sqrt -1))
(neg.f64 (sqrt.f64 #s(literal -1 binary64)))
(- (* -1 (sqrt -1)) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (sqrt.f64 #s(literal -1 binary64)))
(- (+ (* -1 (sqrt -1)) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))) (/ 1/2 (* (pow x 2) (sqrt -1))))
(-.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)))
(- (+ (* -1 (sqrt -1)) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5))))))
(-.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* x (sqrt -1)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64))) x (/.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
(fma.f64 (-.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))) x (/.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite205.0ms (3.6%)

Memory
-3.9MiB live, 267.9MiB allocated
Rules
4 520×lower-fma.f64
4 520×lower-fma.f32
3 106×lower-*.f32
3 104×lower-*.f64
2 972×lower-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0945
01645
16945
262441
3759641
0835441
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
6 → 334
Calls
Call 1
Inputs
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
(/.f64 #s(literal 1 binary64) x)
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 x x)
Outputs
(*.f64 (/.f64 (/.f64 (fma.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) x x) x) (neg.f64 x)) #s(literal -1 binary64))
(*.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (*.f64 x x)) (*.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))))) (*.f64 x x))
(*.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (*.f64 x x)) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))) (*.f64 (*.f64 x x) x))) (fma.f64 (+.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (*.f64 x x))))
(*.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (*.f64 x x)) (+.f64 (neg.f64 x) (*.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) x))) (*.f64 (neg.f64 x) x))
(*.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (*.f64 x x)) (+.f64 (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) x)) (/.f64 (*.f64 (neg.f64 x) x) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))))
(*.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (*.f64 x x)) (-.f64 (/.f64 x (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) x)) (/.f64 (*.f64 x x) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))))
(*.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (*.f64 x x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))) (neg.f64 x))
(*.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))) x)
(*.f64 (/.f64 (*.f64 (fma.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 x x)) (*.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (*.f64 x x)) (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (*.f64 x x))))) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (*.f64 x x))))
(*.f64 (/.f64 (*.f64 (fma.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (fma.f64 (*.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (*.f64 x x)) (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (*.f64 x x))) (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x))))) (fma.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (*.f64 x x)) (-.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 x x))))
(*.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (*.f64 x x)) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (*.f64 x x))) (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x))
(*.f64 (*.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (*.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (*.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (*.f64 (fma.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 (/.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x) (/.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) x) (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))))
(*.f64 (/.f64 (fma.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) x x) x) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))))
(*.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x)))
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (*.f64 x x)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 x x)))) (*.f64 (fma.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))))
(*.f64 (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) x)))
(*.f64 (neg.f64 (*.f64 (fma.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (/.f64 (-.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 x x))))))
(*.f64 (neg.f64 (fma.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) x x)) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x)))
(*.f64 (+.f64 (/.f64 (neg.f64 x) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (neg.f64 x)) (/.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (*.f64 (neg.f64 x) x)))
(*.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) x) (/.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (*.f64 x x)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (*.f64 x x)) (/.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))))
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(pow.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(/.f64 (*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 (neg.f64 x) x) x) x #s(literal 1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)))) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 (*.f64 (neg.f64 x) x) x) x #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x))))) (sqrt.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 (neg.f64 x) x) x) x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x))))) (neg.f64 (sqrt.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 x x) x) x))) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x))))) (sqrt.f64 (neg.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 (neg.f64 x) x) x) x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)))) (sqrt.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (*.f64 (*.f64 (neg.f64 x) x) x) x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))))
(neg.f64 (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))))
(sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))))
(exp.f64 (*.f64 (log1p.f64 (*.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) x))
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(/.f64 (*.f64 (neg.f64 x) x) #s(literal -1 binary64))
(/.f64 (*.f64 x x) #s(literal 1 binary64))
(/.f64 x (/.f64 #s(literal 1 binary64) x))
(neg.f64 (*.f64 (neg.f64 x) x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval190.0ms (3.4%)

Memory
15.5MiB live, 97.3MiB allocated
Compiler

Compiled 10 549 to 1 324 computations (87.4% saved)

prune46.0ms (0.8%)

Memory
-2.8MiB live, 121.1MiB allocated
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New4024406
Fresh000
Picked101
Done000
Total4034407
Accuracy
100.0%
Counts
407 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x))
▶99.4%
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)))
▶98.9%
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
▶0.0%
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))))
Compiler

Compiled 34 to 23 computations (32.4% saved)

simplify157.0ms (2.8%)

Memory
2.1MiB live, 79.2MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
cost-diff0
(+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64))
cost-diff0
(/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x)
cost-diff0
(log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x))
cost-diff0
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64))
cost-diff0
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x))
cost-diff0
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)))
cost-diff320
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)
cost-diff0
(/.f64 #s(literal 2 binary64) x)
cost-diff0
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x))
cost-diff0
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
cost-diff0
(sqrt.f64 #s(literal -1 binary64))
cost-diff0
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64)))
cost-diff0
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))))
Rules
9 494×lower-fma.f32
9 490×lower-fma.f64
2 622×lower-*.f32
2 620×lower-*.f64
2 476×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
028179
044179
159179
267179
378179
491179
5111179
6171179
7376179
8652179
91256179
102343179
113474179
124592164
136135164
08197161
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64)))
(sqrt.f64 #s(literal -1 binary64))
#s(literal -1 binary64)
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)))
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x))
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64))
(*.f64 x x)
x
#s(literal -1/2 binary64)
#s(literal 2 binary64)
(log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x))
(/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x)
(+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64))
(sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(neg.f64 x)
x
#s(literal 1 binary64)
Outputs
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64)))
(sqrt.f64 #s(literal -1 binary64))
#s(literal -1 binary64)
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)))
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x))
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
x
#s(literal -1/2 binary64)
#s(literal 2 binary64)
(log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x))
(log.f64 (/.f64 (-.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal -1 binary64)) x))
(/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x)
(/.f64 (-.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal -1 binary64)) x)
(+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64))
(-.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal -1 binary64))
(sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(neg.f64 x)
x
#s(literal 1 binary64)

localize92.0ms (1.6%)

Memory
1.5MiB live, 115.2MiB allocated
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
accuracy0
(+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy0
(sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
accuracy0
(neg.f64 x)
accuracy0
(log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x))
accuracy0
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)
accuracy0
(*.f64 x x)
accuracy0
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)))
accuracy0
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x))
accuracy0
(/.f64 #s(literal 2 binary64) x)
accuracy0
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
accuracy0
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x))
accuracy0
(sqrt.f64 #s(literal -1 binary64))
accuracy0
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))))
accuracy0
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64)))
Samples
71.0ms256×0invalid
Compiler

Compiled 156 to 26 computations (83.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 47.0ms
ival-add: 20.0ms (42.8% of total)
ival-div: 8.0ms (17.1% of total)
ival-log: 6.0ms (12.8% of total)
ival-mult: 5.0ms (10.7% of total)
ival-sqrt: 5.0ms (10.7% of total)
ival-sub: 1.0ms (2.1% of total)
ival-neg: 1.0ms (2.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series19.0ms (0.3%)

Memory
-21.1MiB live, 16.3MiB allocated
Counts
16 → 180
Calls
Call 1
Inputs
#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64)))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal -1 binary64)) (patch (sqrt.f64 #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())
#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 2 binary64) x) (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x) (patch (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x) #<representation binary64>) () ())
#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x))) #<representation binary64>) () ())
#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x)) (patch (log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x) (patch (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (patch (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())
Outputs
#s(alt (+ (log 2) (* -1 (log x))) (taylor 0 x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64)))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2)))) (taylor 0 x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64)))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4)))) (taylor 0 x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64)))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4)))) (taylor 0 x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64)))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor 0 x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* -1/2 (pow x 2))) x) (taylor 0 x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x) (taylor 0 x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x) (taylor 0 x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (log (* -1 (sqrt -1))) (taylor -inf x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1)))) (taylor -inf x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x))) (taylor -inf x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x))) (taylor -inf x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt -1)) (taylor -inf x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (sqrt -1)) (/ 1 x)) (taylor -inf x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x))) (taylor -inf x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x))) (taylor -inf x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2)) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2)) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2)) (taylor -inf x) (#s(alt (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (log (* -1 (sqrt -1))) (taylor -inf x) (#s(alt (log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x)) (patch (log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1)))) (taylor -inf x) (#s(alt (log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x)) (patch (log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x))) (taylor -inf x) (#s(alt (log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x)) (patch (log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x))) (taylor -inf x) (#s(alt (log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x)) (patch (log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt -1)) (taylor -inf x) (#s(alt (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x) (patch (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (sqrt -1)) (/ 1 x)) (taylor -inf x) (#s(alt (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x) (patch (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x))) (taylor -inf x) (#s(alt (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x) (patch (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x))) (taylor -inf x) (#s(alt (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x) (patch (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt -1))) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (sqrt -1) (/ 1 x)))) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (* -1 (/ (- 1 (* 1/2 (/ 1 (* x (sqrt -1))))) x))))) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (* -1 (/ (+ 1 (* -1 (/ (- (* 1/2 (/ 1 (sqrt -1))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x))) x))))) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (patch (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (patch (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (patch (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (patch (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
((log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt -1) (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/ 2 x) (/ (+ (* (* x x) -1/2) 2) x) (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (+ (* (* x x) -1/2) 2) (log (/ (+ (sqrt (+ (* (neg x) x) 1)) 1) x)) (/ (+ (sqrt (+ (* (neg x) x) 1)) 1) x) (+ (sqrt (+ (* (neg x) x) 1)) 1) (sqrt (+ (* (neg x) x) 1)) (* x x) (neg x))
2.0ms
x
@inf
((log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt -1) (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/ 2 x) (/ (+ (* (* x x) -1/2) 2) x) (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (+ (* (* x x) -1/2) 2) (log (/ (+ (sqrt (+ (* (neg x) x) 1)) 1) x)) (/ (+ (sqrt (+ (* (neg x) x) 1)) 1) x) (+ (sqrt (+ (* (neg x) x) 1)) 1) (sqrt (+ (* (neg x) x) 1)) (* x x) (neg x))
1.0ms
x
@0
((log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt -1) (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/ 2 x) (/ (+ (* (* x x) -1/2) 2) x) (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (+ (* (* x x) -1/2) 2) (log (/ (+ (sqrt (+ (* (neg x) x) 1)) 1) x)) (/ (+ (sqrt (+ (* (neg x) x) 1)) 1) x) (+ (sqrt (+ (* (neg x) x) 1)) 1) (sqrt (+ (* (neg x) x) 1)) (* x x) (neg x))

simplify222.0ms (3.9%)

Memory
5.7MiB live, 181.2MiB allocated
Algorithm
1×egg-herbie
Rules
22 142×lower-fma.f64
22 142×lower-fma.f32
3 454×lower-*.f64
3 454×lower-*.f32
3 330×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01782001
14931924
213551865
339801857
081581765
Stop Event
1×iter limit
1×node limit
Counts
180 → 180
Calls
Call 1
Inputs
(+ (log 2) (* -1 (log x)))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))
(/ 2 x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
(+ (log 2) (* -1 (log x)))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))
(/ 2 x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(+ (log 2) (* -1 (log x)))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))
(/ 2 x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
2
(+ 2 (* -1/2 (pow x 2)))
(+ 2 (* -1/2 (pow x 2)))
(+ 2 (* -1/2 (pow x 2)))
(+ (log 2) (* -1 (log x)))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))
(/ 2 x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
2
(+ 2 (* -1/2 (pow x 2)))
(+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(log (sqrt -1))
(+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))
(- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
(sqrt -1)
(+ (sqrt -1) (/ 1 x))
(+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))
(- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(log (sqrt -1))
(+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))
(- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
(sqrt -1)
(+ (sqrt -1) (/ 1 x))
(+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))
(- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(* -1/2 x)
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(log (sqrt -1))
(+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))
(- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
(sqrt -1)
(+ (sqrt -1) (/ 1 x))
(+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))
(- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(log (sqrt -1))
(+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))
(- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
(sqrt -1)
(+ (sqrt -1) (/ 1 x))
(+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))
(- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (sqrt -1))
(* x (+ (sqrt -1) (/ 1 x)))
(* x (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x))))
(* x (- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(log (* -1 (sqrt -1)))
(- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))
(* -1 (sqrt -1))
(+ (* -1 (sqrt -1)) (/ 1 x))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))
(log (* -1 (sqrt -1)))
(- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))
(* -1 (sqrt -1))
(+ (* -1 (sqrt -1)) (/ 1 x))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(* -1/2 x)
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(log (* -1 (sqrt -1)))
(- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))
(* -1 (sqrt -1))
(+ (* -1 (sqrt -1)) (/ 1 x))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(log (* -1 (sqrt -1)))
(- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))
(* -1 (sqrt -1))
(+ (* -1 (sqrt -1)) (/ 1 x))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))
(* -1 (* x (sqrt -1)))
(* -1 (* x (- (sqrt -1) (/ 1 x))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (- 1 (* 1/2 (/ 1 (* x (sqrt -1))))) x)))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ 1 (* -1 (/ (- (* 1/2 (/ 1 (sqrt -1))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x))) x)))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
Outputs
(+ (log 2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(fma.f64 (*.f64 #s(literal -1/4 binary64) x) x (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))
(fma.f64 (*.f64 (fma.f64 #s(literal -3/32 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x) x (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))
(fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -5/96 binary64) (*.f64 x x) #s(literal -3/32 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) x) x (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64)) x)
(+ (log 2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(fma.f64 (*.f64 #s(literal -1/4 binary64) x) x (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))
(fma.f64 (*.f64 (fma.f64 #s(literal -3/32 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x) x (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))
(fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -5/96 binary64) (*.f64 x x) #s(literal -3/32 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) x) x (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64)) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) x)
(+ (log 2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(fma.f64 (*.f64 #s(literal -1/4 binary64) x) x (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))
(fma.f64 (*.f64 (fma.f64 #s(literal -3/32 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x) x (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))
(fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -5/96 binary64) (*.f64 x x) #s(literal -3/32 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) x) x (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64)) x)
2
#s(literal 2 binary64)
(+ 2 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))
(+ 2 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))
(+ 2 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))
(+ (log 2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(fma.f64 (*.f64 #s(literal -1/4 binary64) x) x (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))
(fma.f64 (*.f64 (fma.f64 #s(literal -3/32 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x) x (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))
(fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -5/96 binary64) (*.f64 x x) #s(literal -3/32 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) x) x (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64)) x)
2
#s(literal 2 binary64)
(+ 2 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))
(-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (log.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x)))
(- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
(-.f64 (+.f64 (+.f64 (/.f64 #s(literal 3/40 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x)))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 x))
(+.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (+.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64))))
(- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (+.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)))))
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))
(-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (log.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x)))
(- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
(-.f64 (+.f64 (+.f64 (/.f64 #s(literal 3/40 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x)))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 x))
(+.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (+.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64))))
(- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (+.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)))))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x))
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))
(-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (log.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x)))
(- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
(-.f64 (+.f64 (+.f64 (/.f64 #s(literal 3/40 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x)))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 x))
(+.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (+.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64))))
(- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (+.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1/2 (pow x 2))
(*.f64 #s(literal -1/2 binary64) (*.f64 x x))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))
(-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (log.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x)))
(- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
(-.f64 (+.f64 (+.f64 (/.f64 #s(literal 3/40 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x)))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 x))
(+.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (+.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64))))
(- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (+.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)))))
(* x (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(* x (+ (sqrt -1) (/ 1 x)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x #s(literal 1 binary64))
(* x (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x))))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal 1 binary64)))
(* x (- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))) x (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal 1 binary64)))
(* x (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(fma.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(log (* -1 (sqrt -1)))
(log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))
(-.f64 (-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))
(-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 3/40 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x))) x))
(* -1 (sqrt -1))
(neg.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (/ 1 x))
(-.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))
(-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))
(-.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1/8 binary64) x)) #s(literal 1 binary64)) x) (sqrt.f64 #s(literal -1 binary64)))
(log (* -1 (sqrt -1)))
(log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))
(-.f64 (-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))
(-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 3/40 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x))) x))
(* -1 (sqrt -1))
(neg.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (/ 1 x))
(-.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))
(-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))
(-.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1/8 binary64) x)) #s(literal 1 binary64)) x) (sqrt.f64 #s(literal -1 binary64)))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(fma.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(fma.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(fma.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x))
(log (* -1 (sqrt -1)))
(log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))
(-.f64 (-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))
(-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 3/40 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x))) x))
(* -1 (sqrt -1))
(neg.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (/ 1 x))
(-.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))
(-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))
(-.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1/8 binary64) x)) #s(literal 1 binary64)) x) (sqrt.f64 #s(literal -1 binary64)))
(* -1/2 (pow x 2))
(*.f64 #s(literal -1/2 binary64) (*.f64 x x))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))
(log (* -1 (sqrt -1)))
(log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))
(-.f64 (-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))
(-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 3/40 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x))) x))
(* -1 (sqrt -1))
(neg.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (/ 1 x))
(-.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))
(-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))
(-.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1/8 binary64) x)) #s(literal 1 binary64)) x) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* x (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(* -1 (* x (- (sqrt -1) (/ 1 x))))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 x) #s(literal 1 binary64))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (- 1 (* 1/2 (/ 1 (* x (sqrt -1))))) x)))))
(-.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ 1 (* -1 (/ (- (* 1/2 (/ 1 (sqrt -1))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x))) x)))))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 1/8 binary64) x)) #s(literal -1 binary64))))
(* -1 (* x (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 x (-.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
(neg.f64 (fma.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)

rewrite226.0ms (4%)

Memory
-16.9MiB live, 224.3MiB allocated
Rules
4 702×lower-/.f32
4 696×lower-/.f64
4 280×lower-fma.f32
4 276×lower-fma.f64
3 874×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
028166
044166
1161154
21215154
08665143
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
16 → 504
Calls
Call 1
Inputs
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64)))
(sqrt.f64 #s(literal -1 binary64))
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 2 binary64) x)
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)))
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64))
(log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x))
(/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x)
(+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64))
(sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
(*.f64 x x)
(neg.f64 x)
Outputs
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))
(pow.f64 #s(literal 1 binary64) #s(literal 1/4 binary64))
(sqrt.f64 #s(literal -1 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) x))
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 x #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))
(/.f64 #s(literal -2 binary64) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 #s(literal -2 binary64) (neg.f64 x))
(/.f64 #s(literal 2 binary64) (neg.f64 (neg.f64 x)))
(/.f64 #s(literal 2 binary64) x)
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 x #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(neg.f64 (/.f64 #s(literal -2 binary64) x))
(exp.f64 (*.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -4 binary64)) x) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64))) #s(literal 1 binary64)))
(*.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -4 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64))) x))
(*.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal 8 binary64)) x) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 x x) #s(literal -1 binary64))))) #s(literal 1 binary64)))
(*.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal 8 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 x x) #s(literal -1 binary64))))) x))
(*.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (pow.f64 (/.f64 x (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -4 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64))))
(*.f64 (pow.f64 (/.f64 x (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal 8 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 x x) #s(literal -1 binary64))))))
(*.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -4 binary64)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64))))
(*.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 x x) #s(literal -1 binary64))))))
(*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) #s(literal -1 binary64)))
(*.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) x))
(*.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -4 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64)) (neg.f64 x))))
(*.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -4 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64)) x)))
(*.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal 8 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 x x) #s(literal -1 binary64)))) (neg.f64 x))))
(*.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal 8 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 x x) #s(literal -1 binary64)))) x)))
(*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -4 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64)))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 x x) #s(literal -1 binary64)))))))
(*.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) x) #s(literal 1 binary64))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) x))
(pow.f64 (/.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -4 binary64)) (/.f64 #s(literal 1 binary64) x))) (neg.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) x))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 x x) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) #s(literal -1 binary64))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 x))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))))) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -4 binary64)) #s(literal -1 binary64))) (neg.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64)) (neg.f64 x))))
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -4 binary64)) #s(literal 1 binary64))) (neg.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64)) x)))
(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal 8 binary64)) #s(literal -1 binary64))) (neg.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 x x) #s(literal -1 binary64)))) (neg.f64 x))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal 8 binary64)) #s(literal 1 binary64))) (neg.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 x x) #s(literal -1 binary64)))) x)))
(/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -4 binary64)) (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64)))
(/.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 x x) #s(literal -1 binary64)))))
(/.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) #s(literal -1 binary64)) (neg.f64 x))
(/.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) x)
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -4 binary64))) (neg.f64 (*.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal 8 binary64))) (neg.f64 (*.f64 x (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 x x) #s(literal -1 binary64)))))))
(/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -4 binary64)) #s(literal -1 binary64)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64)) (neg.f64 x)))
(/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -4 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64)) x))
(/.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal 8 binary64)) #s(literal -1 binary64)) (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 x x) #s(literal -1 binary64)))) (neg.f64 x)))
(/.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal 8 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 x x) #s(literal -1 binary64)))) x))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -4 binary64)) (*.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64))))
(/.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal 8 binary64)) (*.f64 x (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 x x) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))) (neg.f64 x))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) x)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64)) (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -4 binary64)) (/.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 x x) #s(literal -1 binary64)))) (*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64)) (neg.f64 x)) (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -4 binary64)) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64)) x) (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -4 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 x x) #s(literal -1 binary64)))) (neg.f64 x)) (*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal 8 binary64)) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 x x) #s(literal -1 binary64)))) x) (*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal 8 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) #s(literal -4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x) (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 x x) #s(literal -1 binary64))))) (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal 8 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))) x))
(neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) (neg.f64 x)))
(-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x)) (*.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64)))) (/.f64 #s(literal 4 binary64) (*.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 x)) (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) (neg.f64 x)))
(-.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 x x) x) x)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64))) x) (/.f64 (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -2 binary64))) x))
(exp.f64 (*.f64 (log.f64 (/.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)))) #s(literal -1 binary64)))
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(fma.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal 1 binary64))))) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal 1 binary64))))) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
(-.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)))
(+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (sqrt.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(*.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) x))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal 1 binary64))))))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal 1 binary64))))))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(pow.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))
(pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) x)))) (neg.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) x)))) (sqrt.f64 (neg.f64 (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) x))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x)))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) x (fma.f64 x x #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
(fabs.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(exp.f64 (*.f64 (log1p.f64 (*.f64 x x)) #s(literal 1/2 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x)))))
(*.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) x)))
(*.f64 #s(literal -1 binary64) x)
(*.f64 x #s(literal -1 binary64))
(/.f64 (+.f64 #s(literal 0 binary64) (*.f64 (neg.f64 x) (*.f64 x x))) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) (*.f64 #s(literal 0 binary64) (neg.f64 x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) x))) (neg.f64 (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x)))))
(/.f64 (neg.f64 (*.f64 (neg.f64 x) x)) (neg.f64 (+.f64 #s(literal 0 binary64) x)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) x)) (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x))))
(/.f64 (*.f64 (neg.f64 x) x) (+.f64 #s(literal 0 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x))) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x x) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) x) (*.f64 (neg.f64 x) x)))
(neg.f64 x)
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x)))) (/.f64 (*.f64 (*.f64 x x) x) (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x)))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) x)) (/.f64 (*.f64 x x) (+.f64 #s(literal 0 binary64) x)))
(-.f64 #s(literal 0 binary64) x)
(+.f64 #s(literal 0 binary64) (neg.f64 x))

eval114.0ms (2%)

Memory
15.8MiB live, 124.1MiB allocated
Compiler

Compiled 13 539 to 1 970 computations (85.4% saved)

prune104.0ms (1.8%)

Memory
5.4MiB live, 123.7MiB allocated
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New6831684
Fresh000
Picked134
Done000
Total6844688
Accuracy
100.0%
Counts
688 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x))
✓99.4%
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)))
✓98.9%
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
▶0.0%
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))))
Compiler

Compiled 36 to 23 computations (36.1% saved)

simplify161.0ms (2.8%)

Memory
15.7MiB live, 181.7MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 #s(literal -1/2 binary64) x)
cost-diff0
#s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))
cost-diff0
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))
cost-diff0
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))))
Rules
9 446×lower-fma.f64
9 446×lower-fma.f32
2 622×lower-*.f32
2 620×lower-*.f64
2 436×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01771
01971
13271
24071
34871
46371
58371
612671
733171
861771
9123371
10229071
11337071
12446765
13603165
0811462
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))))
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))
#s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
Outputs
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))))
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))
#s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x

localize65.0ms (1.1%)

Memory
-17.2MiB live, 63.6MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 #s(literal -1/2 binary64) x)
accuracy0
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))))
accuracy0.4059940244552071
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))
accuracy62.998508529063805
#s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))
Samples
26.0ms256×0valid
Compiler

Compiled 41 to 17 computations (58.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 18.0ms
ival-div: 5.0ms (27.7% of total)
ival-mult: 4.0ms (22.1% of total)
ival-log: 3.0ms (16.6% of total)
ival-add: 2.0ms (11.1% of total)
ival-sqrt: 2.0ms (11.1% of total)
ival-sub: 1.0ms (5.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory
6.6MiB live, 6.6MiB allocated
Counts
4 → 48
Calls
Call 1
Inputs
#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) #<representation binary64>) () ())
#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())
#s(alt #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal -1/2 binary64) x) (patch (*.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())
Outputs
#s(alt (+ (log 2) (* -1 (log x))) (taylor 0 x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2)))) (taylor 0 x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4)))) (taylor 0 x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4)))) (taylor 0 x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor 0 x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* -1/2 (pow x 2))) x) (taylor 0 x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x) (taylor 0 x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x) (taylor 0 x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor 0 x) (#s(alt #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* -1/2 (pow x 2))) x) (taylor 0 x) (#s(alt #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* -1/2 (pow x 2))) x) (taylor 0 x) (#s(alt #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* -1/2 (pow x 2))) x) (taylor 0 x) (#s(alt #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor 0 x) (#s(alt (*.f64 #s(literal -1/2 binary64) x) (patch (*.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor 0 x) (#s(alt (*.f64 #s(literal -1/2 binary64) x) (patch (*.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor 0 x) (#s(alt (*.f64 #s(literal -1/2 binary64) x) (patch (*.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor 0 x) (#s(alt (*.f64 #s(literal -1/2 binary64) x) (patch (*.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (log (sqrt -1)) (taylor inf x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (taylor inf x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3)))) (taylor inf x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))) (taylor inf x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor inf x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (/ 1 x)) (taylor inf x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x))) (taylor inf x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))) (taylor inf x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor inf x) (#s(alt #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 2 (/ 1 (pow x 2))) 1/2)) (taylor inf x) (#s(alt #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 2 (/ 1 (pow x 2))) 1/2)) (taylor inf x) (#s(alt #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 2 (/ 1 (pow x 2))) 1/2)) (taylor inf x) (#s(alt #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor inf x) (#s(alt (*.f64 #s(literal -1/2 binary64) x) (patch (*.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor inf x) (#s(alt (*.f64 #s(literal -1/2 binary64) x) (patch (*.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor inf x) (#s(alt (*.f64 #s(literal -1/2 binary64) x) (patch (*.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor inf x) (#s(alt (*.f64 #s(literal -1/2 binary64) x) (patch (*.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (log (* -1 (sqrt -1))) (taylor -inf x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1)))) (taylor -inf x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x))) (taylor -inf x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x))) (taylor -inf x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt -1)) (taylor -inf x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (sqrt -1)) (/ 1 x)) (taylor -inf x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x))) (taylor -inf x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x))) (taylor -inf x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) (patch #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (*.f64 #s(literal -1/2 binary64) x) (patch (*.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (*.f64 #s(literal -1/2 binary64) x) (patch (*.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (*.f64 #s(literal -1/2 binary64) x) (patch (*.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (*.f64 #s(literal -1/2 binary64) x) (patch (*.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
((log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/ (+ (* (* x x) -1/2) 2) x) (* -1/2 x))
1.0ms
x
@inf
((log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/ (+ (* (* x x) -1/2) 2) x) (* -1/2 x))
1.0ms
x
@0
((log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/ (+ (* (* x x) -1/2) 2) x) (* -1/2 x))

simplify139.0ms (2.5%)

Memory
22.0MiB live, 174.9MiB allocated
Algorithm
1×egg-herbie
Rules
8 956×lower-fma.f64
8 956×lower-fma.f32
3 258×lower-*.f64
3 258×lower-*.f32
1 682×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0132473
1333458
2857450
32372449
45932437
08086416
Stop Event
1×iter limit
1×node limit
Counts
48 → 48
Calls
Call 1
Inputs
(+ (log 2) (* -1 (log x)))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))
(/ 2 x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
(/ 2 x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(log (sqrt -1))
(+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))
(- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
(sqrt -1)
(+ (sqrt -1) (/ 1 x))
(+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))
(- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(* -1/2 x)
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(log (* -1 (sqrt -1)))
(- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))
(* -1 (sqrt -1))
(+ (* -1 (sqrt -1)) (/ 1 x))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))
(* -1/2 x)
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
Outputs
(+ (log 2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(fma.f64 (*.f64 #s(literal -1/4 binary64) x) x (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))
(fma.f64 (*.f64 (fma.f64 #s(literal -3/32 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x) x (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))
(fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -5/96 binary64) (*.f64 x x) #s(literal -3/32 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) x) x (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64)) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))
(-.f64 (log.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))
(-.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x)) (log.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
(-.f64 (-.f64 (+.f64 (/.f64 #s(literal 3/40 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 x #s(literal 5 binary64)))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 x))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))
(-.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)))
(- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(-.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x))) (*.f64 x x))) (/.f64 #s(literal -1 binary64) x))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(log (* -1 (sqrt -1)))
(log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))
(-.f64 (-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))
(-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (-.f64 (-.f64 (/.f64 #s(literal 3/40 binary64) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x))) x))
(* -1 (sqrt -1))
(neg.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (/ 1 x))
(-.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))
(-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))
(-.f64 (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x))) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) x) (sqrt.f64 #s(literal -1 binary64)))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)

rewrite134.0ms (2.4%)

Memory
-31.5MiB live, 165.1MiB allocated
Rules
6 836×lower-fma.f64
6 836×lower-fma.f32
4 126×lower-*.f32
4 124×lower-*.f64
3 494×lower-/.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01769
01969
19569
282665
0875562
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 11
Calls
Call 1
Inputs
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))))
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))
#s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))
(*.f64 #s(literal -1/2 binary64) x)
Outputs
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))))
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))
#s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))
(*.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 x #s(literal -1/2 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x))
(/.f64 (*.f64 (neg.f64 x) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal -1/2 binary64) (neg.f64 x)) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))
(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x))

eval4.0ms (0.1%)

Memory
9.8MiB live, 9.8MiB allocated
Compiler

Compiled 629 to 124 computations (80.3% saved)

prune5.0ms (0.1%)

Memory
11.8MiB live, 11.8MiB allocated
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New58159
Fresh000
Picked011
Done123
Total59463
Accuracy
100.0%
Counts
63 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x))
✓98.9%
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
▶99.4%
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))))
✓0.0%
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))))
Compiler

Compiled 35 to 22 computations (37.1% saved)

simplify133.0ms (2.4%)

Memory
9.3MiB live, 84.7MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
cost-diff0
#s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))
cost-diff0
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))
cost-diff0
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))))
Rules
9 478×lower-fma.f32
9 476×lower-fma.f64
2 622×lower-*.f64
2 622×lower-*.f32
2 436×lower-/.f32
Iterations

Useful iterations: 12 (0.0ms)

IterNodesCost
01887
02287
13687
24487
35287
46787
58787
613087
733687
862487
9124987
10232187
11341787
12450878
13605378
0812778
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))))
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))
#s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
#s(literal -1/2 binary64)
x
(/.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
Outputs
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))))
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))
#s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
#s(literal -1/2 binary64)
x
(/.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)

localize76.0ms (1.3%)

Memory
-22.0MiB live, 70.6MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(/.f64 #s(literal 2 binary64) x)
accuracy0
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))))
accuracy0
#s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))
accuracy0.4059940244552071
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))
Samples
68.0ms256×0valid
Compiler

Compiled 49 to 19 computations (61.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 48.0ms
ival-add: 28.0ms (58% of total)
ival-div: 9.0ms (18.7% of total)
ival-mult: 5.0ms (10.4% of total)
ival-log: 3.0ms (6.2% of total)
ival-sqrt: 2.0ms (4.1% of total)
ival-sub: 1.0ms (2.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory
5.2MiB live, 5.2MiB allocated
Counts
5 → 60
Calls
Call 1
Inputs
#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))) #<representation binary64>) () ())
#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))) #<representation binary64>) () ())
#s(alt #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))) (patch #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) (patch (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 2 binary64) x) (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())
Outputs
#s(alt (+ (log 2) (* -1 (log x))) (taylor 0 x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2)))) (taylor 0 x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4)))) (taylor 0 x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4)))) (taylor 0 x) (#s(alt (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))) (patch (log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor 0 x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* -1/2 (pow x 2))) x) (taylor 0 x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x) (taylor 0 x) (#s(alt #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))) (patch #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))) #<representation binary64>) () ())) ())
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Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
((log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/ (+ (* (* x x) -1/2) 2) x) (+ (* -1/2 x) (/ 2 x)) (/ 2 x))
1.0ms
x
@-inf
((log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/ (+ (* (* x x) -1/2) 2) x) (+ (* -1/2 x) (/ 2 x)) (/ 2 x))
1.0ms
x
@inf
((log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/ (+ (* (* x x) -1/2) 2) x) (+ (* -1/2 x) (/ 2 x)) (/ 2 x))

simplify145.0ms (2.6%)

Memory
-6.0MiB live, 113.1MiB allocated
Algorithm
1×egg-herbie
Rules
8 956×lower-fma.f64
8 956×lower-fma.f32
3 258×lower-*.f64
3 258×lower-*.f32
1 682×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0132563
1333548
2857540
32364539
45934515
08103485
Stop Event
1×iter limit
1×node limit
Counts
60 → 60
Calls
Call 1
Inputs
(+ (log 2) (* -1 (log x)))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))
(/ 2 x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
(/ 2 x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ 2 x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(log (sqrt -1))
(+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))
(- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
(sqrt -1)
(+ (sqrt -1) (/ 1 x))
(+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))
(- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(* -1/2 x)
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(* -1/2 x)
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(log (* -1 (sqrt -1)))
(- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))
(* -1 (sqrt -1))
(+ (* -1 (sqrt -1)) (/ 1 x))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))
(* -1/2 x)
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(* -1/2 x)
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
Outputs
(+ (log 2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(fma.f64 (*.f64 #s(literal -1/4 binary64) x) x (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))
(fma.f64 (*.f64 (fma.f64 #s(literal -3/32 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x) x (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))
(fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -5/96 binary64) (*.f64 x x) #s(literal -3/32 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) x) x (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64)) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64)) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))
(-.f64 (log.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))
(-.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x)) (log.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
(-.f64 (-.f64 (+.f64 (/.f64 #s(literal 3/40 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 x #s(literal 5 binary64)))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x))) (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 x))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))
(-.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)))
(- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(-.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x))) (*.f64 x x))) (/.f64 #s(literal -1 binary64) x))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(log (* -1 (sqrt -1)))
(log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))
(-.f64 (-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))
(-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (-.f64 (-.f64 (/.f64 #s(literal 3/40 binary64) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x))) x))
(* -1 (sqrt -1))
(neg.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (/ 1 x))
(-.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))
(-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))
(-.f64 (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) x))) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))) x) (sqrt.f64 #s(literal -1 binary64)))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)

rewrite145.0ms (2.6%)

Memory
11.5MiB live, 119.4MiB allocated
Rules
5 702×lower-fma.f32
5 700×lower-fma.f64
3 842×lower-/.f32
3 840×lower-/.f64
3 260×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01884
02284
111784
2103380
0878177
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
5 → 68
Calls
Call 1
Inputs
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))))
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))
#s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 2 binary64) x)
Outputs
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))))
#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))
#s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))
(*.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 #s(literal -1/2 binary64) x))))
(*.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (/.f64 #s(literal -4 binary64) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))
(*.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x) (/.f64 #s(literal 8 binary64) (*.f64 (*.f64 x x) x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 (/.f64 x x) #s(literal -1 binary64)))))))
(*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (/.f64 #s(literal -4 binary64) (*.f64 x x))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))
(*.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x) (/.f64 #s(literal 8 binary64) (*.f64 (*.f64 x x) x))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (/.f64 x x) #s(literal -1 binary64))))))
(*.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x) (/.f64 #s(literal 8 binary64) (*.f64 (*.f64 x x) x))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 (/.f64 x x) #s(literal -1 binary64))))))
(*.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))) #s(literal -1 binary64))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal -2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal -2 binary64) x)))) (*.f64 (/.f64 (/.f64 #s(literal -4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x))) (/.f64 (/.f64 #s(literal -4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))) (+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal -2 binary64) x))) (/.f64 (/.f64 #s(literal -4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal -2 binary64) x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (/.f64 #s(literal -4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal -2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal -2 binary64) x))) (fma.f64 (/.f64 (/.f64 #s(literal -4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x))) (/.f64 (/.f64 #s(literal -4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x))) (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal -2 binary64) x))) (/.f64 (/.f64 #s(literal -4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))))))
(/.f64 (neg.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (neg.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 #s(literal -1/2 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (/.f64 #s(literal -4 binary64) (*.f64 x x))))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x) (/.f64 #s(literal 8 binary64) (*.f64 (*.f64 x x) x))))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 (/.f64 x x) #s(literal -1 binary64)))))))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal -2 binary64) x))) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal -2 binary64) x)) (/.f64 #s(literal 4 binary64) (*.f64 x x)))) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal -2 binary64) x)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal -2 binary64) x))))
(/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (-.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 #s(literal -1/2 binary64) x)))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (/.f64 #s(literal -4 binary64) (*.f64 x x)))) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x) (/.f64 #s(literal 8 binary64) (*.f64 (*.f64 x x) x)))) (neg.f64 (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (/.f64 x x) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x) (/.f64 #s(literal 8 binary64) (*.f64 (*.f64 x x) x)))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 (/.f64 x x) #s(literal -1 binary64))))))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (/.f64 #s(literal -4 binary64) (*.f64 x x))) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal -2 binary64) x)))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x) (/.f64 #s(literal 8 binary64) (*.f64 (*.f64 x x) x))) (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (/.f64 x x) #s(literal -1 binary64)))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x) (/.f64 #s(literal 8 binary64) (*.f64 (*.f64 x x) x))) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 (/.f64 x x) #s(literal -1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 #s(literal -1/2 binary64) x)) (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (/.f64 x x) #s(literal -1 binary64)))) (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x) (/.f64 #s(literal 8 binary64) (*.f64 (*.f64 x x) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (/.f64 #s(literal -4 binary64) (*.f64 x x)))) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal -2 binary64) x))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x) (/.f64 #s(literal 8 binary64) (*.f64 (*.f64 x x) x)))) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 (/.f64 x x) #s(literal -1 binary64))))))
(neg.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (/.f64 #s(literal -4 binary64) (*.f64 x x))) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))
(neg.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x) (/.f64 #s(literal 8 binary64) (*.f64 (*.f64 x x) x))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 (/.f64 x x) #s(literal -1 binary64)))))))
(fma.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) x))
(fma.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x))) (neg.f64 (/.f64 (/.f64 #s(literal -4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))))
(fma.f64 (neg.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) x))
(fma.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) x) (*.f64 #s(literal -1/2 binary64) x))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) x) (*.f64 #s(literal -1/2 binary64) x))
(fma.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 2 binary64) x))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(fma.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x))
(fma.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x) (*.f64 #s(literal -1/2 binary64) x))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
(fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64) (*.f64 #s(literal -1/2 binary64) x))
(fma.f64 x #s(literal -1/2 binary64) (/.f64 #s(literal 2 binary64) x))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x) (*.f64 #s(literal -1/2 binary64) x))
(-.f64 (/.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 #s(literal -1/2 binary64) x))))
(-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal -2 binary64) x))) (/.f64 (/.f64 #s(literal -4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))
(-.f64 (*.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal -2 binary64) x))
(+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal -2 binary64) x))) (neg.f64 (/.f64 (/.f64 #s(literal -4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))))
(+.f64 (*.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 2 binary64) x))
(+.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 #s(literal -1/2 binary64) x))
(*.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal -1/2 binary64)))
(*.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) x))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) x))
(*.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))
(/.f64 #s(literal -2 binary64) (neg.f64 x))
(/.f64 #s(literal -1 binary64) (*.f64 #s(literal -1/2 binary64) x))
(/.f64 #s(literal 2 binary64) x)
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(neg.f64 (*.f64 (/.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)))
(neg.f64 (/.f64 #s(literal -2 binary64) x))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -2 binary64) x))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64)))

eval13.0ms (0.2%)

Memory
15.8MiB live, 15.8MiB allocated
Compiler

Compiled 2 132 to 322 computations (84.9% saved)

prune47.0ms (0.8%)

Memory
-24.3MiB live, 26.2MiB allocated
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New1280128
Fresh000
Picked011
Done033
Total1284132
Accuracy
100.0%
Counts
132 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x))
✓98.9%
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
✓99.4%
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))))
✓0.0%
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))))
Compiler

Compiled 94 to 51 computations (45.7% saved)

regimes9.0ms (0.2%)

Memory
8.3MiB live, 8.3MiB allocated
Counts
7 → 1
Calls
Call 1
Inputs
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))))
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))))
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))))
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)))
(log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x))
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
Outputs
(log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x))
Calls

3 calls:

3.0ms
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
3.0ms
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
3.0ms
x
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
100.0%1(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
Compiler

Compiled 29 to 18 computations (37.9% saved)

regimes7.0ms (0.1%)

Memory
7.5MiB live, 7.5MiB allocated
Counts
5 → 1
Calls
Call 1
Inputs
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))))
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))))
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))))
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)))
Outputs
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))))
Calls

3 calls:

2.0ms
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
2.0ms
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
2.0ms
x
Results
AccuracySegmentsBranch
99.4%1x
99.4%1(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
99.4%1(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
Compiler

Compiled 29 to 18 computations (37.9% saved)

regimes26.0ms (0.5%)

Memory
-29.5MiB live, 9.5MiB allocated
Counts
3 → 1
Calls
Call 1
Inputs
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))))
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))))
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
Outputs
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
Calls

3 calls:

22.0ms
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
2.0ms
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
2.0ms
x
Results
AccuracySegmentsBranch
98.9%1x
98.9%1(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
98.9%1(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
Compiler

Compiled 29 to 18 computations (37.9% saved)

regimes5.0ms (0.1%)

Memory
11.0MiB live, 11.0MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
2 → 1
Calls
Call 1
Inputs
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))))
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))))
Outputs
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))))
Calls

3 calls:

2.0ms
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
2.0ms
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
1.0ms
x
Results
AccuracySegmentsBranch
0.0%1x
0.0%1(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
0.0%1(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
Compiler

Compiled 29 to 18 computations (37.9% saved)

simplify6.0ms (0.1%)

Memory
10.9MiB live, 10.9MiB allocated
Algorithm
1×egg-herbie
Rules
4×*-commutative_binary64
4×+-commutative_binary64
2×sub-neg_binary64
2×1-exp_binary64
2×neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03085
13885
24085
34185
Stop Event
1×saturated
Calls
Call 1
Inputs
(log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x))
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))))
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))))
Outputs
(log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x))
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))))
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))))

soundness761.0ms (13.4%)

Memory
-17.6MiB live, 376.9MiB allocated
Rules
22 142×lower-fma.f64
22 142×lower-fma.f32
17 138×lower-fma.f64
17 138×lower-fma.f32
8 956×lower-fma.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0132473
1333458
2857450
32372449
45932437
08086416
0155803
1409778
21098758
33208745
47995745
08477716
01782001
14931924
213551865
339801857
081581765
0945
01645
16945
262441
3759641
0835441
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 96 to 55 computations (42.7% saved)

preprocess242.0ms (4.3%)

Memory
12.0MiB live, 51.4MiB allocated
Compiler

Compiled 92 to 50 computations (45.7% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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