arccos

Time bar (total: 21.3s)

analyze14.0ms (0.1%)

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%100%0%0%0%0%3
33.3%25%50%0%0%25%0%4
60%37.5%25%0%0%37.5%0%5
77.8%43.7%12.5%0%0%43.7%0%6
88.2%46.9%6.2%0%0%46.9%0%7
93.9%48.4%3.1%0%0%48.4%0%8
96.9%49.2%1.6%0%0%49.2%0%9
98.4%49.6%0.8%0%0%49.6%0%10
99.2%49.8%0.4%0%0%49.8%0%11
99.6%49.9%0.2%0%0%49.9%0%12
Compiler

Compiled 13 to 10 computations (23.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-sub: 1.0ms (14.6% of total)
ival-div: 1.0ms (14.6% of total)
ival-add: 1.0ms (14.6% of total)
ival-mult: 1.0ms (14.6% of total)
ival-sqrt: 1.0ms (14.6% of total)
ival-atan: 1.0ms (14.6% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample1.7s (7.8%)

Results
1.2s8256×0valid
2.0ms13×0invalid
Precisions
Click to see histograms. Total time spent on operations: 903.0ms
ival-atan: 190.0ms (21% of total)
ival-sqrt: 152.0ms (16.8% of total)
ival-mult: 151.0ms (16.7% of total)
ival-add: 134.0ms (14.8% of total)
ival-div: 125.0ms (13.8% of total)
ival-sub: 118.0ms (13.1% of total)
const: 28.0ms (3.1% of total)
backward-pass: 5.0ms (0.6% of total)
Bogosity

preprocess152.0ms (0.7%)

Algorithm
2×egg-herbie
Rules
1016×fnmadd-define
792×sum3-define
642×fma-define
532×fmsub-define
516×fnmsub-define
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01735
14233
27433
315133
432133
575733
6206933
7308633
8340933
0911
11811
22511
33711
46311
510911
618111
728911
866011
9121311
10169611
11171611
0171611
Stop Event
1×iter limit
1×saturated
1×saturated
Calls
Call 1
Inputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
Outputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
Call 2
Inputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 (neg x)) (+ 1 (neg x))))))
(neg (* 2 (atan (sqrt (/ (- 1 (neg x)) (+ 1 (neg x)))))))
Outputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 (neg x)) (+ 1 (neg x))))))
(* 2 (atan (sqrt (/ (+ 1 x) (- 1 x)))))
(neg (* 2 (atan (sqrt (/ (- 1 (neg x)) (+ 1 (neg x)))))))
(* (atan (sqrt (/ (+ 1 x) (- 1 x)))) -2)

explain186.0ms (0.9%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-x
00-0-(+.f64 #s(literal 1 binary64) x)
00-0-(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
00-0-#s(literal 2 binary64)
00-0-(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
00-0-#s(literal 1 binary64)
00-0-(-.f64 #s(literal 1 binary64) x)
00-0-(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
00-0-(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
Results
115.0ms512×0valid
Compiler

Compiled 104 to 29 computations (72.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 59.0ms
ival-sub: 14.0ms (23.8% of total)
ival-atan: 10.0ms (17% of total)
ival-mult: 9.0ms (15.3% of total)
ival-sqrt: 9.0ms (15.3% of total)
ival-div: 8.0ms (13.6% of total)
ival-add: 7.0ms (11.9% of total)
const: 2.0ms (3.4% of total)
backward-pass: 0.0ms (0% of total)

eval1.0ms (0%)

Compiler

Compiled 12 to 9 computations (25% saved)

prune2.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
Compiler

Compiled 12 to 9 computations (25% saved)

simplify75.0ms (0.4%)

Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
✓cost-diff0
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
✓cost-diff0
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
Rules
446×fnmadd-define
400×sum3-define
324×fma-define
294×fmsub-define
282×fnmsub-define
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0944
11844
22544
33744
46344
510944
618144
728944
866044
9121344
10169644
11171644
0171644
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
2
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(sqrt (/ (- 1 x) (+ 1 x)))
(/ (- 1 x) (+ 1 x))
(- 1 x)
1
x
(+ 1 x)
Outputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
2
#s(literal 2 binary64)
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(sqrt (/ (- 1 x) (+ 1 x)))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(/ (- 1 x) (+ 1 x))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)

localize85.0ms (0.4%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
✓accuracy100.0%
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
✓accuracy100.0%
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
✓accuracy100.0%
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
Results
57.0ms256×0valid
Compiler

Compiled 46 to 10 computations (78.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 26.0ms
ival-mult: 5.0ms (19.4% of total)
ival-atan: 5.0ms (19.4% of total)
ival-sub: 4.0ms (15.5% of total)
ival-div: 4.0ms (15.5% of total)
ival-sqrt: 4.0ms (15.5% of total)
ival-add: 3.0ms (11.6% of total)
const: 1.0ms (3.9% of total)
backward-pass: 0.0ms (0% of total)

series10.0ms (0%)

Counts
4 → 48
Calls
Call 1
Inputs
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (sqrt (/ (- 1 x) (+ 1 x)))>
#<alt (/ (- 1 x) (+ 1 x))>
Outputs
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))>
#<alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))>
#<alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))>
#<alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))>
#<alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (- 1 x) (+ 1 x))))>
#<alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))>
#<alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))>
#<alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))>
#<alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))>
#<alt (sqrt -1)>
#<alt (+ (sqrt -1) (/ 1 (* x (sqrt -1))))>
#<alt (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))>
#<alt (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))>
#<alt (sqrt -1)>
#<alt (+ (sqrt -1) (/ 1 (* x (sqrt -1))))>
#<alt (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))>
#<alt (+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))>
#<alt 1>
#<alt (+ 1 (* -2 x))>
#<alt (+ 1 (* x (- (* 2 x) 2)))>
#<alt (+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))>
#<alt -1>
#<alt (- (* 2 (/ 1 x)) 1)>
#<alt (- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))>
#<alt (- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))>
#<alt -1>
#<alt (- (* 2 (/ 1 x)) 1)>
#<alt (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)>
#<alt (- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)>
Calls

12 calls:

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

rewrite599.0ms (2.8%)

Algorithm
1×batch-egg-rewrite
Rules
2432×/-lowering-/.f32
2432×/-lowering-/.f64
2382×*-lowering-*.f32
2382×*-lowering-*.f64
1310×fma-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0935
14635
234735
3481135
0813335
Stop Event
1×iter limit
1×node limit
Counts
4 → 237
Calls
Call 1
Inputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(sqrt (/ (- 1 x) (+ 1 x)))
(/ (- 1 x) (+ 1 x))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(neg.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))
(/.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (-.f64 #s(literal -1 binary64) x) x))) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 x (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 x (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))))))
(/.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))) (neg.f64 (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x))))
(*.f64 (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))))
(*.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
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(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal -1 binary64) x)))
(*.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (-.f64 #s(literal -1 binary64) x) x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))
(*.f64 (*.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 x (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 x (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (+.f64 x #s(literal -1 binary64)))
(*.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))
(*.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))))
(*.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal -1 binary64) (*.f64 x x))) (+.f64 x #s(literal -1 binary64)))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (+.f64 #s(literal -1 binary64) (neg.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x))))) (+.f64 #s(literal -1 binary64) (neg.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (*.f64 x x) #s(literal -1 binary64))) (+.f64 x #s(literal -1 binary64)))
(*.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) (*.f64 x (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 #s(literal 1 binary64) x))))))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) (-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))))
(*.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))))

simplify531.0ms (2.5%)

Algorithm
1×egg-herbie
Rules
2544×*-lowering-*.f32
2544×*-lowering-*.f64
1990×+-lowering-+.f64
1990×+-lowering-+.f32
1986×fma-lowering-fma.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0107519
1313449
2908437
32496429
08510429
Stop Event
1×iter limit
1×node limit
Counts
48 → 48
Calls
Call 1
Inputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
1
(+ 1 (* -2 x))
(+ 1 (* x (- (* 2 x) 2)))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
-1
(- (* 2 (/ 1 x)) 1)
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
-1
(- (* 2 (/ 1 x)) 1)
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)
Outputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x) (*.f64 x x))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64)))) x)) x))
1
#s(literal 1 binary64)
(+ 1 (* -2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -2 binary64)))
(+ 1 (* x (- (* 2 x) 2)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) x))))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -2 binary64) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 x #s(literal -2 binary64)))))))
-1
#s(literal -1 binary64)
(- (* 2 (/ 1 x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) x))
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(-.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) x))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) x)) x))
-1
#s(literal -1 binary64)
(- (* 2 (/ 1 x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) x))
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) x))
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) x)) x))

eval105.0ms (0.5%)

Compiler

Compiled 6693 to 1310 computations (80.4% saved)

prune121.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2805285
Fresh000
Picked011
Done000
Total2806286
Accuracy
100.0%
Counts
286 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.1%
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
▶99.5%
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))))
▶99.4%
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
▶100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x))))))
✓100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
▶98.2%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
Compiler

Compiled 144 to 101 computations (29.9% saved)

simplify498.0ms (2.3%)

Algorithm
1×egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
✓cost-diff128
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))
✓cost-diff128
(atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))))
✓cost-diff128
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))))
✓cost-diff0
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
✓cost-diff0
(atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
✓cost-diff0
(-.f64 #s(literal 1 binary64) x)
✓cost-diff0
(atan.f64 (-.f64 #s(literal 1 binary64) x))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
✓cost-diff0
(atan.f64 #s(literal 1 binary64))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
✓cost-diff768
(/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x)))
✓cost-diff768
(sqrt.f64 (/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x))))
✓cost-diff768
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x)))))
✓cost-diff768
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x))))))
Rules
2508×*-lowering-*.f32
2508×*-lowering-*.f64
1772×/-lowering-/.f32
1772×/-lowering-/.f64
1676×+-lowering-+.f64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
031270
174254
2208206
3479199
41655196
57831196
08608196
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* 2 (atan (sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (* (+ 1 x) (/ (+ 1 x) x))))))
2
(atan (sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (* (+ 1 x) (/ (+ 1 x) x)))))
(sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (* (+ 1 x) (/ (+ 1 x) x))))
(/ (- (/ (+ 1 x) x) (+ 1 x)) (* (+ 1 x) (/ (+ 1 x) x)))
(- (/ (+ 1 x) x) (+ 1 x))
(/ (+ 1 x) x)
(+ 1 x)
1
x
(* (+ 1 x) (/ (+ 1 x) x))
(* 2 (atan 1))
2
(atan 1)
1
(* 2 (atan (- 1 x)))
2
(atan (- 1 x))
(- 1 x)
1
x
(* 2 (atan (+ 1 (* x (+ -1 (* x 1/2))))))
2
(atan (+ 1 (* x (+ -1 (* x 1/2)))))
(+ 1 (* x (+ -1 (* x 1/2))))
1
(* x (+ -1 (* x 1/2)))
x
(+ -1 (* x 1/2))
-1
(* x 1/2)
1/2
(* 2 (atan (+ 1 (* x (+ -1 (* x (* (- 1 x) 1/2)))))))
2
(atan (+ 1 (* x (+ -1 (* x (* (- 1 x) 1/2))))))
(+ 1 (* x (+ -1 (* x (* (- 1 x) 1/2)))))
1
(* x (+ -1 (* x (* (- 1 x) 1/2))))
x
(+ -1 (* x (* (- 1 x) 1/2)))
-1
(* x (* (- 1 x) 1/2))
(* (- 1 x) 1/2)
(- 1 x)
1/2
Outputs
(* 2 (atan (sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (* (+ 1 x) (/ (+ 1 x) x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
2
#s(literal 2 binary64)
(atan (sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (* (+ 1 x) (/ (+ 1 x) x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (* (+ 1 x) (/ (+ 1 x) x))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(/ (- (/ (+ 1 x) x) (+ 1 x)) (* (+ 1 x) (/ (+ 1 x) x)))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
(- (/ (+ 1 x) x) (+ 1 x))
(+.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal -1 binary64) x))
(/ (+ 1 x) x)
(-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(* (+ 1 x) (/ (+ 1 x) x))
(+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))
(* 2 (atan 1))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
2
#s(literal 2 binary64)
(atan 1)
(atan.f64 #s(literal 1 binary64))
1
#s(literal 1 binary64)
(* 2 (atan (- 1 x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
2
#s(literal 2 binary64)
(atan (- 1 x))
(atan.f64 (-.f64 #s(literal 1 binary64) x))
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(* 2 (atan (+ 1 (* x (+ -1 (* x 1/2))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
2
#s(literal 2 binary64)
(atan (+ 1 (* x (+ -1 (* x 1/2)))))
(atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))))
(+ 1 (* x (+ -1 (* x 1/2))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
1
#s(literal 1 binary64)
(* x (+ -1 (* x 1/2)))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))
x
(+ -1 (* x 1/2))
(+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))
-1
#s(literal -1 binary64)
(* x 1/2)
(*.f64 x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(* 2 (atan (+ 1 (* x (+ -1 (* x (* (- 1 x) 1/2)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))))))
2
#s(literal 2 binary64)
(atan (+ 1 (* x (+ -1 (* x (* (- 1 x) 1/2))))))
(atan.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64))))))
(+ 1 (* x (+ -1 (* x (* (- 1 x) 1/2)))))
(*.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))))
1
#s(literal 1 binary64)
(* x (+ -1 (* x (* (- 1 x) 1/2))))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64))))))
x
(+ -1 (* x (* (- 1 x) 1/2)))
(+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64)))))
-1
#s(literal -1 binary64)
(* x (* (- 1 x) 1/2))
(*.f64 x (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64))))
(* (- 1 x) 1/2)
(-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64)))
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
1/2
#s(literal 1/2 binary64)

localize402.0ms (1.9%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))))
✓accuracy100.0%
(atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))))
✓accuracy100.0%
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
✓accuracy100.0%
(*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
✓accuracy100.0%
(*.f64 x #s(literal 1/2 binary64))
✓accuracy100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
✓accuracy100.0%
(atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))))
✓accuracy100.0%
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))
✓accuracy100.0%
(-.f64 #s(literal 1 binary64) x)
✓accuracy100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
✓accuracy100.0%
(atan.f64 (-.f64 #s(literal 1 binary64) x))
✓accuracy100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
✓accuracy100.0%
(atan.f64 #s(literal 1 binary64))
✓accuracy100.0%
(sqrt.f64 (/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x))))
✓accuracy100.0%
(/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x)))
✓accuracy100.0%
(/.f64 (+.f64 #s(literal 1 binary64) x) x)
✓accuracy100.0%
(*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x))
Results
268.0ms256×0valid
Compiler

Compiled 272 to 32 computations (88.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 126.0ms
ival-mult: 65.0ms (51.5% of total)
ival-atan: 24.0ms (19% of total)
ival-add: 16.0ms (12.7% of total)
ival-div: 9.0ms (7.1% of total)
ival-sub: 6.0ms (4.8% of total)
ival-sqrt: 5.0ms (4% of total)
const: 1.0ms (0.8% of total)
backward-pass: 0.0ms (0% of total)

series44.0ms (0.2%)

Counts
21 → 228
Calls
Call 1
Inputs
#<alt (* 2 (atan (sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (* (+ 1 x) (/ (+ 1 x) x))))))>
#<alt (atan (sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (* (+ 1 x) (/ (+ 1 x) x)))))>
#<alt (sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (* (+ 1 x) (/ (+ 1 x) x))))>
#<alt (/ (- (/ (+ 1 x) x) (+ 1 x)) (* (+ 1 x) (/ (+ 1 x) x)))>
#<alt (* 2 (atan 1))>
#<alt (atan 1)>
#<alt (* 2 (atan (- 1 x)))>
#<alt (atan (- 1 x))>
#<alt (- 1 x)>
#<alt (* 2 (atan (+ 1 (* x (+ -1 (* x 1/2))))))>
#<alt (atan (+ 1 (* x (+ -1 (* x 1/2)))))>
#<alt (+ 1 (* x (+ -1 (* x 1/2))))>
#<alt (* x (+ -1 (* x 1/2)))>
#<alt (* 2 (atan (+ 1 (* x (+ -1 (* x (* (- 1 x) 1/2)))))))>
#<alt (atan (+ 1 (* x (+ -1 (* x (* (- 1 x) 1/2))))))>
#<alt (+ 1 (* x (+ -1 (* x (* (- 1 x) 1/2)))))>
#<alt (* x (+ -1 (* x (* (- 1 x) 1/2))))>
#<alt (* (+ 1 x) (/ (+ 1 x) x))>
#<alt (/ (+ 1 x) x)>
#<alt (* x 1/2)>
#<alt (* x (* (- 1 x) 1/2))>
Outputs
#<alt (* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))>
#<alt (* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))>
#<alt (* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))>
#<alt (* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))>
#<alt (* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))>
#<alt (* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))>
#<alt (* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))>
#<alt (* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))>
#<alt (* 2 (atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x))))))>
#<alt (* 2 (atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x))))))>
#<alt (* 2 (atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x))))))>
#<alt (* 2 (atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x))))))>
#<alt (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))>
#<alt (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))>
#<alt (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))>
#<alt (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))>
#<alt (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))>
#<alt (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))>
#<alt (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))>
#<alt (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))>
#<alt (atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x)))))>
#<alt (atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x)))))>
#<alt (atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x)))))>
#<alt (atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x)))))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))>
#<alt (sqrt -1)>
#<alt (+ (sqrt -1) (* -1 (/ (sqrt -1) x)))>
#<alt (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) x)) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))) (/ (sqrt -1) (pow x 2)))))>
#<alt (- (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) x)) (+ (* -1 (/ (sqrt -1) (pow x 3))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))) (/ (sqrt -1) (pow x 2)))))) (/ 1/2 (* (pow x 3) (sqrt -1))))>
#<alt (* -1 (sqrt -1))>
#<alt (+ (* -1 (sqrt -1)) (/ (sqrt -1) x))>
#<alt (+ (* -1 (sqrt -1)) (* -1 (/ (+ (* -1 (sqrt -1)) (* -1 (/ (+ (* -1 (sqrt -1)) (* 1/2 (sqrt -1))) x))) x)))>
#<alt (+ (* -1 (sqrt -1)) (* -1 (/ (+ (* -1 (sqrt -1)) (* -1 (/ (+ (* -1 (sqrt -1)) (+ (* -1 (/ (+ (* -1 (sqrt -1)) (* 1/2 (sqrt -1))) x)) (* 1/2 (sqrt -1)))) x))) x)))>
#<alt 1>
#<alt (+ 1 (* -2 x))>
#<alt (+ 1 (* x (- (* 2 x) 2)))>
#<alt (+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))>
#<alt -1>
#<alt (- (* 2 (/ 1 x)) 1)>
#<alt (- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))>
#<alt (- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))>
#<alt -1>
#<alt (- (* 2 (/ 1 x)) 1)>
#<alt (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)>
#<alt (- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (- 1 x)))>
#<alt (* 2 (atan (+ 1 (* -1 x))))>
#<alt (* 2 (atan (+ 1 (* -1 x))))>
#<alt (* 2 (atan (+ 1 (* -1 x))))>
#<alt (* 2 (atan (+ 1 (* -1 x))))>
#<alt (atan (- 1 x))>
#<alt (atan (- 1 x))>
#<alt (atan (- 1 x))>
#<alt (atan (- 1 x))>
#<alt (atan (- 1 x))>
#<alt (atan (- 1 x))>
#<alt (atan (- 1 x))>
#<alt (atan (- 1 x))>
#<alt (atan (+ 1 (* -1 x)))>
#<alt (atan (+ 1 (* -1 x)))>
#<alt (atan (+ 1 (* -1 x)))>
#<alt (atan (+ 1 (* -1 x)))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))>
#<alt (* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))>
#<alt (* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))>
#<alt (* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))>
#<alt (* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))>
#<alt (atan (+ 1 (* x (- (* 1/2 x) 1))))>
#<alt (atan (+ 1 (* x (- (* 1/2 x) 1))))>
#<alt (atan (+ 1 (* x (- (* 1/2 x) 1))))>
#<alt (atan (+ 1 (* x (- (* 1/2 x) 1))))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) x))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) x))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) x))>
#<alt (atan (- (+ 1 (* 1/2 (pow x 2))) x))>
#<alt (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))>
#<alt (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))>
#<alt (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))>
#<alt (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))>
#<alt (* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))>
#<alt (* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))>
#<alt (* -1 x)>
#<alt (* x (- (* 1/2 x) 1))>
#<alt (* x (- (* 1/2 x) 1))>
#<alt (* x (- (* 1/2 x) 1))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x)))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x)))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x)))>
#<alt (* 2 (atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x)))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))>
#<alt (* 2 (atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))>
#<alt (atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))>
#<alt (atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))>
#<alt (atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))>
#<alt (atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))>
#<alt (atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x))>
#<alt (atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x))>
#<alt (atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x))>
#<alt (atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x))>
#<alt (atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))>
#<alt (atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))>
#<alt (atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))>
#<alt (atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))>
#<alt (* -1/2 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))>
#<alt (* -1 x)>
#<alt (* x (- (* 1/2 x) 1))>
#<alt (* x (- (* x (+ 1/2 (* -1/2 x))) 1))>
#<alt (* x (- (* x (+ 1/2 (* -1/2 x))) 1))>
#<alt (* -1/2 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* 2 x)) x)>
#<alt (/ (+ 1 (* x (+ 2 x))) x)>
#<alt (/ (+ 1 (* x (+ 2 x))) x)>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (+ (* 2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* x (+ 1 (+ (* 2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* -1 (* x (- (* -1 (/ (+ 2 (/ 1 x)) x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ (+ 2 (/ 1 x)) x)) 1)))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 x) x)>
#<alt (/ (+ 1 x) x)>
#<alt (/ (+ 1 x) x)>
#<alt 1>
#<alt (+ 1 (/ 1 x))>
#<alt (+ 1 (/ 1 x))>
#<alt (+ 1 (/ 1 x))>
#<alt 1>
#<alt (+ 1 (/ 1 x))>
#<alt (+ 1 (/ 1 x))>
#<alt (+ 1 (/ 1 x))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/2 x)))>
#<alt (* x (+ 1/2 (* -1/2 x)))>
#<alt (* x (+ 1/2 (* -1/2 x)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))>
Calls

57 calls:

TimeVariablePointExpression
6.0ms
x
@-inf
(* 2 (atan (+ 1 (* x (+ -1 (* x 1/2))))))
3.0ms
x
@-inf
(* 2 (atan (sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (* (+ 1 x) (/ (+ 1 x) x))))))
1.0ms
x
@inf
(sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (* (+ 1 x) (/ (+ 1 x) x))))
1.0ms
x
@inf
(* 2 (atan (sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (* (+ 1 x) (/ (+ 1 x) x))))))
1.0ms
x
@-inf
(* 2 (atan (+ 1 (* x (+ -1 (* x (* (- 1 x) 1/2)))))))

rewrite848.0ms (4%)

Algorithm
1×batch-egg-rewrite
Rules
4786×*-lowering-*.f32
4786×*-lowering-*.f64
3104×/-lowering-/.f32
3104×/-lowering-/.f64
2686×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
031218
1160194
21615186
08348186
Stop Event
1×iter limit
1×node limit
Counts
21 → 320
Calls
Call 1
Inputs
(* 2 (atan (sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (* (+ 1 x) (/ (+ 1 x) x))))))
(atan (sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (* (+ 1 x) (/ (+ 1 x) x)))))
(sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (* (+ 1 x) (/ (+ 1 x) x))))
(/ (- (/ (+ 1 x) x) (+ 1 x)) (* (+ 1 x) (/ (+ 1 x) x)))
(* 2 (atan 1))
(atan 1)
(* 2 (atan (- 1 x)))
(atan (- 1 x))
(- 1 x)
(* 2 (atan (+ 1 (* x (+ -1 (* x 1/2))))))
(atan (+ 1 (* x (+ -1 (* x 1/2)))))
(+ 1 (* x (+ -1 (* x 1/2))))
(* x (+ -1 (* x 1/2)))
(* 2 (atan (+ 1 (* x (+ -1 (* x (* (- 1 x) 1/2)))))))
(atan (+ 1 (* x (+ -1 (* x (* (- 1 x) 1/2))))))
(+ 1 (* x (+ -1 (* x (* (- 1 x) 1/2)))))
(* x (+ -1 (* x (* (- 1 x) 1/2))))
(* (+ 1 x) (/ (+ 1 x) x))
(/ (+ 1 x) x)
(* x 1/2)
(* x (* (- 1 x) 1/2))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x))) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x))) (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x))) (+.f64 #s(literal 1 binary64) x))))
(exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x))) (+.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x))) (+.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x))) (+.f64 #s(literal 1 binary64) x)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x))) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) x))))
(/.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))) (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 x (+.f64 #s(literal 1 binary64) x)))) (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (sqrt.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))) (+.f64 (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x)))))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x)))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (sqrt.f64 (/.f64 (/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x))) (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x)))) (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 x (+.f64 #s(literal 1 binary64) x)))) (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x)))) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x))))) (sqrt.f64 (neg.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) x)))))
(/.f64 (sqrt.f64 (neg.f64 (/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (/.f64 (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (*.f64 x (*.f64 x x)))))) (sqrt.f64 (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x)))) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x)))))))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x)))) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))))))) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x)))))))
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(/.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 x (+.f64 #s(literal 1 binary64) x)))) (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (/.f64 (/.f64 x (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (+.f64 (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x))))))
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(+.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 x (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))
(+.f64 (*.f64 x (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (-.f64 #s(literal 0 binary64) x))
(+.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))
(+.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64)) (*.f64 (*.f64 x (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x) (*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))
(fma.f64 x #s(literal -1 binary64) (*.f64 x (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))
(fma.f64 x (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 0 binary64) x))
(fma.f64 #s(literal -1 binary64) x (*.f64 x (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)) (*.f64 x x) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))) x (-.f64 #s(literal 0 binary64) x))
(fma.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (*.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 x #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (*.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) x))
(/.f64 (+.f64 (*.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))) (+.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))) (*.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 x (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))) (-.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 x (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))
(/.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))) (-.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)))))
(/.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))) (-.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))) x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))) (-.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))) x) (-.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))
(*.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))
(*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) x)
(*.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))
(*.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))) x)
(+.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (*.f64 x (/.f64 (+.f64 #s(literal 1 binary64) x) x)))
(+.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)) (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) x))
(+.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) x) (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)))
(+.f64 (*.f64 x (/.f64 (+.f64 #s(literal 1 binary64) x) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) x))
(fma.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) x) (*.f64 x (/.f64 (+.f64 #s(literal 1 binary64) x) x)))
(fma.f64 x (/.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x))
(fma.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x) (*.f64 x (/.f64 (+.f64 #s(literal 1 binary64) x) x)))
(fma.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64) (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) x))
(fma.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) x (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)))
(fma.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (*.f64 x (/.f64 (+.f64 #s(literal 1 binary64) x) x)))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x) (*.f64 x (/.f64 (+.f64 #s(literal 1 binary64) x) x)))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) x)
(/.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64)))) (/.f64 x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 x (+.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (/.f64 x (+.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (*.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64)))) x))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64)))) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x)) (*.f64 x (-.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x))) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (/.f64 x (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64))))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 (/.f64 x (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64))))))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 x (-.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64))))))
(/.f64 (*.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64)))))
(/.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 (+.f64 #s(literal 1 binary64) x) x)) (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (+.f64 #s(literal 1 binary64) x) x)) (-.f64 #s(literal 1 binary64) x))
(pow.f64 (/.f64 x (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))
(*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x))
(*.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) x))
(exp.f64 (*.f64 (log.f64 (/.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) x)))
(neg.f64 (/.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x)) x))
(/.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(/.f64 (+.f64 #s(literal 1 binary64) x) x)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64))))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 x (-.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64)))) x))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 x (-.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x))) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x))
(pow.f64 (/.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) x))
(*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x))
(*.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64))))))
(*.f64 (pow.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))
(*.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))
(*.f64 (*.f64 x #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) x))
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)) x)
(*.f64 (*.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))

simplify543.0ms (2.6%)

Algorithm
1×egg-herbie
Rules
3072×*-lowering-*.f32
3072×*-lowering-*.f64
1846×+-lowering-+.f64
1846×+-lowering-+.f32
1700×--lowering--.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01992002
15861803
216931678
365051664
082841664
Stop Event
1×iter limit
1×node limit
Counts
228 → 228
Calls
Call 1
Inputs
(* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))
(* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))
(* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))
(* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))
(* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))
(* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))
(* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))
(* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))
(* 2 (atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x))))))
(* 2 (atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x))))))
(* 2 (atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x))))))
(* 2 (atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x))))))
(atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))
(atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))
(atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))
(atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))
(atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))
(atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))
(atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))
(atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))
(atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x)))))
(atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x)))))
(atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x)))))
(atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x)))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(sqrt -1)
(+ (sqrt -1) (* -1 (/ (sqrt -1) x)))
(+ (sqrt -1) (+ (* -1 (/ (sqrt -1) x)) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))) (/ (sqrt -1) (pow x 2)))))
(- (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) x)) (+ (* -1 (/ (sqrt -1) (pow x 3))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))) (/ (sqrt -1) (pow x 2)))))) (/ 1/2 (* (pow x 3) (sqrt -1))))
(* -1 (sqrt -1))
(+ (* -1 (sqrt -1)) (/ (sqrt -1) x))
(+ (* -1 (sqrt -1)) (* -1 (/ (+ (* -1 (sqrt -1)) (* -1 (/ (+ (* -1 (sqrt -1)) (* 1/2 (sqrt -1))) x))) x)))
(+ (* -1 (sqrt -1)) (* -1 (/ (+ (* -1 (sqrt -1)) (* -1 (/ (+ (* -1 (sqrt -1)) (+ (* -1 (/ (+ (* -1 (sqrt -1)) (* 1/2 (sqrt -1))) x)) (* 1/2 (sqrt -1)))) x))) x)))
1
(+ 1 (* -2 x))
(+ 1 (* x (- (* 2 x) 2)))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
-1
(- (* 2 (/ 1 x)) 1)
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
-1
(- (* 2 (/ 1 x)) 1)
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)
(* 2 (atan (- 1 x)))
(* 2 (atan (- 1 x)))
(* 2 (atan (- 1 x)))
(* 2 (atan (- 1 x)))
(* 2 (atan (- 1 x)))
(* 2 (atan (- 1 x)))
(* 2 (atan (- 1 x)))
(* 2 (atan (- 1 x)))
(* 2 (atan (+ 1 (* -1 x))))
(* 2 (atan (+ 1 (* -1 x))))
(* 2 (atan (+ 1 (* -1 x))))
(* 2 (atan (+ 1 (* -1 x))))
(atan (- 1 x))
(atan (- 1 x))
(atan (- 1 x))
(atan (- 1 x))
(atan (- 1 x))
(atan (- 1 x))
(atan (- 1 x))
(atan (- 1 x))
(atan (+ 1 (* -1 x)))
(atan (+ 1 (* -1 x)))
(atan (+ 1 (* -1 x)))
(atan (+ 1 (* -1 x)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))
(* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))
(* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))
(* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(* 2 (atan (- (+ 1 (* 1/2 (pow x 2))) x)))
(* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))
(* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))
(* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))
(* 2 (atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2))))))
(atan (+ 1 (* x (- (* 1/2 x) 1))))
(atan (+ 1 (* x (- (* 1/2 x) 1))))
(atan (+ 1 (* x (- (* 1/2 x) 1))))
(atan (+ 1 (* x (- (* 1/2 x) 1))))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan (- (+ 1 (* 1/2 (pow x 2))) x))
(atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))
(atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))
(atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))
(atan (+ 1 (+ (* -1 x) (* 1/2 (pow x 2)))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* 1/2 x) 1)))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(* -1 x)
(* x (- (* 1/2 x) 1))
(* x (- (* 1/2 x) 1))
(* x (- (* 1/2 x) 1))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* 2 (atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))
(* 2 (atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))
(* 2 (atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))
(* 2 (atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))
(* 2 (atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x)))
(* 2 (atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x)))
(* 2 (atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x)))
(* 2 (atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x)))
(* 2 (atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))
(* 2 (atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))
(* 2 (atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))
(* 2 (atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))
(atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))
(atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))
(atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))
(atan (+ 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))
(atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x))
(atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x))
(atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x))
(atan (- (+ 1 (* 1/2 (* (pow x 2) (- 1 x)))) x))
(atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))
(atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))
(atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))
(atan (+ 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(* -1/2 (pow x 3))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(* -1 x)
(* x (- (* 1/2 x) 1))
(* x (- (* x (+ 1/2 (* -1/2 x))) 1))
(* x (- (* x (+ 1/2 (* -1/2 x))) 1))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* -1/2 (pow x 3))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(/ 1 x)
(/ (+ 1 (* 2 x)) x)
(/ (+ 1 (* x (+ 2 x))) x)
(/ (+ 1 (* x (+ 2 x))) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (+ (* 2 (/ 1 x)) (/ 1 (pow x 2)))))
(* x (+ 1 (+ (* 2 (/ 1 x)) (/ 1 (pow x 2)))))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* -1 (* x (- (* -1 (/ (+ 2 (/ 1 x)) x)) 1)))
(* -1 (* x (- (* -1 (/ (+ 2 (/ 1 x)) x)) 1)))
(/ 1 x)
(/ (+ 1 x) x)
(/ (+ 1 x) x)
(/ (+ 1 x) x)
1
(+ 1 (/ 1 x))
(+ 1 (/ 1 x))
(+ 1 (/ 1 x))
1
(+ 1 (/ 1 x))
(+ 1 (/ 1 x))
(+ 1 (/ 1 x))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* x (+ 1/2 (* -1/2 x)))
(* x (+ 1/2 (* -1/2 x)))
(* x (+ 1/2 (* -1/2 x)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
Outputs
(* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64)))))
(* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64)))))
(* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64)))))
(* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64)))))
(* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64)))))
(* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64)))))
(* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64)))))
(* 2 (atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64)))))
(* 2 (atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (neg.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64))))))
(* 2 (atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (neg.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64))))))
(* 2 (atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (neg.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64))))))
(* 2 (atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (neg.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64))))))
(atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))
(atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64))))
(atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))
(atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64))))
(atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))
(atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64))))
(atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))
(atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64))))
(atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))
(atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64))))
(atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))
(atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64))))
(atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))
(atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64))))
(atan (* (sqrt (* x (- (/ 1 x) x))) (/ 1 (+ 1 x))))
(atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64))))
(atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x)))))
(atan.f64 (neg.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64)))))
(atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x)))))
(atan.f64 (neg.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64)))))
(atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x)))))
(atan.f64 (neg.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64)))))
(atan (* (sqrt (* x (+ (* -1 x) (/ 1 x)))) (/ (pow (sqrt -1) 2) (- 1 (* -1 x)))))
(atan.f64 (neg.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (* -1 (/ (sqrt -1) x)))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) x))
(+ (sqrt -1) (+ (* -1 (/ (sqrt -1) x)) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))) (/ (sqrt -1) (pow x 2)))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (-.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) (/.f64 (sqrt.f64 #s(literal -1 binary64)) x))))
(- (+ (sqrt -1) (+ (* -1 (/ (sqrt -1) x)) (+ (* -1 (/ (sqrt -1) (pow x 3))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))) (/ (sqrt -1) (pow x 2)))))) (/ 1/2 (* (pow x 3) (sqrt -1))))
(+.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) x) x))) (+.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (/.f64 (/.f64 #s(literal -1/2 binary64) x) (*.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))))
(* -1 (sqrt -1))
(-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (/ (sqrt -1) x))
(-.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* -1 (/ (+ (* -1 (sqrt -1)) (* -1 (/ (+ (* -1 (sqrt -1)) (* 1/2 (sqrt -1))) x))) x)))
(-.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x))) (-.f64 #s(literal 0 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* -1 (/ (+ (* -1 (sqrt -1)) (* -1 (/ (+ (* -1 (sqrt -1)) (+ (* -1 (/ (+ (* -1 (sqrt -1)) (* 1/2 (sqrt -1))) x)) (* 1/2 (sqrt -1)))) x))) x)))
(-.f64 (/.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64))) x)) x) (sqrt.f64 #s(literal -1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -2 binary64)))
(+ 1 (* x (- (* 2 x) 2)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) x))))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -2 binary64) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 x #s(literal -2 binary64)))))))
-1
#s(literal -1 binary64)
(- (* 2 (/ 1 x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) x))
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -2 binary64) x)) x))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) x)) x))
-1
#s(literal -1 binary64)
(- (* 2 (/ 1 x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) x))
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -2 binary64) x)) x))
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) x)) x))
(* 2 (atan (- 1 x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(* 2 (atan (- 1 x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(* 2 (atan (- 1 x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(* 2 (atan (- 1 x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(* 2 (atan (- 1 x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(* 2 (atan (- 1 x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(* 2 (atan (- 1 x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(* 2 (atan (- 1 x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(* 2 (atan (+ 1 (* -1 x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(* 2 (atan (+ 1 (* -1 x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(* 2 (atan (+ 1 (* -1 x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(* 2 (atan (+ 1 (* -1 x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(atan (- 1 x))
(atan.f64 (-.f64 #s(literal 1 binary64) x))
(atan (- 1 x))
(atan.f64 (-.f64 #s(literal 1 binary64) x))
(atan (- 1 x))
(atan.f64 (-.f64 #s(literal 1 binary64) x))
(atan (- 1 x))
(atan.f64 (-.f64 #s(literal 1 binary64) x))
(atan (- 1 x))
(atan.f64 (-.f64 #s(literal 1 binary64) x))
(atan (- 1 x))
(atan.f64 (-.f64 #s(literal 1 binary64) x))
(atan (- 1 x))
(atan.f64 (-.f64 #s(literal 1 binary64) x))
(atan (- 1 x))
(atan.f64 (-.f64 #s(literal 1 binary64) x))
(atan (+ 1 (* -1 x)))
(atan.f64 (-.f64 #s(literal 1 binary64) x))
(atan (+ 1 (* -1 x)))
(atan.f64 (-.f64 #s(literal 1 binary64) x))
(atan (+ 1 (* -1 x)))
(atan.f64 (-.f64 #s(literal 1 binary64) x))
(atan (+ 1 (* -1 x)))
(atan.f64 (-.f64 #s(literal 1 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
(* 2 (atan (+ 1 (* x (- (* 1/2 x) 1)))))
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(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/2 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))

eval302.0ms (1.4%)

Compiler

Compiled 13827 to 2020 computations (85.4% saved)

prune2.2s (10.3%)

Pruning

8 alts after pruning (3 fresh and 5 done)

PrunedKeptTotal
New6153618
Fresh000
Picked145
Done011
Total6168624
Accuracy
100.0%
Counts
624 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.1%
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
✓99.5%
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))))
✓99.4%
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
▶99.5%
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))))
▶99.5%
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))))
▶100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))))))
✓100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
✓98.2%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
Compiler

Compiled 136 to 86 computations (36.8% saved)

simplify671.0ms (3.2%)

Algorithm
1×egg-herbie
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))
✓cost-diff128
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))
✓cost-diff128
(atan.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))))))
✓cost-diff128
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64))))
✓cost-diff0
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))
✓cost-diff0
(atan.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x)))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))))
✓cost-diff0
(/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))))
✓cost-diff0
(sqrt.f64 (/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))))
✓cost-diff0
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))))))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))))))
Rules
4170×*-lowering-*.f32
4170×*-lowering-*.f64
1414×+-lowering-+.f64
1414×+-lowering-+.f32
1172×fma-define
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
034422
188391
2269382
31035361
46121361
08166361
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* 2 (atan (sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (+ x (+ 2 (/ 1 x)))))))
2
(atan (sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (+ x (+ 2 (/ 1 x))))))
(sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (+ x (+ 2 (/ 1 x)))))
(/ (- (/ (+ 1 x) x) (+ 1 x)) (+ x (+ 2 (/ 1 x))))
(- (/ (+ 1 x) x) (+ 1 x))
(/ (+ 1 x) x)
(+ 1 x)
1
x
(+ x (+ 2 (/ 1 x)))
(+ 2 (/ 1 x))
(/ 1 x)
(* 2 (atan (* (+ 1 (* x (* x 1/2))) (- 1 x))))
2
(atan (* (+ 1 (* x (* x 1/2))) (- 1 x)))
(* (+ 1 (* x (* x 1/2))) (- 1 x))
(+ 1 (* x (* x 1/2)))
1
(* x (* x 1/2))
x
(* x 1/2)
1/2
(- 1 x)
(* 2 (atan (* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x)))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))))
2
(atan (* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x)))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x)))))))))
(* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x)))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))
(- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x))))))))
1
(* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x)))))))
x
(* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x))))))
(+ -1 (* 1/2 (* x (- 1 x))))
-1
(* 1/2 (* x (- 1 x)))
1/2
(* x (- 1 x))
(- 1 x)
(* x (+ -1 (* 1/2 (* x (- 1 x)))))
(/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x)))))))
(- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))
Outputs
(* 2 (atan (sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (+ x (+ 2 (/ 1 x)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 #s(literal -1 binary64) x)) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))))
2
#s(literal 2 binary64)
(atan (sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (+ x (+ 2 (/ 1 x))))))
(atan.f64 (sqrt.f64 (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 #s(literal -1 binary64) x)) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))))
(sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (+ x (+ 2 (/ 1 x)))))
(sqrt.f64 (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 #s(literal -1 binary64) x)) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))
(/ (- (/ (+ 1 x) x) (+ 1 x)) (+ x (+ 2 (/ 1 x))))
(/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 #s(literal -1 binary64) x)) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))
(- (/ (+ 1 x) x) (+ 1 x))
(+.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 #s(literal -1 binary64) x))
(/ (+ 1 x) x)
(/.f64 (+.f64 #s(literal 1 binary64) x) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(+ x (+ 2 (/ 1 x)))
(+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
(+ 2 (/ 1 x))
(+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* 2 (atan (* (+ 1 (* x (* x 1/2))) (- 1 x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))))
2
#s(literal 2 binary64)
(atan (* (+ 1 (* x (* x 1/2))) (- 1 x)))
(atan.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x)))
(* (+ 1 (* x (* x 1/2))) (- 1 x))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))
(+ 1 (* x (* x 1/2)))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64))))
1
#s(literal 1 binary64)
(* x (* x 1/2))
(*.f64 x (*.f64 x #s(literal 1/2 binary64)))
x
(* x 1/2)
(*.f64 x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
(* 2 (atan (* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x)))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 x #s(literal -1 binary64)))))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 x #s(literal -1 binary64))))))))))
2
#s(literal 2 binary64)
(atan (* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x)))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x)))))))))
(atan.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 x #s(literal -1 binary64)))))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 x #s(literal -1 binary64)))))))))
(* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x)))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 x #s(literal -1 binary64)))))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 x #s(literal -1 binary64))))))))
(- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x))))))))
(+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 x #s(literal -1 binary64))))))))
1
#s(literal 1 binary64)
(* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x)))))))
(*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))))
x
(* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x))))))
(*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))
(+ -1 (* 1/2 (* x (- 1 x))))
(+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))
-1
#s(literal -1 binary64)
(* 1/2 (* x (- 1 x)))
(*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))
1/2
#s(literal 1/2 binary64)
(* x (- 1 x))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
(* x (+ -1 (* 1/2 (* x (- 1 x)))))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))
(/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x)))))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 x #s(literal -1 binary64))))))))
(- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 x #s(literal -1 binary64)))))))

localize572.0ms (2.7%)

Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))
✓accuracy100.0%
(*.f64 x (-.f64 #s(literal 1 binary64) x))
✓accuracy100.0%
(*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))))
✓accuracy100.0%
(*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))
✓accuracy100.0%
(*.f64 x #s(literal 1/2 binary64))
✓accuracy100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))))
✓accuracy100.0%
(atan.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x)))
✓accuracy100.0%
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))
✓accuracy100.0%
(+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))
✓accuracy100.0%
(sqrt.f64 (/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))))
✓accuracy100.0%
(/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))))
✓accuracy100.0%
(/.f64 (+.f64 #s(literal 1 binary64) x) x)
Results
372.0ms256×0valid
Compiler

Compiled 435 to 35 computations (92% saved)

Precisions
Click to see histograms. Total time spent on operations: 122.0ms
ival-mult: 52.0ms (42.7% of total)
ival-div: 18.0ms (14.8% of total)
ival-atan: 18.0ms (14.8% of total)
ival-add: 16.0ms (13.1% of total)
ival-sub: 12.0ms (9.8% of total)
ival-sqrt: 5.0ms (4.1% of total)
const: 1.0ms (0.8% of total)
backward-pass: 0.0ms (0% of total)

series36.0ms (0.2%)

Counts
19 → 228
Calls
Call 1
Inputs
#<alt (* 2 (atan (sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (+ x (+ 2 (/ 1 x)))))))>
#<alt (atan (sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (+ x (+ 2 (/ 1 x))))))>
#<alt (sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (+ x (+ 2 (/ 1 x)))))>
#<alt (/ (- (/ (+ 1 x) x) (+ 1 x)) (+ x (+ 2 (/ 1 x))))>
#<alt (* 2 (atan (* (+ 1 (* x (* x 1/2))) (- 1 x))))>
#<alt (atan (* (+ 1 (* x (* x 1/2))) (- 1 x)))>
#<alt (* (+ 1 (* x (* x 1/2))) (- 1 x))>
#<alt (+ 1 (* x (* x 1/2)))>
#<alt (* 2 (atan (* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x)))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))))>
#<alt (atan (* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x)))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x)))))))))>
#<alt (* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x)))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))>
#<alt (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x))))))))>
#<alt (/ (+ 1 x) x)>
#<alt (+ x (+ 2 (/ 1 x)))>
#<alt (* x 1/2)>
#<alt (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x))))))>
#<alt (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x)))))))>
#<alt (* x (- 1 x))>
#<alt (* x (+ -1 (* 1/2 (* x (- 1 x)))))>
Outputs
#<alt (* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))>
#<alt (* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))>
#<alt (* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))>
#<alt (* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))>
#<alt (* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))>
#<alt (* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))>
#<alt (* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))>
#<alt (* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))>
#<alt (* 2 (atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x))))))>
#<alt (* 2 (atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x))))))>
#<alt (* 2 (atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x))))))>
#<alt (* 2 (atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x))))))>
#<alt (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))>
#<alt (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))>
#<alt (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))>
#<alt (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))>
#<alt (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))>
#<alt (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))>
#<alt (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))>
#<alt (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))>
#<alt (atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x)))))>
#<alt (atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x)))))>
#<alt (atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x)))))>
#<alt (atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x)))))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))>
#<alt (sqrt -1)>
#<alt (+ (sqrt -1) (/ 1 (* x (sqrt -1))))>
#<alt (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))>
#<alt (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))>
#<alt (sqrt -1)>
#<alt (+ (sqrt -1) (/ 1 (* x (sqrt -1))))>
#<alt (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))>
#<alt (+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))>
#<alt 1>
#<alt (+ 1 (* -2 x))>
#<alt (+ 1 (* x (- (* 2 x) 2)))>
#<alt (+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))>
#<alt -1>
#<alt (- (* 2 (/ 1 x)) 1)>
#<alt (- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))>
#<alt (- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))>
#<alt -1>
#<alt (- (* 2 (/ 1 x)) 1)>
#<alt (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)>
#<alt (- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)>
#<alt (* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))>
#<alt (* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))>
#<alt (* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))>
#<alt (* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))>
#<alt (* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))>
#<alt (* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))>
#<alt (* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))>
#<alt (* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))>
#<alt (* 2 (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2))))))>
#<alt (* 2 (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2))))))>
#<alt (* 2 (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2))))))>
#<alt (* 2 (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2))))))>
#<alt (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))>
#<alt (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))>
#<alt (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))>
#<alt (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))>
#<alt (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))>
#<alt (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))>
#<alt (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))>
#<alt (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))>
#<alt (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2)))))>
#<alt (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2)))))>
#<alt (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2)))))>
#<alt (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2)))))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))>
#<alt (* -1/2 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (pow x 2)))>
#<alt (+ 1 (* 1/2 (pow x 2)))>
#<alt (+ 1 (* 1/2 (pow x 2)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))>
#<alt (* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))))>
#<alt (* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))))>
#<alt (* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))))>
#<alt (* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))))>
#<alt (* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x)))))))>
#<alt (* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x)))))))>
#<alt (* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x)))))))>
#<alt (* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x)))))))>
#<alt (* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (+ 1 (* -1 x)))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))))>
#<alt (* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (+ 1 (* -1 x)))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))))>
#<alt (* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (+ 1 (* -1 x)))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))))>
#<alt (* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (+ 1 (* -1 x)))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))))>
#<alt (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))>
#<alt (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))>
#<alt (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))>
#<alt (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))>
#<alt (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x))))))>
#<alt (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x))))))>
#<alt (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x))))))>
#<alt (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x))))))>
#<alt (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (+ 1 (* -1 x)))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))>
#<alt (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (+ 1 (* -1 x)))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))>
#<alt (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (+ 1 (* -1 x)))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))>
#<alt (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (+ 1 (* -1 x)))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))>
#<alt (* -1/2 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))>
#<alt 1>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- x 1)))>
#<alt (+ 1 (* (pow x 2) (- (* x (+ 1 (* -5/4 x))) 1)))>
#<alt (* -1/4 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* (pow x 6) (- (* 1/2 (/ 1 x)) (+ 1/4 (/ 5/4 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 5/4 (pow x 2)))))>
#<alt (* -1/4 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* (pow x 6) (- (* -1 (/ (- (* 5/4 (/ 1 x)) 1/2) x)) 1/4))>
#<alt (* (pow x 6) (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 5/4) x)) 1/2) x)) 1/4))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 x) x)>
#<alt (/ (+ 1 x) x)>
#<alt (/ (+ 1 x) x)>
#<alt 1>
#<alt (+ 1 (/ 1 x))>
#<alt (+ 1 (/ 1 x))>
#<alt (+ 1 (/ 1 x))>
#<alt 1>
#<alt (+ 1 (/ 1 x))>
#<alt (+ 1 (/ 1 x))>
#<alt (+ 1 (/ 1 x))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* 2 x)) x)>
#<alt (/ (+ 1 (* x (+ 2 x))) x)>
#<alt (/ (+ 1 (* x (+ 2 x))) x)>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (+ (* 2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* x (+ 1 (+ (* 2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* -1 (* x (- (* -1 (/ (+ 2 (/ 1 x)) x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ (+ 2 (/ 1 x)) x)) 1)))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt x>
#<alt (* x (+ 1 (* -1 x)))>
#<alt (* x (+ 1 (* x (- (* 5/4 x) 1))))>
#<alt (* x (+ 1 (* x (- (* x (+ 5/4 (* -1/2 x))) 1))))>
#<alt (* 1/4 (pow x 5))>
#<alt (* (pow x 5) (- 1/4 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 5) (- (+ 1/4 (/ 5/4 (pow x 2))) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 5) (- (+ 1/4 (/ 5/4 (pow x 2))) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3)))))>
#<alt (* 1/4 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- (* 1/2 (/ 1 x)) 1/4)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (- (* 5/4 (/ 1 x)) 1/2) x)) 1/4)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 5/4) x)) 1/2) x)) 1/4)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 x)))>
#<alt (* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))>
#<alt (* (pow x 2) (+ 1 (* x (- (* x (+ 5/4 (* -1/2 x))) 1))))>
#<alt (* 1/4 (pow x 6))>
#<alt (* (pow x 6) (- 1/4 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 6) (- (+ 1/4 (/ 5/4 (pow x 2))) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 6) (- (+ 1/4 (/ 5/4 (pow x 2))) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3)))))>
#<alt (* 1/4 (pow x 6))>
#<alt (* (pow x 6) (- 1/4 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 6) (+ 1/4 (* -1 (/ (- 1/2 (* 5/4 (/ 1 x))) x))))>
#<alt (* (pow x 6) (+ 1/4 (* -1 (/ (+ 1/2 (* -1 (/ (- 5/4 (/ 1 x)) x))) x))))>
#<alt x>
#<alt (* x (+ 1 (* -1 x)))>
#<alt (* x (+ 1 (* -1 x)))>
#<alt (* x (+ 1 (* -1 x)))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 x) 1))>
#<alt (* (pow x 2) (- (/ 1 x) 1))>
#<alt (* (pow x 2) (- (/ 1 x) 1))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 x) 1))>
#<alt (* (pow x 2) (- (/ 1 x) 1))>
#<alt (* (pow x 2) (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* x (- (* 1/2 x) 1))>
#<alt (* x (- (* x (+ 1/2 (* -1/2 x))) 1))>
#<alt (* x (- (* x (+ 1/2 (* -1/2 x))) 1))>
#<alt (* -1/2 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))>
Calls

57 calls:

TimeVariablePointExpression
8.0ms
x
@inf
(* 2 (atan (sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (+ x (+ 2 (/ 1 x)))))))
3.0ms
x
@-inf
(* 2 (atan (* (+ 1 (* x (* x 1/2))) (- 1 x))))
2.0ms
x
@-inf
(* 2 (atan (sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (+ x (+ 2 (/ 1 x)))))))
2.0ms
x
@-inf
(* 2 (atan (* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x)))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))))
2.0ms
x
@inf
(* 2 (atan (* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x)))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))))

rewrite996.0ms (4.7%)

Algorithm
1×batch-egg-rewrite
Rules
5530×*-lowering-*.f32
5530×*-lowering-*.f64
3310×/-lowering-/.f32
3310×/-lowering-/.f64
3034×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
034335
1211220
22121210
010159210
Stop Event
1×iter limit
1×node limit
Counts
19 → 452
Calls
Call 1
Inputs
(* 2 (atan (sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (+ x (+ 2 (/ 1 x)))))))
(atan (sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (+ x (+ 2 (/ 1 x))))))
(sqrt (/ (- (/ (+ 1 x) x) (+ 1 x)) (+ x (+ 2 (/ 1 x)))))
(/ (- (/ (+ 1 x) x) (+ 1 x)) (+ x (+ 2 (/ 1 x))))
(* 2 (atan (* (+ 1 (* x (* x 1/2))) (- 1 x))))
(atan (* (+ 1 (* x (* x 1/2))) (- 1 x)))
(* (+ 1 (* x (* x 1/2))) (- 1 x))
(+ 1 (* x (* x 1/2)))
(* 2 (atan (* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x)))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))))
(atan (* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x)))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x)))))))))
(* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x)))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))
(- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x))))))))
(/ (+ 1 x) x)
(+ x (+ 2 (/ 1 x)))
(* x 1/2)
(* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x))))))
(* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* 1/2 (* x (- 1 x)))))))
(* x (- 1 x))
(* x (+ -1 (* 1/2 (* x (- 1 x)))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) x))))) #s(literal 2 binary64))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) x)))))
(exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) x)))) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) x)) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) x)) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) x))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (*.f64 x (*.f64 x x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (sqrt.f64 (*.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) x)) (+.f64 (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x)))))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 x (+.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (*.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) x)) (+.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) x)))))
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(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x) (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (-.f64 #s(literal 1 binary64) x)) x))))
(fma.f64 x #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (-.f64 #s(literal 1 binary64) x)) x)))
(fma.f64 x (*.f64 x (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 0 binary64) x))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (-.f64 #s(literal 1 binary64) x)) x) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) x))
(fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (-.f64 #s(literal 1 binary64) x)) x)))
(fma.f64 (*.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 x #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) x))
(fma.f64 (*.f64 x (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))) x (-.f64 #s(literal 0 binary64) x))
(fma.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (-.f64 #s(literal 1 binary64) x)) x)) #s(literal 1 binary64)))
(fma.f64 (*.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) x))
(/.f64 (+.f64 (neg.f64 (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))) (+.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (-.f64 #s(literal 1 binary64) x)) x)) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (-.f64 #s(literal 1 binary64) x)) x))) (*.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (-.f64 #s(literal 1 binary64) x)) x))))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (-.f64 #s(literal 1 binary64) x)) x)) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (-.f64 #s(literal 1 binary64) x)) x)))) (-.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x (-.f64 #s(literal 1 binary64) x)) x))))
(/.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))) (-.f64 (*.f64 x (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)))))
(/.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))) (+.f64 #s(literal -1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))) x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))) (-.f64 (*.f64 x (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 x (-.f64 #s(literal 1 binary64) x))))) x) (+.f64 #s(literal -1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))
(*.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))))))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x)))))
(*.f64 (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x)))) x)
(*.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))
(*.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))))) x)

simplify600.0ms (2.8%)

Algorithm
1×egg-herbie
Rules
3158×*-lowering-*.f32
3158×*-lowering-*.f64
2146×+-lowering-+.f64
2146×+-lowering-+.f32
1658×sum4-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02842705
18772507
225842349
376522349
085222349
Stop Event
1×iter limit
1×node limit
Counts
228 → 228
Calls
Call 1
Inputs
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(* 2 (atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x))))))
(* 2 (atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x))))))
(* 2 (atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x))))))
(* 2 (atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x)))))
(atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x)))))
(atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x)))))
(atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x)))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
1
(+ 1 (* -2 x))
(+ 1 (* x (- (* 2 x) 2)))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
-1
(- (* 2 (/ 1 x)) 1)
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
-1
(- (* 2 (/ 1 x)) 1)
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(* 2 (atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x))))
(* 2 (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2))))))
(* 2 (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2))))))
(* 2 (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2))))))
(* 2 (atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2))))))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan (* (+ 1 (* 1/2 (pow x 2))) (- 1 x)))
(atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2)))))
(atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2)))))
(atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2)))))
(atan (* (+ 1 (* -1 x)) (+ 1 (* 1/2 (pow x 2)))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(* -1/2 (pow x 3))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* 1/2 (pow x 2)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))
(* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))))
(* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))))
(* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))))
(* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))))
(* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x)))))))
(* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x)))))))
(* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x)))))))
(* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x)))))))
(* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (+ 1 (* -1 x)))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))))
(* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (+ 1 (* -1 x)))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))))
(* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (+ 1 (* -1 x)))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))))
(* 2 (atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (+ 1 (* -1 x)))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))))
(atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))
(atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))
(atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))
(atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))
(atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x))))))
(atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x))))))
(atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x))))))
(atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (- 1 x))) 1) 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x))))))
(atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (+ 1 (* -1 x)))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))
(atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (+ 1 (* -1 x)))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))
(atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (+ 1 (* -1 x)))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))
(atan (/ (- 1 (* (pow x 2) (pow (- (* 1/2 (* x (+ 1 (* -1 x)))) 1) 2))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(* -1/2 (pow x 3))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- x 1)))
(+ 1 (* (pow x 2) (- (* x (+ 1 (* -5/4 x))) 1)))
(* -1/4 (pow x 6))
(* (pow x 6) (- (* 1/2 (/ 1 x)) 1/4))
(* (pow x 6) (- (* 1/2 (/ 1 x)) (+ 1/4 (/ 5/4 (pow x 2)))))
(* (pow x 6) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 5/4 (pow x 2)))))
(* -1/4 (pow x 6))
(* (pow x 6) (- (* 1/2 (/ 1 x)) 1/4))
(* (pow x 6) (- (* -1 (/ (- (* 5/4 (/ 1 x)) 1/2) x)) 1/4))
(* (pow x 6) (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 5/4) x)) 1/2) x)) 1/4))
(/ 1 x)
(/ (+ 1 x) x)
(/ (+ 1 x) x)
(/ (+ 1 x) x)
1
(+ 1 (/ 1 x))
(+ 1 (/ 1 x))
(+ 1 (/ 1 x))
1
(+ 1 (/ 1 x))
(+ 1 (/ 1 x))
(+ 1 (/ 1 x))
(/ 1 x)
(/ (+ 1 (* 2 x)) x)
(/ (+ 1 (* x (+ 2 x))) x)
(/ (+ 1 (* x (+ 2 x))) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (+ (* 2 (/ 1 x)) (/ 1 (pow x 2)))))
(* x (+ 1 (+ (* 2 (/ 1 x)) (/ 1 (pow x 2)))))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* -1 (* x (- (* -1 (/ (+ 2 (/ 1 x)) x)) 1)))
(* -1 (* x (- (* -1 (/ (+ 2 (/ 1 x)) x)) 1)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
x
(* x (+ 1 (* -1 x)))
(* x (+ 1 (* x (- (* 5/4 x) 1))))
(* x (+ 1 (* x (- (* x (+ 5/4 (* -1/2 x))) 1))))
(* 1/4 (pow x 5))
(* (pow x 5) (- 1/4 (* 1/2 (/ 1 x))))
(* (pow x 5) (- (+ 1/4 (/ 5/4 (pow x 2))) (* 1/2 (/ 1 x))))
(* (pow x 5) (- (+ 1/4 (/ 5/4 (pow x 2))) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3)))))
(* 1/4 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/2 (/ 1 x)) 1/4)))
(* -1 (* (pow x 5) (- (* -1 (/ (- (* 5/4 (/ 1 x)) 1/2) x)) 1/4)))
(* -1 (* (pow x 5) (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 5/4) x)) 1/2) x)) 1/4)))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 x)))
(* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))
(* (pow x 2) (+ 1 (* x (- (* x (+ 5/4 (* -1/2 x))) 1))))
(* 1/4 (pow x 6))
(* (pow x 6) (- 1/4 (* 1/2 (/ 1 x))))
(* (pow x 6) (- (+ 1/4 (/ 5/4 (pow x 2))) (* 1/2 (/ 1 x))))
(* (pow x 6) (- (+ 1/4 (/ 5/4 (pow x 2))) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3)))))
(* 1/4 (pow x 6))
(* (pow x 6) (- 1/4 (* 1/2 (/ 1 x))))
(* (pow x 6) (+ 1/4 (* -1 (/ (- 1/2 (* 5/4 (/ 1 x))) x))))
(* (pow x 6) (+ 1/4 (* -1 (/ (+ 1/2 (* -1 (/ (- 5/4 (/ 1 x)) x))) x))))
x
(* x (+ 1 (* -1 x)))
(* x (+ 1 (* -1 x)))
(* x (+ 1 (* -1 x)))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 x) 1))
(* (pow x 2) (- (/ 1 x) 1))
(* (pow x 2) (- (/ 1 x) 1))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 x) 1))
(* (pow x 2) (- (/ 1 x) 1))
(* (pow x 2) (- (/ 1 x) 1))
(* -1 x)
(* x (- (* 1/2 x) 1))
(* x (- (* x (+ 1/2 (* -1/2 x))) 1))
(* x (- (* x (+ 1/2 (* -1/2 x))) 1))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* -1/2 (pow x 3))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
Outputs
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
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(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
x
(* x (+ 1 (* -1 x)))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(* x (+ 1 (* x (- (* 5/4 x) 1))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 5/4 binary64))))))
(* x (+ 1 (* x (- (* x (+ 5/4 (* -1/2 x))) 1))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 5/4 binary64)))))))
(* 1/4 (pow x 5))
(*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (- 1/4 (* 1/2 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)))
(* (pow x 5) (- (+ 1/4 (/ 5/4 (pow x 2))) (* 1/2 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 5/4 binary64) x)) x)))
(* (pow x 5) (- (+ 1/4 (/ 5/4 (pow x 2))) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3)))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 5/4 binary64) (/.f64 #s(literal -1 binary64) x)) x)) x)))
(* 1/4 (pow x 5))
(*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* 1/2 (/ 1 x)) 1/4)))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)))
(* -1 (* (pow x 5) (- (* -1 (/ (- (* 5/4 (/ 1 x)) 1/2) x)) 1/4)))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 5/4 binary64) x)) x)))
(* -1 (* (pow x 5) (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 5/4) x)) 1/2) x)) 1/4)))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 5/4 binary64) (/.f64 #s(literal -1 binary64) x)) x)) x)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 x)))
(*.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) x)))
(* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))
(*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 5/4 binary64)))))))
(* (pow x 2) (+ 1 (* x (- (* x (+ 5/4 (* -1/2 x))) 1))))
(*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 5/4 binary64))))))))
(* 1/4 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/4 binary64))
(* (pow x 6) (- 1/4 (* 1/2 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)))
(* (pow x 6) (- (+ 1/4 (/ 5/4 (pow x 2))) (* 1/2 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 5/4 binary64) x)) x)))
(* (pow x 6) (- (+ 1/4 (/ 5/4 (pow x 2))) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3)))))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 5/4 binary64) (/.f64 #s(literal -1 binary64) x)) x)) x)))
(* 1/4 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/4 binary64))
(* (pow x 6) (- 1/4 (* 1/2 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)))
(* (pow x 6) (+ 1/4 (* -1 (/ (- 1/2 (* 5/4 (/ 1 x))) x))))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 5/4 binary64) x)) x)))
(* (pow x 6) (+ 1/4 (* -1 (/ (+ 1/2 (* -1 (/ (- 5/4 (/ 1 x)) x))) x))))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 5/4 binary64) (/.f64 #s(literal -1 binary64) x)) x)) x)))
x
(* x (+ 1 (* -1 x)))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(* x (+ 1 (* -1 x)))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(* x (+ 1 (* -1 x)))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 x) 1))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(* (pow x 2) (- (/ 1 x) 1))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(* (pow x 2) (- (/ 1 x) 1))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 x) 1))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(* (pow x 2) (- (/ 1 x) 1))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(* (pow x 2) (- (/ 1 x) 1))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* x (- (* 1/2 x) 1))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))
(* x (- (* x (+ 1/2 (* -1/2 x))) 1))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* x (- (* x (+ 1/2 (* -1/2 x))) 1))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* -1/2 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal -1/2 binary64))))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(*.f64 (*.f64 x x) (*.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)))
(* -1/2 (pow x 3))
(*.f64 x (*.f64 x (*.f64 x #s(literal -1/2 binary64))))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(*.f64 (*.f64 x x) (*.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)))

eval319.0ms (1.5%)

Compiler

Compiled 31524 to 3331 computations (89.4% saved)

prune182.0ms (0.9%)

Pruning

11 alts after pruning (5 fresh and 6 done)

PrunedKeptTotal
New7615766
Fresh000
Picked213
Done055
Total76311774
Accuracy
100.0%
Counts
774 → 11
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.5%
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x x))))))
✓99.1%
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
✓99.5%
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))))
✓99.4%
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
▶99.6%
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))))
▶99.5%
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 5/4 binary64)))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))))
✓99.5%
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))))
▶31.6%
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x)))))
▶100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))))))
✓100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
✓98.2%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
Compiler

Compiled 357 to 231 computations (35.3% saved)

simplify491.0ms (2.3%)

Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
✓cost-diff128
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))
✓cost-diff128
(atan.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))))))
✓cost-diff128
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))))
✓cost-diff0
(-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 5/4 binary64))))))))
✓cost-diff128
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 5/4 binary64)))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))
✓cost-diff128
(atan.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 5/4 binary64)))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))))))
✓cost-diff128
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 5/4 binary64)))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))))
✓cost-diff0
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) x))
✓cost-diff0
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x x))))
✓cost-diff0
(atan.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x x))))))
✓cost-diff0
(*.f64 x (*.f64 x x))
✓cost-diff0
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x)))
✓cost-diff0
(atan.f64 (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x))))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x)))))
✓cost-diff0
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))))
✓cost-diff0
(sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))))
✓cost-diff0
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))))))
✓cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))))))
Rules
3746×*-lowering-*.f32
3746×*-lowering-*.f64
3010×+-lowering-+.f64
3010×+-lowering-+.f32
1544×distribute-lft-in
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
061776
1176707
2553680
32217656
47989656
08036656
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ x (+ 2 (/ 1 x)))))))
2
(atan (sqrt (/ (- (/ 1 x) x) (+ x (+ 2 (/ 1 x))))))
(sqrt (/ (- (/ 1 x) x) (+ x (+ 2 (/ 1 x)))))
(/ (- (/ 1 x) x) (+ x (+ 2 (/ 1 x))))
(- (/ 1 x) x)
(/ 1 x)
1
x
(+ x (+ 2 (/ 1 x)))
(+ 2 (/ 1 x))
(* 2 (atan (* (* x (* x x)) (+ -1/2 (/ (+ 1/2 (/ (+ (/ 1 x) -1) x)) x)))))
2
(atan (* (* x (* x x)) (+ -1/2 (/ (+ 1/2 (/ (+ (/ 1 x) -1) x)) x))))
(* (* x (* x x)) (+ -1/2 (/ (+ 1/2 (/ (+ (/ 1 x) -1) x)) x)))
(* x (* x x))
x
(* x x)
(+ -1/2 (/ (+ 1/2 (/ (+ (/ 1 x) -1) x)) x))
-1/2
(/ (+ 1/2 (/ (+ (/ 1 x) -1) x)) x)
(+ 1/2 (/ (+ (/ 1 x) -1) x))
1/2
(/ (+ (/ 1 x) -1) x)
(+ (/ 1 x) -1)
(/ 1 x)
1
-1
(* 2 (atan (/ (* (- 1 (* (* (* x x) (* x x)) 1/4)) (- 1 x)) (- 1 (* 1/2 (* x x))))))
2
(atan (/ (* (- 1 (* (* (* x x) (* x x)) 1/4)) (- 1 x)) (- 1 (* 1/2 (* x x)))))
(/ (* (- 1 (* (* (* x x) (* x x)) 1/4)) (- 1 x)) (- 1 (* 1/2 (* x x))))
(* (- 1 (* (* (* x x) (* x x)) 1/4)) (- 1 x))
(- 1 (* (* (* x x) (* x x)) 1/4))
1
(* (* (* x x) (* x x)) 1/4)
(* (* x x) (* x x))
(* x x)
x
1/4
(- 1 x)
(- 1 (* 1/2 (* x x)))
(* 1/2 (* x x))
1/2
(* 2 (atan (* (- 1 (* x (* x (+ 1 (* x (+ -1 (* x 5/4))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))))
2
(atan (* (- 1 (* x (* x (+ 1 (* x (+ -1 (* x 5/4))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x)))))))))
(* (- 1 (* x (* x (+ 1 (* x (+ -1 (* x 5/4))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))
(- 1 (* x (* x (+ 1 (* x (+ -1 (* x 5/4)))))))
1
(* x (* x (+ 1 (* x (+ -1 (* x 5/4))))))
x
(* x (+ 1 (* x (+ -1 (* x 5/4)))))
(+ 1 (* x (+ -1 (* x 5/4))))
(* x (+ -1 (* x 5/4)))
(+ -1 (* x 5/4))
-1
(* x 5/4)
5/4
(/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x)))))))
(- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))
(* x (+ -1 (* 1/2 (* x (- 1 x)))))
(+ -1 (* 1/2 (* x (- 1 x))))
(* 1/2 (* x (- 1 x)))
1/2
(* x (- 1 x))
(- 1 x)
(* 2 (atan (* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2)))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))))
2
(atan (* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2)))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x)))))))))
(* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2)))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))
(- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2))))))
1
(* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2)))))
x
(* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2))))
(+ -1 (* 1/2 (* x (- 1 x))))
-1
(* 1/2 (* x (- 1 x)))
1/2
(* x (- 1 x))
(- 1 x)
(* x (+ -1 (* x 1/2)))
(+ -1 (* x 1/2))
(* x 1/2)
(/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x)))))))
(- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))
(* x (+ -1 (* 1/2 (* x (- 1 x)))))
Outputs
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ x (+ 2 (/ 1 x)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))))))
2
#s(literal 2 binary64)
(atan (sqrt (/ (- (/ 1 x) x) (+ x (+ 2 (/ 1 x))))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))))))
(sqrt (/ (- (/ 1 x) x) (+ x (+ 2 (/ 1 x)))))
(sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))))
(/ (- (/ 1 x) x) (+ x (+ 2 (/ 1 x))))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))))
(- (/ 1 x) x)
(-.f64 (/.f64 #s(literal 1 binary64) x) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(+ x (+ 2 (/ 1 x)))
(+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))
(+ 2 (/ 1 x))
(+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))
(* 2 (atan (* (* x (* x x)) (+ -1/2 (/ (+ 1/2 (/ (+ (/ 1 x) -1) x)) x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x))))))
2
#s(literal 2 binary64)
(atan (* (* x (* x x)) (+ -1/2 (/ (+ 1/2 (/ (+ (/ 1 x) -1) x)) x))))
(atan.f64 (*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x)))))
(* (* x (* x x)) (+ -1/2 (/ (+ 1/2 (/ (+ (/ 1 x) -1) x)) x)))
(*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x))))
(* x (* x x))
(*.f64 x (*.f64 x x))
x
(* x x)
(*.f64 x x)
(+ -1/2 (/ (+ 1/2 (/ (+ (/ 1 x) -1) x)) x))
(+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x))
-1/2
#s(literal -1/2 binary64)
(/ (+ 1/2 (/ (+ (/ 1 x) -1) x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x)
(+ 1/2 (/ (+ (/ 1 x) -1) x))
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x))
1/2
#s(literal 1/2 binary64)
(/ (+ (/ 1 x) -1) x)
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)
(+ (/ 1 x) -1)
(+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
-1
#s(literal -1 binary64)
(* 2 (atan (/ (* (- 1 (* (* (* x x) (* x x)) 1/4)) (- 1 x)) (- 1 (* 1/2 (* x x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/4 binary64))))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))))))
2
#s(literal 2 binary64)
(atan (/ (* (- 1 (* (* (* x x) (* x x)) 1/4)) (- 1 x)) (- 1 (* 1/2 (* x x)))))
(atan.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/4 binary64))))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))))
(/ (* (- 1 (* (* (* x x) (* x x)) 1/4)) (- 1 x)) (- 1 (* 1/2 (* x x))))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/4 binary64))))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))))
(* (- 1 (* (* (* x x) (* x x)) 1/4)) (- 1 x))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/4 binary64))))) (-.f64 #s(literal 1 binary64) x))
(- 1 (* (* (* x x) (* x x)) 1/4))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/4 binary64)))))
1
#s(literal 1 binary64)
(* (* (* x x) (* x x)) 1/4)
(*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/4 binary64))))
(* (* x x) (* x x))
(*.f64 x (*.f64 x (*.f64 x x)))
(* x x)
(*.f64 x x)
x
1/4
#s(literal 1/4 binary64)
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
(- 1 (* 1/2 (* x x)))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))
(* 1/2 (* x x))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(* 2 (atan (* (- 1 (* x (* x (+ 1 (* x (+ -1 (* x 5/4))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 5/4 binary64)))))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))))))
2
#s(literal 2 binary64)
(atan (* (- 1 (* x (* x (+ 1 (* x (+ -1 (* x 5/4))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x)))))))))
(atan.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 5/4 binary64)))))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))
(* (- 1 (* x (* x (+ 1 (* x (+ -1 (* x 5/4))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 5/4 binary64)))))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))))
(- 1 (* x (* x (+ 1 (* x (+ -1 (* x 5/4)))))))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 5/4 binary64))))))))
1
#s(literal 1 binary64)
(* x (* x (+ 1 (* x (+ -1 (* x 5/4))))))
(*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 (*.f64 x #s(literal 5/4 binary64)) #s(literal 1 binary64))))))
x
(* x (+ 1 (* x (+ -1 (* x 5/4)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 (*.f64 x #s(literal 5/4 binary64)) #s(literal 1 binary64)))))
(+ 1 (* x (+ -1 (* x 5/4))))
(+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 (*.f64 x #s(literal 5/4 binary64)) #s(literal 1 binary64))))
(* x (+ -1 (* x 5/4)))
(*.f64 x (-.f64 (*.f64 x #s(literal 5/4 binary64)) #s(literal 1 binary64)))
(+ -1 (* x 5/4))
(+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 5/4 binary64)))
-1
#s(literal -1 binary64)
(* x 5/4)
(*.f64 x #s(literal 5/4 binary64))
5/4
#s(literal 5/4 binary64)
(/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x)))))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))))
(- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))
(* x (+ -1 (* 1/2 (* x (- 1 x)))))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(+ -1 (* 1/2 (* x (- 1 x))))
(+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))))
(* 1/2 (* x (- 1 x)))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))
1/2
#s(literal 1/2 binary64)
(* x (- 1 x))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
(* 2 (atan (* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2)))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))) (*.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))))))
2
#s(literal 2 binary64)
(atan (* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2)))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x)))))))))
(atan.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))) (*.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))
(* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2)))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))) (*.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))))
(- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2))))))
(+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))) (*.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
1
#s(literal 1 binary64)
(* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2)))))
(*.f64 (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))) (*.f64 x (*.f64 x (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
x
(* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2))))
(*.f64 (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))) (*.f64 x (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(+ -1 (* 1/2 (* x (- 1 x))))
(+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))))
-1
#s(literal -1 binary64)
(* 1/2 (* x (- 1 x)))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))
1/2
#s(literal 1/2 binary64)
(* x (- 1 x))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
(* x (+ -1 (* x 1/2)))
(*.f64 x (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(+ -1 (* x 1/2))
(+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* x 1/2)
(*.f64 x #s(literal 1/2 binary64))
(/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x)))))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))))
(- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))
(* x (+ -1 (* 1/2 (* x (- 1 x)))))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))

localize780.0ms (3.7%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))))
✓accuracy100.0%
(*.f64 x (-.f64 #s(literal 1 binary64) x))
✓accuracy100.0%
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))
✓accuracy100.0%
(*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
✓accuracy100.0%
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 5/4 binary64))))
✓accuracy100.0%
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))
✓accuracy100.0%
(*.f64 x (-.f64 #s(literal 1 binary64) x))
✓accuracy100.0%
(*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 5/4 binary64)))))))
✓accuracy100.0%
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) x))
✓accuracy100.0%
(atan.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
✓accuracy100.0%
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x x))))
✓accuracy99.8%
(*.f64 (*.f64 x x) (*.f64 x x))
✓accuracy99.9%
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x)
✓accuracy99.9%
(*.f64 x (*.f64 x x))
✓accuracy99.8%
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)
✓accuracy33.7%
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x)))
✓accuracy100.0%
(-.f64 (/.f64 #s(literal 1 binary64) x) x)
✓accuracy100.0%
(+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))
✓accuracy100.0%
(sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))))
✓accuracy100.0%
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))))
Results
457.0ms256×0valid
Compiler

Compiled 829 to 62 computations (92.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 228.0ms
ival-mult: 113.0ms (49.6% of total)
ival-atan: 30.0ms (13.2% of total)
ival-add: 29.0ms (12.7% of total)
ival-div: 26.0ms (11.4% of total)
ival-sub: 22.0ms (9.7% of total)
ival-sqrt: 4.0ms (1.8% of total)
const: 2.0ms (0.9% of total)
backward-pass: 0.0ms (0% of total)

series75.0ms (0.4%)

Counts
32 → 384
Calls
Call 1
Inputs
#<alt (* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ x (+ 2 (/ 1 x)))))))>
#<alt (atan (sqrt (/ (- (/ 1 x) x) (+ x (+ 2 (/ 1 x))))))>
#<alt (sqrt (/ (- (/ 1 x) x) (+ x (+ 2 (/ 1 x)))))>
#<alt (/ (- (/ 1 x) x) (+ x (+ 2 (/ 1 x))))>
#<alt (* 2 (atan (* (* x (* x x)) (+ -1/2 (/ (+ 1/2 (/ (+ (/ 1 x) -1) x)) x)))))>
#<alt (atan (* (* x (* x x)) (+ -1/2 (/ (+ 1/2 (/ (+ (/ 1 x) -1) x)) x))))>
#<alt (* (* x (* x x)) (+ -1/2 (/ (+ 1/2 (/ (+ (/ 1 x) -1) x)) x)))>
#<alt (* x (* x x))>
#<alt (* 2 (atan (/ (* (- 1 (* (* (* x x) (* x x)) 1/4)) (- 1 x)) (- 1 (* 1/2 (* x x))))))>
#<alt (atan (/ (* (- 1 (* (* (* x x) (* x x)) 1/4)) (- 1 x)) (- 1 (* 1/2 (* x x)))))>
#<alt (/ (* (- 1 (* (* (* x x) (* x x)) 1/4)) (- 1 x)) (- 1 (* 1/2 (* x x))))>
#<alt (* (- 1 (* (* (* x x) (* x x)) 1/4)) (- 1 x))>
#<alt (* 2 (atan (* (- 1 (* x (* x (+ 1 (* x (+ -1 (* x 5/4))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))))>
#<alt (atan (* (- 1 (* x (* x (+ 1 (* x (+ -1 (* x 5/4))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x)))))))))>
#<alt (* (- 1 (* x (* x (+ 1 (* x (+ -1 (* x 5/4))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))>
#<alt (- 1 (* x (* x (+ 1 (* x (+ -1 (* x 5/4)))))))>
#<alt (* 2 (atan (* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2)))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))))>
#<alt (atan (* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2)))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x)))))))))>
#<alt (* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2)))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))>
#<alt (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2))))))>
#<alt (+ x (+ 2 (/ 1 x)))>
#<alt (- (/ 1 x) x)>
#<alt (/ (+ (/ 1 x) -1) x)>
#<alt (/ (+ 1/2 (/ (+ (/ 1 x) -1) x)) x)>
#<alt (* (* x x) (* x x))>
#<alt (* x (* x (+ 1 (* x (+ -1 (* x 5/4))))))>
#<alt (* x (- 1 x))>
#<alt (* x (+ -1 (* 1/2 (* x (- 1 x)))))>
#<alt (* x (+ -1 (* x 5/4)))>
#<alt (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2))))>
#<alt (* x (+ -1 (* x 1/2)))>
#<alt (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2)))))>
Outputs
#<alt (* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))>
#<alt (* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))>
#<alt (* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))>
#<alt (* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))>
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#<alt (* (pow x 5) (- (+ 1/4 (/ 1 (pow x 2))) (+ (* 3/4 (/ 1 x)) (/ 1 (pow x 3)))))>
#<alt (* 1/4 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- (* 3/4 (/ 1 x)) 1/4)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (- (/ 1 x) 3/4) x)) 1/4)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 3/4) x)) 1/4)))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* 2 x)) x)>
#<alt (/ (+ 1 (* x (+ 2 x))) x)>
#<alt (/ (+ 1 (* x (+ 2 x))) x)>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (+ (* 2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* x (+ 1 (+ (* 2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* -1 (* x (- (* -1 (/ (+ 2 (/ 1 x)) x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ (+ 2 (/ 1 x)) x)) 1)))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* -1 (pow x 2))) x)>
#<alt (/ (+ 1 (* -1 (pow x 2))) x)>
#<alt (/ (+ 1 (* -1 (pow x 2))) x)>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 (pow x 2)) 1))>
#<alt (* x (- (/ 1 (pow x 2)) 1))>
#<alt (* x (- (/ 1 (pow x 2)) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 (pow x 2)))))>
#<alt (* -1 (* x (- 1 (/ 1 (pow x 2)))))>
#<alt (* -1 (* x (- 1 (/ 1 (pow x 2)))))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (+ 1 (* -1 x)) (pow x 2))>
#<alt (/ (+ 1 (* -1 x)) (pow x 2))>
#<alt (/ (+ 1 (* -1 x)) (pow x 2))>
#<alt (/ -1 x)>
#<alt (/ (- (/ 1 x) 1) x)>
#<alt (/ (- (/ 1 x) 1) x)>
#<alt (/ (- (/ 1 x) 1) x)>
#<alt (/ -1 x)>
#<alt (* -1 (/ (- 1 (/ 1 x)) x))>
#<alt (* -1 (/ (- 1 (/ 1 x)) x))>
#<alt (* -1 (/ (- 1 (/ 1 x)) x))>
#<alt (/ 1 (pow x 3))>
#<alt (/ (+ 1 (* -1 x)) (pow x 3))>
#<alt (/ (+ 1 (* x (- (* 1/2 x) 1))) (pow x 3))>
#<alt (/ (+ 1 (* x (- (* 1/2 x) 1))) (pow x 3))>
#<alt (/ 1/2 x)>
#<alt (/ (- 1/2 (/ 1 x)) x)>
#<alt (/ (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)) x)>
#<alt (/ (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (/ 1 x) 1/2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1/2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1/2) x))>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 x)))>
#<alt (* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))>
#<alt (* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))>
#<alt (* 5/4 (pow x 4))>
#<alt (* (pow x 4) (- 5/4 (/ 1 x)))>
#<alt (* (pow x 4) (- (+ 5/4 (/ 1 (pow x 2))) (/ 1 x)))>
#<alt (* (pow x 4) (- (+ 5/4 (/ 1 (pow x 2))) (/ 1 x)))>
#<alt (* 5/4 (pow x 4))>
#<alt (* (pow x 4) (- 5/4 (/ 1 x)))>
#<alt (* (pow x 4) (+ 5/4 (* -1 (/ (- 1 (/ 1 x)) x))))>
#<alt (* (pow x 4) (+ 5/4 (* -1 (/ (- 1 (/ 1 x)) x))))>
#<alt x>
#<alt (* x (+ 1 (* -1 x)))>
#<alt (* x (+ 1 (* -1 x)))>
#<alt (* x (+ 1 (* -1 x)))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 x) 1))>
#<alt (* (pow x 2) (- (/ 1 x) 1))>
#<alt (* (pow x 2) (- (/ 1 x) 1))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 x) 1))>
#<alt (* (pow x 2) (- (/ 1 x) 1))>
#<alt (* (pow x 2) (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* x (- (* 1/2 x) 1))>
#<alt (* x (- (* x (+ 1/2 (* -1/2 x))) 1))>
#<alt (* x (- (* x (+ 1/2 (* -1/2 x))) 1))>
#<alt (* -1/2 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))>
#<alt (* -1 x)>
#<alt (* x (- (* 5/4 x) 1))>
#<alt (* x (- (* 5/4 x) 1))>
#<alt (* x (- (* 5/4 x) 1))>
#<alt (* 5/4 (pow x 2))>
#<alt (* (pow x 2) (- 5/4 (/ 1 x)))>
#<alt (* (pow x 2) (- 5/4 (/ 1 x)))>
#<alt (* (pow x 2) (- 5/4 (/ 1 x)))>
#<alt (* 5/4 (pow x 2))>
#<alt (* (pow x 2) (- 5/4 (/ 1 x)))>
#<alt (* (pow x 2) (- 5/4 (/ 1 x)))>
#<alt (* (pow x 2) (- 5/4 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (* -1 x)))>
#<alt (* x (+ 1 (* x (- (* 3/4 x) 1))))>
#<alt (* x (+ 1 (* x (- (* x (+ 3/4 (* -1/4 x))) 1))))>
#<alt (* -1/4 (pow x 4))>
#<alt (* (pow x 4) (- (* 3/4 (/ 1 x)) 1/4))>
#<alt (* (pow x 4) (- (* 3/4 (/ 1 x)) (+ 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ (* 3/4 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1 (pow x 2)))))>
#<alt (* -1/4 (pow x 4))>
#<alt (* (pow x 4) (- (* 3/4 (/ 1 x)) 1/4))>
#<alt (* (pow x 4) (- (* -1 (/ (- (/ 1 x) 3/4) x)) 1/4))>
#<alt (* (pow x 4) (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 3/4) x)) 1/4))>
#<alt (* -1 x)>
#<alt (* x (- (* 1/2 x) 1))>
#<alt (* x (- (* 1/2 x) 1))>
#<alt (* x (- (* 1/2 x) 1))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (- 1/2 (/ 1 x)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 x)))>
#<alt (* (pow x 2) (+ 1 (* x (- (* 3/4 x) 1))))>
#<alt (* (pow x 2) (+ 1 (* x (- (* x (+ 3/4 (* -1/4 x))) 1))))>
#<alt (* -1/4 (pow x 5))>
#<alt (* (pow x 5) (- (* 3/4 (/ 1 x)) 1/4))>
#<alt (* (pow x 5) (- (* 3/4 (/ 1 x)) (+ 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (- (+ (* 3/4 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1 (pow x 2)))))>
#<alt (* -1/4 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- 1/4 (* 3/4 (/ 1 x)))))>
#<alt (* -1 (* (pow x 5) (+ 1/4 (* -1 (/ (- 3/4 (/ 1 x)) x)))))>
#<alt (* -1 (* (pow x 5) (+ 1/4 (* -1 (/ (+ 3/4 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))>
Calls

96 calls:

TimeVariablePointExpression
15.0ms
x
@0
(/ (+ 1/2 (/ (+ (/ 1 x) -1) x)) x)
4.0ms
x
@-inf
(* 2 (atan (* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2)))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))))
3.0ms
x
@inf
(* (- 1 (* x (* x (+ 1 (* x (+ -1 (* x 5/4))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))
2.0ms
x
@-inf
(* 2 (atan (* (- 1 (* x (* x (+ 1 (* x (+ -1 (* x 5/4))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))))
2.0ms
x
@inf
(* 2 (atan (* (- 1 (* x (* x (+ 1 (* x (+ -1 (* x 5/4))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))))

rewrite1.1s (5.1%)

Algorithm
1×batch-egg-rewrite
Rules
3498×*-lowering-*.f32
3498×*-lowering-*.f64
2296×fma-lowering-fma.f32
2296×fma-lowering-fma.f64
1534×pow-lowering-pow.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
061532
1387462
23763444
08142444
Stop Event
1×iter limit
1×node limit
Counts
32 → 602
Calls
Call 1
Inputs
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ x (+ 2 (/ 1 x)))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ x (+ 2 (/ 1 x))))))
(sqrt (/ (- (/ 1 x) x) (+ x (+ 2 (/ 1 x)))))
(/ (- (/ 1 x) x) (+ x (+ 2 (/ 1 x))))
(* 2 (atan (* (* x (* x x)) (+ -1/2 (/ (+ 1/2 (/ (+ (/ 1 x) -1) x)) x)))))
(atan (* (* x (* x x)) (+ -1/2 (/ (+ 1/2 (/ (+ (/ 1 x) -1) x)) x))))
(* (* x (* x x)) (+ -1/2 (/ (+ 1/2 (/ (+ (/ 1 x) -1) x)) x)))
(* x (* x x))
(* 2 (atan (/ (* (- 1 (* (* (* x x) (* x x)) 1/4)) (- 1 x)) (- 1 (* 1/2 (* x x))))))
(atan (/ (* (- 1 (* (* (* x x) (* x x)) 1/4)) (- 1 x)) (- 1 (* 1/2 (* x x)))))
(/ (* (- 1 (* (* (* x x) (* x x)) 1/4)) (- 1 x)) (- 1 (* 1/2 (* x x))))
(* (- 1 (* (* (* x x) (* x x)) 1/4)) (- 1 x))
(* 2 (atan (* (- 1 (* x (* x (+ 1 (* x (+ -1 (* x 5/4))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))))
(atan (* (- 1 (* x (* x (+ 1 (* x (+ -1 (* x 5/4))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x)))))))))
(* (- 1 (* x (* x (+ 1 (* x (+ -1 (* x 5/4))))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))
(- 1 (* x (* x (+ 1 (* x (+ -1 (* x 5/4)))))))
(* 2 (atan (* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2)))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))))
(atan (* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2)))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x)))))))))
(* (- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2)))))) (/ 1 (- 1 (* x (+ -1 (* 1/2 (* x (- 1 x))))))))
(- 1 (* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2))))))
(+ x (+ 2 (/ 1 x)))
(- (/ 1 x) x)
(/ (+ (/ 1 x) -1) x)
(/ (+ 1/2 (/ (+ (/ 1 x) -1) x)) x)
(* (* x x) (* x x))
(* x (* x (+ 1 (* x (+ -1 (* x 5/4))))))
(* x (- 1 x))
(* x (+ -1 (* 1/2 (* x (- 1 x)))))
(* x (+ -1 (* x 5/4)))
(* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2))))
(* x (+ -1 (* x 1/2)))
(* x (* (+ -1 (* 1/2 (* x (- 1 x)))) (* x (+ -1 (* x 1/2)))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))))
(exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))) (-.f64 (/.f64 #s(literal 1 binary64) x) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)) (pow.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x))) (pow.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64))) (neg.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64))))
(pow.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))) (-.f64 (/.f64 #s(literal 1 binary64) x) x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)) (pow.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))) #s(literal -1/2 binary64)) (pow.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))))
(*.f64 (pow.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)) (-.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))))
(*.f64 (pow.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (-.f64 (*.f64 x x) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))))) #s(literal 1/2 binary64)) (pow.f64 (-.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))) x)) (neg.f64 (/.f64 x (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))))
(exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))) (-.f64 (/.f64 #s(literal 1 binary64) x) x))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))) x)) (/.f64 x (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))) x)) (neg.f64 (/.f64 x (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) (neg.f64 (/.f64 x (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))))) (+.f64 (*.f64 x x) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)) (-.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)) x))) (neg.f64 (/.f64 x (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 (*.f64 x x) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))))) (-.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))) (neg.f64 (/.f64 x (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))))
(neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))) (-.f64 (/.f64 #s(literal 1 binary64) x) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) #s(literal 1 binary64)))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))) (-.f64 (/.f64 #s(literal 1 binary64) x) x))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x x))) (*.f64 (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x x)))))
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(*.f64 (*.f64 x (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x)))))) (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))
(*.f64 (*.f64 x (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))) (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x)))))
(*.f64 (*.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))))) x) (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))) x)

simplify738.0ms (3.5%)

Algorithm
1×egg-herbie
Rules
4892×*-lowering-*.f32
4892×*-lowering-*.f64
2986×+-lowering-+.f64
2986×+-lowering-+.f32
1584×distribute-lft-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04445073
113784730
242654508
089714508
Stop Event
1×iter limit
1×node limit
Counts
384 → 384
Calls
Call 1
Inputs
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(* 2 (atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x))))))
(* 2 (atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x))))))
(* 2 (atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x))))))
(* 2 (atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x)))))
(atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x)))))
(atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x)))))
(atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x)))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
1
(+ 1 (* -2 x))
(+ 1 (* x (- (* 2 x) 2)))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
-1
(- (* 2 (/ 1 x)) 1)
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
-1
(- (* 2 (/ 1 x)) 1)
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2))))))
(atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2))))))
(atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2))))))
(atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2))))))
(atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2))))))
(atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2))))))
(atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2))))))
(atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2))))))
(atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2))))))
(atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2))))))
(atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2))))))
(atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2))))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(* -1/2 (pow x 3))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 2 (atan (/ (* (- 1 x) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2))))))
(* 2 (atan (/ (* (- 1 x) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2))))))
(* 2 (atan (/ (* (- 1 x) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2))))))
(* 2 (atan (/ (* (- 1 x) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2))))))
(* 2 (atan (/ (* (- 1 x) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2))))))
(* 2 (atan (/ (* (- 1 x) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2))))))
(* 2 (atan (/ (* (- 1 x) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2))))))
(* 2 (atan (/ (* (- 1 x) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2))))))
(* 2 (atan (/ (* (+ 1 (* -1 x)) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2))))))
(* 2 (atan (/ (* (+ 1 (* -1 x)) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2))))))
(* 2 (atan (/ (* (+ 1 (* -1 x)) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2))))))
(* 2 (atan (/ (* (+ 1 (* -1 x)) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2))))))
(atan (/ (* (- 1 x) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2)))))
(atan (/ (* (- 1 x) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2)))))
(atan (/ (* (- 1 x) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2)))))
(atan (/ (* (- 1 x) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2)))))
(atan (/ (* (- 1 x) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2)))))
(atan (/ (* (- 1 x) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2)))))
(atan (/ (* (- 1 x) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2)))))
(atan (/ (* (- 1 x) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2)))))
(atan (/ (* (+ 1 (* -1 x)) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2)))))
(atan (/ (* (+ 1 (* -1 x)) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2)))))
(atan (/ (* (+ 1 (* -1 x)) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2)))))
(atan (/ (* (+ 1 (* -1 x)) (- 1 (* 1/4 (pow x 4)))) (- 1 (* 1/2 (pow x 2)))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(* -1/2 (pow x 3))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* -1/4 (pow x 3)) 1)))
(+ 1 (* x (- (* (pow x 3) (- (* 1/4 x) 1/4)) 1)))
(* 1/4 (pow x 5))
(* (pow x 5) (- 1/4 (* 1/4 (/ 1 x))))
(* (pow x 5) (+ 1/4 (* -1 (/ (+ 1/4 (/ 1 (pow x 3))) x))))
(* (pow x 5) (- (+ 1/4 (/ 1 (pow x 5))) (+ (* 1/4 (/ 1 x)) (/ 1 (pow x 4)))))
(* 1/4 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/4 (/ 1 x)) 1/4)))
(* -1 (* (pow x 5) (- (+ (* 1/4 (/ 1 x)) (/ 1 (pow x 4))) 1/4)))
(* -1 (* (pow x 5) (- (* -1 (/ (- (* -1 (/ (- 1 (/ 1 x)) (pow x 3))) 1/4) x)) 1/4)))
(* 2 (atan (/ (- 1 (* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))))
(* 2 (atan (/ (- 1 (* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))))
(* 2 (atan (/ (- 1 (* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))))
(* 2 (atan (/ (- 1 (* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))))
(* 2 (atan (/ (- (+ 1 (pow x 3)) (+ (* 5/4 (pow x 4)) (pow x 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x)))))))
(* 2 (atan (/ (- (+ 1 (pow x 3)) (+ (* 5/4 (pow x 4)) (pow x 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x)))))))
(* 2 (atan (/ (- (+ 1 (pow x 3)) (+ (* 5/4 (pow x 4)) (pow x 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x)))))))
(* 2 (atan (/ (- (+ 1 (pow x 3)) (+ (* 5/4 (pow x 4)) (pow x 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x)))))))
(* 2 (atan (/ (- 1 (+ (* -1 (pow x 3)) (+ (* 5/4 (pow x 4)) (pow x 2)))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))))
(* 2 (atan (/ (- 1 (+ (* -1 (pow x 3)) (+ (* 5/4 (pow x 4)) (pow x 2)))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))))
(* 2 (atan (/ (- 1 (+ (* -1 (pow x 3)) (+ (* 5/4 (pow x 4)) (pow x 2)))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))))
(* 2 (atan (/ (- 1 (+ (* -1 (pow x 3)) (+ (* 5/4 (pow x 4)) (pow x 2)))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))))
(atan (/ (- 1 (* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))
(atan (/ (- 1 (* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))
(atan (/ (- 1 (* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))
(atan (/ (- 1 (* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))
(atan (/ (- (+ 1 (pow x 3)) (+ (* 5/4 (pow x 4)) (pow x 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x))))))
(atan (/ (- (+ 1 (pow x 3)) (+ (* 5/4 (pow x 4)) (pow x 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x))))))
(atan (/ (- (+ 1 (pow x 3)) (+ (* 5/4 (pow x 4)) (pow x 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x))))))
(atan (/ (- (+ 1 (pow x 3)) (+ (* 5/4 (pow x 4)) (pow x 2))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x))))))
(atan (/ (- 1 (+ (* -1 (pow x 3)) (+ (* 5/4 (pow x 4)) (pow x 2)))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))
(atan (/ (- 1 (+ (* -1 (pow x 3)) (+ (* 5/4 (pow x 4)) (pow x 2)))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))
(atan (/ (- 1 (+ (* -1 (pow x 3)) (+ (* 5/4 (pow x 4)) (pow x 2)))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))
(atan (/ (- 1 (+ (* -1 (pow x 3)) (+ (* 5/4 (pow x 4)) (pow x 2)))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(* -5/2 x)
(* -1 (* x (+ 5/2 (* 1/2 (/ 1 x)))))
(* x (- (/ 5/2 (pow x 2)) (+ 5/2 (* 1/2 (/ 1 x)))))
(* x (- (+ (* 17/2 (/ 1 (pow x 3))) (/ 5/2 (pow x 2))) (+ 5/2 (* 1/2 (/ 1 x)))))
(* -5/2 x)
(* -1 (* x (+ 5/2 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 5/2 (* -1 (/ (- (* 5/2 (/ 1 x)) 1/2) x)))))
(* -1 (* x (+ 5/2 (* -1 (/ (- (+ (* 5/2 (/ 1 x)) (/ 17/2 (pow x 2))) 1/2) x)))))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- x 1)))
(+ 1 (* (pow x 2) (- (* x (+ 1 (* -5/4 x))) 1)))
(* -5/4 (pow x 4))
(* (pow x 4) (- (/ 1 x) 5/4))
(* (pow x 4) (- (/ 1 x) (+ 5/4 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ (/ 1 x) (/ 1 (pow x 4))) (+ 5/4 (/ 1 (pow x 2)))))
(* -5/4 (pow x 4))
(* (pow x 4) (- (/ 1 x) 5/4))
(* (pow x 4) (- (* -1 (/ (- (/ 1 x) 1) x)) 5/4))
(* (pow x 4) (- (* -1 (/ (- (* -1 (/ (- (/ 1 (pow x 2)) 1) x)) 1) x)) 5/4))
(* 2 (atan (/ (- 1 (* (pow x 2) (* (- (* 1/2 x) 1) (- (* 1/2 (* x (- 1 x))) 1)))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))))
(* 2 (atan (/ (- 1 (* (pow x 2) (* (- (* 1/2 x) 1) (- (* 1/2 (* x (- 1 x))) 1)))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))))
(* 2 (atan (/ (- 1 (* (pow x 2) (* (- (* 1/2 x) 1) (- (* 1/2 (* x (- 1 x))) 1)))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))))
(* 2 (atan (/ (- 1 (* (pow x 2) (* (- (* 1/2 x) 1) (- (* 1/2 (* x (- 1 x))) 1)))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1))))))
(* 2 (atan (/ (- 1 (* (pow x 2) (* (- (* 1/2 x) 1) (- (* 1/2 (* x (- 1 x))) 1)))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x)))))))
(* 2 (atan (/ (- 1 (* (pow x 2) (* (- (* 1/2 x) 1) (- (* 1/2 (* x (- 1 x))) 1)))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x)))))))
(* 2 (atan (/ (- 1 (* (pow x 2) (* (- (* 1/2 x) 1) (- (* 1/2 (* x (- 1 x))) 1)))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x)))))))
(* 2 (atan (/ (- 1 (* (pow x 2) (* (- (* 1/2 x) 1) (- (* 1/2 (* x (- 1 x))) 1)))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x)))))))
(* 2 (atan (/ (- 1 (* -1 (* (pow x 2) (* (+ 1 (* -1/2 x)) (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))))
(* 2 (atan (/ (- 1 (* -1 (* (pow x 2) (* (+ 1 (* -1/2 x)) (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))))
(* 2 (atan (/ (- 1 (* -1 (* (pow x 2) (* (+ 1 (* -1/2 x)) (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))))
(* 2 (atan (/ (- 1 (* -1 (* (pow x 2) (* (+ 1 (* -1/2 x)) (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))))
(atan (/ (- 1 (* (pow x 2) (* (- (* 1/2 x) 1) (- (* 1/2 (* x (- 1 x))) 1)))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))
(atan (/ (- 1 (* (pow x 2) (* (- (* 1/2 x) 1) (- (* 1/2 (* x (- 1 x))) 1)))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))
(atan (/ (- 1 (* (pow x 2) (* (- (* 1/2 x) 1) (- (* 1/2 (* x (- 1 x))) 1)))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))
(atan (/ (- 1 (* (pow x 2) (* (- (* 1/2 x) 1) (- (* 1/2 (* x (- 1 x))) 1)))) (- 1 (* x (- (* 1/2 (* x (- 1 x))) 1)))))
(atan (/ (- 1 (* (pow x 2) (* (- (* 1/2 x) 1) (- (* 1/2 (* x (- 1 x))) 1)))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x))))))
(atan (/ (- 1 (* (pow x 2) (* (- (* 1/2 x) 1) (- (* 1/2 (* x (- 1 x))) 1)))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x))))))
(atan (/ (- 1 (* (pow x 2) (* (- (* 1/2 x) 1) (- (* 1/2 (* x (- 1 x))) 1)))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x))))))
(atan (/ (- 1 (* (pow x 2) (* (- (* 1/2 x) 1) (- (* 1/2 (* x (- 1 x))) 1)))) (- (+ 1 x) (* 1/2 (* (pow x 2) (- 1 x))))))
(atan (/ (- 1 (* -1 (* (pow x 2) (* (+ 1 (* -1/2 x)) (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))
(atan (/ (- 1 (* -1 (* (pow x 2) (* (+ 1 (* -1/2 x)) (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))
(atan (/ (- 1 (* -1 (* (pow x 2) (* (+ 1 (* -1/2 x)) (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))
(atan (/ (- 1 (* -1 (* (pow x 2) (* (+ 1 (* -1/2 x)) (- (* 1/2 (* x (+ 1 (* -1 x)))) 1))))) (- 1 (* x (- (* 1/2 (* x (+ 1 (* -1 x)))) 1)))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (* -1 (/ (+ 1 (/ 1 (pow x 2))) x))))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 4))) (+ (/ 1 x) (/ 1 (pow x 3)))))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (* -1 (/ (+ 1 (/ 1 (pow x 2))) x))))
(* (pow x 2) (+ 1/2 (* -1 (/ (- (+ 1 (/ 1 (pow x 2))) (/ 1 (pow x 3))) x))))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- x 1)))
(+ 1 (* (pow x 2) (- (* x (+ 1 (* -3/4 x))) 1)))
(* 1/4 (pow x 5))
(* (pow x 5) (- 1/4 (* 3/4 (/ 1 x))))
(* (pow x 5) (- (+ 1/4 (/ 1 (pow x 2))) (* 3/4 (/ 1 x))))
(* (pow x 5) (- (+ 1/4 (/ 1 (pow x 2))) (+ (* 3/4 (/ 1 x)) (/ 1 (pow x 3)))))
(* 1/4 (pow x 5))
(* -1 (* (pow x 5) (- (* 3/4 (/ 1 x)) 1/4)))
(* -1 (* (pow x 5) (- (* -1 (/ (- (/ 1 x) 3/4) x)) 1/4)))
(* -1 (* (pow x 5) (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 3/4) x)) 1/4)))
(/ 1 x)
(/ (+ 1 (* 2 x)) x)
(/ (+ 1 (* x (+ 2 x))) x)
(/ (+ 1 (* x (+ 2 x))) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (+ (* 2 (/ 1 x)) (/ 1 (pow x 2)))))
(* x (+ 1 (+ (* 2 (/ 1 x)) (/ 1 (pow x 2)))))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* -1 (* x (- (* -1 (/ (+ 2 (/ 1 x)) x)) 1)))
(* -1 (* x (- (* -1 (/ (+ 2 (/ 1 x)) x)) 1)))
(/ 1 x)
(/ (+ 1 (* -1 (pow x 2))) x)
(/ (+ 1 (* -1 (pow x 2))) x)
(/ (+ 1 (* -1 (pow x 2))) x)
(* -1 x)
(* x (- (/ 1 (pow x 2)) 1))
(* x (- (/ 1 (pow x 2)) 1))
(* x (- (/ 1 (pow x 2)) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 (pow x 2)))))
(* -1 (* x (- 1 (/ 1 (pow x 2)))))
(* -1 (* x (- 1 (/ 1 (pow x 2)))))
(/ 1 (pow x 2))
(/ (+ 1 (* -1 x)) (pow x 2))
(/ (+ 1 (* -1 x)) (pow x 2))
(/ (+ 1 (* -1 x)) (pow x 2))
(/ -1 x)
(/ (- (/ 1 x) 1) x)
(/ (- (/ 1 x) 1) x)
(/ (- (/ 1 x) 1) x)
(/ -1 x)
(* -1 (/ (- 1 (/ 1 x)) x))
(* -1 (/ (- 1 (/ 1 x)) x))
(* -1 (/ (- 1 (/ 1 x)) x))
(/ 1 (pow x 3))
(/ (+ 1 (* -1 x)) (pow x 3))
(/ (+ 1 (* x (- (* 1/2 x) 1))) (pow x 3))
(/ (+ 1 (* x (- (* 1/2 x) 1))) (pow x 3))
(/ 1/2 x)
(/ (- 1/2 (/ 1 x)) x)
(/ (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)) x)
(/ (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)) x)
(/ 1/2 x)
(* -1 (/ (- (/ 1 x) 1/2) x))
(* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1/2) x))
(* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1/2) x))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 x)))
(* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))
(* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))
(* 5/4 (pow x 4))
(* (pow x 4) (- 5/4 (/ 1 x)))
(* (pow x 4) (- (+ 5/4 (/ 1 (pow x 2))) (/ 1 x)))
(* (pow x 4) (- (+ 5/4 (/ 1 (pow x 2))) (/ 1 x)))
(* 5/4 (pow x 4))
(* (pow x 4) (- 5/4 (/ 1 x)))
(* (pow x 4) (+ 5/4 (* -1 (/ (- 1 (/ 1 x)) x))))
(* (pow x 4) (+ 5/4 (* -1 (/ (- 1 (/ 1 x)) x))))
x
(* x (+ 1 (* -1 x)))
(* x (+ 1 (* -1 x)))
(* x (+ 1 (* -1 x)))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 x) 1))
(* (pow x 2) (- (/ 1 x) 1))
(* (pow x 2) (- (/ 1 x) 1))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 x) 1))
(* (pow x 2) (- (/ 1 x) 1))
(* (pow x 2) (- (/ 1 x) 1))
(* -1 x)
(* x (- (* 1/2 x) 1))
(* x (- (* x (+ 1/2 (* -1/2 x))) 1))
(* x (- (* x (+ 1/2 (* -1/2 x))) 1))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* -1/2 (pow x 3))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 x)
(* x (- (* 5/4 x) 1))
(* x (- (* 5/4 x) 1))
(* x (- (* 5/4 x) 1))
(* 5/4 (pow x 2))
(* (pow x 2) (- 5/4 (/ 1 x)))
(* (pow x 2) (- 5/4 (/ 1 x)))
(* (pow x 2) (- 5/4 (/ 1 x)))
(* 5/4 (pow x 2))
(* (pow x 2) (- 5/4 (/ 1 x)))
(* (pow x 2) (- 5/4 (/ 1 x)))
(* (pow x 2) (- 5/4 (/ 1 x)))
x
(* x (+ 1 (* -1 x)))
(* x (+ 1 (* x (- (* 3/4 x) 1))))
(* x (+ 1 (* x (- (* x (+ 3/4 (* -1/4 x))) 1))))
(* -1/4 (pow x 4))
(* (pow x 4) (- (* 3/4 (/ 1 x)) 1/4))
(* (pow x 4) (- (* 3/4 (/ 1 x)) (+ 1/4 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ (* 3/4 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1 (pow x 2)))))
(* -1/4 (pow x 4))
(* (pow x 4) (- (* 3/4 (/ 1 x)) 1/4))
(* (pow x 4) (- (* -1 (/ (- (/ 1 x) 3/4) x)) 1/4))
(* (pow x 4) (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 3/4) x)) 1/4))
(* -1 x)
(* x (- (* 1/2 x) 1))
(* x (- (* 1/2 x) 1))
(* x (- (* 1/2 x) 1))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- 1/2 (/ 1 x)))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 x)))
(* (pow x 2) (+ 1 (* x (- (* 3/4 x) 1))))
(* (pow x 2) (+ 1 (* x (- (* x (+ 3/4 (* -1/4 x))) 1))))
(* -1/4 (pow x 5))
(* (pow x 5) (- (* 3/4 (/ 1 x)) 1/4))
(* (pow x 5) (- (* 3/4 (/ 1 x)) (+ 1/4 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ (* 3/4 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1 (pow x 2)))))
(* -1/4 (pow x 5))
(* -1 (* (pow x 5) (- 1/4 (* 3/4 (/ 1 x)))))
(* -1 (* (pow x 5) (+ 1/4 (* -1 (/ (- 3/4 (/ 1 x)) x)))))
(* -1 (* (pow x 5) (+ 1/4 (* -1 (/ (+ 3/4 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
Outputs
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))))
(* 2 (atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))))
(* 2 (atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))))
(* 2 (atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))))
(* 2 (atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))))
(* 2 (atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))))
(atan (sqrt (/ (- (/ 1 x) x) (+ 2 (+ x (/ 1 x))))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))))
(atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))))
(atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))))
(atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))))
(atan (sqrt (/ (+ (* -1 x) (/ 1 x)) (- (+ 2 (/ 1 x)) (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 2 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x x))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x x)))) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (*.f64 x x))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))))) x)) x))
1
#s(literal 1 binary64)
(+ 1 (* -2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -2 binary64)))
(+ 1 (* x (- (* 2 x) 2)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) x))))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -2 binary64) (*.f64 x (+.f64 #s(literal 2 binary64) (*.f64 x #s(literal -2 binary64)))))))
-1
#s(literal -1 binary64)
(- (* 2 (/ 1 x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) x))
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(+.f64 (/.f64 #s(literal 2 binary64) x) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
(+.f64 (/.f64 #s(literal 2 binary64) x) (+.f64 (/.f64 (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) x) x) #s(literal -1 binary64)))
-1
#s(literal -1 binary64)
(- (* 2 (/ 1 x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) x))
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -2 binary64) x)) x))
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) x)) x))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 x x)) #s(literal -1/2 binary64)))))))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 x x)) #s(literal -1/2 binary64)))))))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 x x)) #s(literal -1/2 binary64)))))))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 x x)) #s(literal -1/2 binary64)))))))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 x x)) #s(literal -1/2 binary64)))))))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 x x)) #s(literal -1/2 binary64)))))))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 x x)) #s(literal -1/2 binary64)))))))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 x x)) #s(literal -1/2 binary64)))))))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 x x)) #s(literal -1/2 binary64)))))))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 x x)) #s(literal -1/2 binary64)))))))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 x x)) #s(literal -1/2 binary64)))))))
(* 2 (atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 x x)) #s(literal -1/2 binary64)))))))
(atan (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2))))))
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(/.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x (*.f64 x x)))
(/ (+ 1 (* x (- (* 1/2 x) 1))) (pow x 3))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))) (*.f64 x (*.f64 x x)))
(/ (+ 1 (* x (- (* 1/2 x) 1))) (pow x 3))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))) (*.f64 x (*.f64 x x)))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (- 1/2 (/ 1 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)
(/ (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x)
(/ (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* -1 (/ (- (/ 1 x) 1/2) x))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)
(* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1/2) x))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x)
(* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1/2) x))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x)
(pow x 4)
(*.f64 (*.f64 x (*.f64 x x)) x)
(pow x 4)
(*.f64 (*.f64 x (*.f64 x x)) x)
(pow x 4)
(*.f64 (*.f64 x (*.f64 x x)) x)
(pow x 4)
(*.f64 (*.f64 x (*.f64 x x)) x)
(pow x 4)
(*.f64 (*.f64 x (*.f64 x x)) x)
(pow x 4)
(*.f64 (*.f64 x (*.f64 x x)) x)
(pow x 4)
(*.f64 (*.f64 x (*.f64 x x)) x)
(pow x 4)
(*.f64 (*.f64 x (*.f64 x x)) x)
(pow x 4)
(*.f64 (*.f64 x (*.f64 x x)) x)
(pow x 4)
(*.f64 (*.f64 x (*.f64 x x)) x)
(pow x 4)
(*.f64 (*.f64 x (*.f64 x x)) x)
(pow x 4)
(*.f64 (*.f64 x (*.f64 x x)) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 x)))
(*.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) x)))
(* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 5/4 binary64))))))
(* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 5/4 binary64))))))
(* 5/4 (pow x 4))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) x) #s(literal 5/4 binary64))
(* (pow x 4) (- 5/4 (/ 1 x)))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) x) (+.f64 #s(literal 5/4 binary64) (/.f64 #s(literal -1 binary64) x)))
(* (pow x 4) (- (+ 5/4 (/ 1 (pow x 2))) (/ 1 x)))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) x) (+.f64 #s(literal 5/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)))
(* (pow x 4) (- (+ 5/4 (/ 1 (pow x 2))) (/ 1 x)))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) x) (+.f64 #s(literal 5/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)))
(* 5/4 (pow x 4))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) x) #s(literal 5/4 binary64))
(* (pow x 4) (- 5/4 (/ 1 x)))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) x) (+.f64 #s(literal 5/4 binary64) (/.f64 #s(literal -1 binary64) x)))
(* (pow x 4) (+ 5/4 (* -1 (/ (- 1 (/ 1 x)) x))))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) x) (+.f64 #s(literal 5/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)))
(* (pow x 4) (+ 5/4 (* -1 (/ (- 1 (/ 1 x)) x))))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) x) (+.f64 #s(literal 5/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)))
x
(* x (+ 1 (* -1 x)))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(* x (+ 1 (* -1 x)))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(* x (+ 1 (* -1 x)))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 x) 1))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(* (pow x 2) (- (/ 1 x) 1))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(* (pow x 2) (- (/ 1 x) 1))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 x) 1))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(* (pow x 2) (- (/ 1 x) 1))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(* (pow x 2) (- (/ 1 x) 1))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* x (- (* 1/2 x) 1))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))
(* x (- (* x (+ 1/2 (* -1/2 x))) 1))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* x (- (* x (+ 1/2 (* -1/2 x))) 1))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(* -1/2 (pow x 3))
(*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x))))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x))))
(* -1/2 (pow x 3))
(*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x))))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* x (- (* 5/4 x) 1))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 5/4 binary64))))
(* x (- (* 5/4 x) 1))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 5/4 binary64))))
(* x (- (* 5/4 x) 1))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 5/4 binary64))))
(* 5/4 (pow x 2))
(*.f64 x (*.f64 x #s(literal 5/4 binary64)))
(* (pow x 2) (- 5/4 (/ 1 x)))
(*.f64 x (*.f64 x (+.f64 #s(literal 5/4 binary64) (/.f64 #s(literal -1 binary64) x))))
(* (pow x 2) (- 5/4 (/ 1 x)))
(*.f64 x (*.f64 x (+.f64 #s(literal 5/4 binary64) (/.f64 #s(literal -1 binary64) x))))
(* (pow x 2) (- 5/4 (/ 1 x)))
(*.f64 x (*.f64 x (+.f64 #s(literal 5/4 binary64) (/.f64 #s(literal -1 binary64) x))))
(* 5/4 (pow x 2))
(*.f64 x (*.f64 x #s(literal 5/4 binary64)))
(* (pow x 2) (- 5/4 (/ 1 x)))
(*.f64 x (*.f64 x (+.f64 #s(literal 5/4 binary64) (/.f64 #s(literal -1 binary64) x))))
(* (pow x 2) (- 5/4 (/ 1 x)))
(*.f64 x (*.f64 x (+.f64 #s(literal 5/4 binary64) (/.f64 #s(literal -1 binary64) x))))
(* (pow x 2) (- 5/4 (/ 1 x)))
(*.f64 x (*.f64 x (+.f64 #s(literal 5/4 binary64) (/.f64 #s(literal -1 binary64) x))))
x
(* x (+ 1 (* -1 x)))
(*.f64 x (-.f64 #s(literal 1 binary64) x))
(* x (+ 1 (* x (- (* 3/4 x) 1))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 3/4 binary64))))))
(* x (+ 1 (* x (- (* x (+ 3/4 (* -1/4 x))) 1))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 3/4 binary64) (*.f64 x #s(literal -1/4 binary64))))))))
(* -1/4 (pow x 4))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) x) #s(literal -1/4 binary64))
(* (pow x 4) (- (* 3/4 (/ 1 x)) 1/4))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) x) (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 3/4 binary64) x)))
(* (pow x 4) (- (* 3/4 (/ 1 x)) (+ 1/4 (/ 1 (pow x 2)))))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) x) (+.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 #s(literal 3/4 binary64) (/.f64 #s(literal -1 binary64) x)) x)))
(* (pow x 4) (- (+ (* 3/4 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1 (pow x 2)))))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) x) (+.f64 (/.f64 #s(literal 3/4 binary64) x) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 x x)) #s(literal -1/4 binary64))))
(* -1/4 (pow x 4))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) x) #s(literal -1/4 binary64))
(* (pow x 4) (- (* 3/4 (/ 1 x)) 1/4))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) x) (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 3/4 binary64) x)))
(* (pow x 4) (- (* -1 (/ (- (/ 1 x) 3/4) x)) 1/4))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) x) (+.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 #s(literal 3/4 binary64) (/.f64 #s(literal -1 binary64) x)) x)))
(* (pow x 4) (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 3/4) x)) 1/4))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) x) (+.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x) #s(literal 3/4 binary64)) x)))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* x (- (* 1/2 x) 1))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))
(* x (- (* 1/2 x) 1))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))
(* x (- (* 1/2 x) 1))
(*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))
(* 1/2 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/2 binary64)))
(* (pow x 2) (- 1/2 (/ 1 x)))
(*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x))))
(* (pow x 2) (- 1/2 (/ 1 x)))
(*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x))))
(* (pow x 2) (- 1/2 (/ 1 x)))
(*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x))))
(* 1/2 (pow x 2))
(*.f64 x (*.f64 x #s(literal 1/2 binary64)))
(* (pow x 2) (- 1/2 (/ 1 x)))
(*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x))))
(* (pow x 2) (- 1/2 (/ 1 x)))
(*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x))))
(* (pow x 2) (- 1/2 (/ 1 x)))
(*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 x)))
(*.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) x)))
(* (pow x 2) (+ 1 (* x (- (* 3/4 x) 1))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 3/4 binary64))))))
(* (pow x 2) (+ 1 (* x (- (* x (+ 3/4 (* -1/4 x))) 1))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 3/4 binary64) (*.f64 x #s(literal -1/4 binary64))))))))
(* -1/4 (pow x 5))
(*.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (- (* 3/4 (/ 1 x)) 1/4))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 3/4 binary64) x)))
(* (pow x 5) (- (* 3/4 (/ 1 x)) (+ 1/4 (/ 1 (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 #s(literal 3/4 binary64) (/.f64 #s(literal -1 binary64) x)) x)))
(* (pow x 5) (- (+ (* 3/4 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1 (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (/.f64 #s(literal 3/4 binary64) x) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 x x)) #s(literal -1/4 binary64))))
(* -1/4 (pow x 5))
(*.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- 1/4 (* 3/4 (/ 1 x)))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 3/4 binary64) x)))
(* -1 (* (pow x 5) (+ 1/4 (* -1 (/ (- 3/4 (/ 1 x)) x)))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 #s(literal 3/4 binary64) (/.f64 #s(literal -1 binary64) x)) x)))
(* -1 (* (pow x 5) (+ 1/4 (* -1 (/ (+ 3/4 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x) #s(literal 3/4 binary64)) x)))

eval611.0ms (2.9%)

Compiler

Compiled 40109 to 4246 computations (89.4% saved)

prune235.0ms (1.1%)

Pruning

6 alts after pruning (1 fresh and 5 done)

PrunedKeptTotal
New107111072
Fresh000
Picked415
Done246
Total107761083
Accuracy
100.0%
Counts
1083 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.6%
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x x))))))
✓99.1%
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
✓99.4%
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
✓100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))))))
✓100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
✓98.2%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
Compiler

Compiled 375 to 158 computations (57.9% saved)

regimes35.0ms (0.2%)

Counts
15 → 1
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 5/4 binary64)))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) x))))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
Calls

5 calls:

7.0ms
x
6.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
6.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
6.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
6.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
100.0%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
100.0%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
100.0%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Compiler

Compiled 41 to 28 computations (31.7% saved)

regimes10.0ms (0%)

Counts
11 → 1
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 5/4 binary64)))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))))
Calls

1 calls:

7.0ms
x
Results
AccuracySegmentsBranch
99.6%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes6.0ms (0%)

Counts
9 → 1
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 5/4 binary64)))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x x))))))
Calls

1 calls:

5.0ms
x
Results
AccuracySegmentsBranch
99.6%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Counts
4 → 1
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))))
Calls

1 calls:

3.0ms
x
Results
AccuracySegmentsBranch
99.5%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Counts
3 → 1
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
Calls

1 calls:

3.0ms
x
Results
AccuracySegmentsBranch
99.4%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Counts
2 → 1
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
Calls

1 calls:

3.0ms
x
Results
AccuracySegmentsBranch
99.1%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
Calls

1 calls:

2.0ms
x
Results
AccuracySegmentsBranch
98.2%1x
Compiler

Compiled 2 to 1 computations (50% saved)

simplify91.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
234×distribute-lft-neg-in_binary64
190×unsub-neg_binary64
134×neg-mul-1_binary64
124×distribute-neg-in_binary64
106×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
044101
185101
2114101
3141101
4170101
5190101
6211101
7232101
8291101
9427101
10557101
11609101
12632101
13673101
14718101
15757101
16772101
17775101
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x)))) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) #s(literal -1 binary64))))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 2 binary64) (atan.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))

soundness5.2s (24.3%)

Rules
5530×*-lowering-*.f32
5530×*-lowering-*.f64
4892×*-lowering-*.f32
4892×*-lowering-*.f64
4786×*-lowering-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04445073
113784730
242654508
089714508
031218
1160194
21615186
08348186
034335
1211220
22121210
010159210
01992002
15861803
216931678
365051664
082841664
0935
14635
234735
3481135
0813335
02842705
18772507
225842349
376522349
085222349
0107519
1313449
2908437
32496429
08510429
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 250 to 136 computations (45.6% saved)

preprocess174.0ms (0.8%)

Compiler

Compiled 228 to 108 computations (52.6% saved)

end0.0ms (0%)

Profiling

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