2isqrt (example 3.6)

Time bar (total: 10.8s)

analyze3.0ms (0%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%25%75%0%0%0%0
0%0%25%75%0%0%0%1
50%12.5%12.5%75%0%0%0%2
75%18.7%6.2%75%0%0%0%3
87.5%21.9%3.1%75%0%0%0%4
93.8%23.4%1.6%75%0%0%0%5
96.9%24.2%0.8%75%0%0%0%6
98.4%24.6%0.4%75%0%0%0%7
99.2%24.8%0.2%75%0%0%0%8
99.6%24.9%0.1%75%0%0%0%9
99.8%24.9%0%75%0%0%0%10
99.9%25%0%75%0%0%0%11
100%25%0%75%0%0%0%12
Compiler

Compiled 19 to 12 computations (36.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.0ms
ival-div: 0.0ms (0% of total)
ival-add: 0.0ms (0% of total)
ival-sub: 0.0ms (0% of total)
ival-and: 0.0ms (0% of total)
ival-sqrt: 0.0ms (0% of total)
...c/correct-round.rkt:119:19: 0.0ms (0% of total)
const: 0.0ms (0% of total)
ival->: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)
ival-<: 0.0ms (0% of total)

sample2.3s (21.8%)

Results
1.4s6482×1valid
538.0ms1599×2valid
22.0ms175×0valid
Precisions
Click to see histograms. Total time spent on operations: 1.4s
ival-sqrt: 373.0ms (25.8% of total)
ival-div: 298.0ms (20.6% of total)
backward-pass: 184.0ms (12.7% of total)
...c/correct-round.rkt:119:19: 172.0ms (11.9% of total)
ival-add: 124.0ms (8.6% of total)
ival-sub: 123.0ms (8.5% of total)
ival->: 82.0ms (5.7% of total)
ival-and: 37.0ms (2.6% of total)
ival-<: 33.0ms (2.3% of total)
const: 16.0ms (1.1% of total)
Bogosity

preprocess60.0ms (0.6%)

Algorithm
2×egg-herbie
Rules
308×fnmadd-define
302×sum3-define
248×fmsub-define
232×fnmsub-define
194×fma-define
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01626
13724
27123
313123
423323
544723
667323
789723
8103723
9118323
10129323
11132923
12133723
087
1177
2257
3367
4507
5877
61577
72527
83517
94837
105947
116307
126387
06387
Stop Event
1×iter limit
1×saturated
1×saturated
Calls
Call 1
Inputs
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
Outputs
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
(+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
Call 2
Inputs
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
(- (/ 1 (sqrt (neg x))) (/ 1 (sqrt (+ (neg x) 1))))
(neg (- (/ 1 (sqrt (neg x))) (/ 1 (sqrt (+ (neg x) 1)))))
Outputs
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
(- (rsqrt x) (rsqrt (+ 1 x)))
(- (/ 1 (sqrt (neg x))) (/ 1 (sqrt (+ (neg x) 1))))
(- (rsqrt (neg x)) (rsqrt (- 1 x)))
(neg (- (/ 1 (sqrt (neg x))) (/ 1 (sqrt (+ (neg x) 1)))))
(- (rsqrt (- 1 x)) (rsqrt (neg x)))

explain184.0ms (1.7%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1781(2.9262400951680808e+215)0-(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
00-0-x
00-0-(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
00-0-#s(literal 1 binary64)
00-0-(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
00-0-(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
00-0-(sqrt.f64 x)
00-0-(+.f64 x #s(literal 1 binary64))
Results
105.0ms402×1valid
36.0ms96×2valid
2.0ms14×0valid
Compiler

Compiled 80 to 26 computations (67.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 64.0ms
ival-sqrt: 21.0ms (32.6% of total)
ival-div: 17.0ms (26.4% of total)
backward-pass: 15.0ms (23.3% of total)
ival-add: 6.0ms (9.3% of total)
ival-sub: 5.0ms (7.8% of total)
const: 1.0ms (1.6% of total)

eval0.0ms (0%)

Compiler

Compiled 12 to 9 computations (25% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶37.0%
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify24.0ms (0.2%)

Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓cost-diff0
(sqrt.f64 x)
✓cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓cost-diff0
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Rules
156×fnmadd-define
138×sum3-define
112×fma-lowering-fma.f32
112×fnmsub-define
112×fmsub-define
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0824
11724
22524
33624
45024
58724
615724
725224
835124
948324
1059424
1163024
1263824
063824
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
(/ 1 (sqrt x))
1
(sqrt x)
x
(/ 1 (sqrt (+ x 1)))
(sqrt (+ x 1))
(+ x 1)
Outputs
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
(+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/ 1 (sqrt x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
1
#s(literal 1 binary64)
(sqrt x)
(sqrt.f64 x)
x
(/ 1 (sqrt (+ x 1)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(sqrt (+ x 1))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+ x 1)
(+.f64 #s(literal 1 binary64) x)

localize98.0ms (0.9%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(sqrt.f64 x)
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓accuracy37.0%
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Results
67.0ms201×1valid
17.0ms48×2valid
1.0ms7×0valid
Compiler

Compiled 34 to 9 computations (73.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 51.0ms
ival-sub: 15.0ms (29.4% of total)
ival-sqrt: 14.0ms (27.5% of total)
ival-div: 12.0ms (23.5% of total)
backward-pass: 7.0ms (13.7% of total)
ival-add: 3.0ms (5.9% of total)
const: 1.0ms (2% of total)

series5.0ms (0%)

Counts
4 → 48
Calls
Call 1
Inputs
#<alt (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))>
#<alt (/ 1 (sqrt x))>
#<alt (sqrt x)>
#<alt (/ 1 (sqrt (+ x 1)))>
Outputs
#<alt (sqrt (/ 1 x))>
#<alt (/ (+ (sqrt x) (* -1 x)) x)>
#<alt (/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)>
#<alt (/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))>
#<alt (/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))>
#<alt (/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))>
#<alt (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* 3/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))>
#<alt (sqrt (/ 1 x))>
#<alt (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))>
#<alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))>
#<alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
Calls

12 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
1.0ms
x
@inf
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
1.0ms
x
@-inf
(/ 1 (sqrt (+ x 1)))
1.0ms
x
@-inf
(/ 1 (sqrt x))
0.0ms
x
@0
(/ 1 (sqrt x))

rewrite264.0ms (2.5%)

Algorithm
1×batch-egg-rewrite
Rules
2958×*-lowering-*.f32
2958×*-lowering-*.f64
2750×/-lowering-/.f32
2750×/-lowering-/.f64
1418×sum5-define
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0815
16415
260115
3727915
0816015
Stop Event
1×iter limit
1×node limit
Counts
4 → 220
Calls
Call 1
Inputs
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
(/ 1 (sqrt x))
(sqrt x)
(/ 1 (sqrt (+ x 1)))
Outputs
(+.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(+.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))
(+.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (+.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(+.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (fma.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(+.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (fma.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(+.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (fma.f64 (neg.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(+.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (*.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))
(+.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (*.f64 (+.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(+.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (+.f64 (+.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (+.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))
(+.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(+.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (+.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))
(+.f64 (+.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(+.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (sqrt.f64 (/.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) x))))))
(+.f64 (/.f64 (pow.f64 x #s(literal -3/2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))) (neg.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -3/2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))))))
(+.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))) (neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))))
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))
(-.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64))))
(-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(-.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (/.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(-.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (-.f64 (sqrt.f64 (/.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (+.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (pow.f64 x #s(literal -3/2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))) (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -3/2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))))
(-.f64 (/.f64 (pow.f64 x #s(literal -3/2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))) (-.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -3/2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))) (+.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))) (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))) (+.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))
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(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (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)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) (*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.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 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))

simplify196.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
3318×*-lowering-*.f32
3318×*-lowering-*.f64
1694×sum4-define
1580×sum3-define
1304×times-frac
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0114458
1334394
21141371
34906370
08253370
Stop Event
1×iter limit
1×node limit
Counts
48 → 48
Calls
Call 1
Inputs
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
Outputs
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ (+ (sqrt x) (* -1 x)) x)
(/.f64 (-.f64 (sqrt.f64 x) x) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/.f64 (+.f64 (sqrt.f64 x) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(/.f64 (+.f64 (sqrt.f64 x) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -3/8 binary64))))))) x)
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(*.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64))))) (*.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (*.f64 x x))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64))))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) (*.f64 x x))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(-.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))) (*.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64)))) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x x)))))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 3/8 binary64)))))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 #s(literal 3/8 binary64) (*.f64 x #s(literal -5/16 binary64)))))))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))
(+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64)))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))
(+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64)) (-.f64 (*.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64)))) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))

eval30.0ms (0.3%)

Compiler

Compiled 6533 to 714 computations (89.1% saved)

prune40.0ms (0.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New25414268
Fresh000
Picked101
Done000
Total25514269
Accuracy
81.7%
Counts
269 → 14
Alt Table
Click to see full alt table
StatusAccuracyProgram
39.1%
(/.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
▶39.2%
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
39.2%
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (*.f64 (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))))
37.3%
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x))) (+.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
▶80.2%
(/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64))))) (*.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (*.f64 x x))
39.1%
(/.f64 (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (*.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)))
▶37.0%
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
29.4%
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
27.2%
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
30.5%
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
39.1%
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
▶79.0%
(*.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))
68.0%
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))
▶5.8%
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
Compiler

Compiled 478 to 286 computations (40.2% saved)

simplify157.0ms (1.5%)

Algorithm
1×egg-herbie
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(+.f64 #s(literal 1 binary64) x)
✓cost-diff0
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
✓cost-diff0
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
✓cost-diff256
(-.f64 (+.f64 #s(literal 1 binary64) x) x)
✓cost-diff0
(/.f64 #s(literal 1 binary64) x)
✓cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓cost-diff0
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
✓cost-diff0
(*.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))
✓cost-diff0
(+.f64 #s(literal 1 binary64) x)
✓cost-diff0
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
✓cost-diff0
(pow.f64 x #s(literal -1/2 binary64))
✓cost-diff0
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓cost-diff0
(/.f64 #s(literal 1 binary64) x)
✓cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓cost-diff0
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64)))))
✓cost-diff0
(+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64))))) (*.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
✓cost-diff0
(/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64))))) (*.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (*.f64 x x))
✓cost-diff128
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64))))
Rules
1808×*-lowering-*.f32
1808×*-lowering-*.f64
1576×fma-define
1440×sum4-define
1386×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
033239
185217
2199210
3511210
41033210
52427210
67384210
08081210
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ (+ (* (sqrt (/ 1 (* x (* x x)))) (* 1/2 (+ 1 (* x 1/4)))) (* -1/2 (- (sqrt (/ 1 x)) (sqrt x)))) (* x x))
(+ (* (sqrt (/ 1 (* x (* x x)))) (* 1/2 (+ 1 (* x 1/4)))) (* -1/2 (- (sqrt (/ 1 x)) (sqrt x))))
(* (sqrt (/ 1 (* x (* x x)))) (* 1/2 (+ 1 (* x 1/4))))
(sqrt (/ 1 (* x (* x x))))
(/ 1 (* x (* x x)))
1
(* x (* x x))
x
(* x x)
(* 1/2 (+ 1 (* x 1/4)))
1/2
(+ 1 (* x 1/4))
(* x 1/4)
1/4
(* -1/2 (- (sqrt (/ 1 x)) (sqrt x)))
-1/2
(- (sqrt (/ 1 x)) (sqrt x))
(sqrt (/ 1 x))
(/ 1 x)
(sqrt x)
(sqrt (/ 1 x))
(/ 1 x)
1
x
(- (pow x -1/2) (pow (+ 1 x) -1/2))
(pow x -1/2)
x
-1/2
(pow (+ 1 x) -1/2)
(+ 1 x)
1
(* (- (sqrt (/ 1 x)) (sqrt x)) (/ -1/2 (* x x)))
(- (sqrt (/ 1 x)) (sqrt x))
(sqrt (/ 1 x))
(/ 1 x)
1
x
(sqrt x)
(/ -1/2 (* x x))
-1/2
(* x x)
(/ (/ (- (+ 1 x) x) (+ x (sqrt (* x (+ 1 x))))) (pow (+ 1 x) 1/2))
(/ (- (+ 1 x) x) (+ x (sqrt (* x (+ 1 x)))))
(- (+ 1 x) x)
(+ 1 x)
1
x
(+ x (sqrt (* x (+ 1 x))))
(sqrt (* x (+ 1 x)))
(* x (+ 1 x))
(pow (+ 1 x) 1/2)
1/2
Outputs
(/ (+ (* (sqrt (/ 1 (* x (* x x)))) (* 1/2 (+ 1 (* x 1/4)))) (* -1/2 (- (sqrt (/ 1 x)) (sqrt x)))) (* x x))
(/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (*.f64 x x))
(+ (* (sqrt (/ 1 (* x (* x x)))) (* 1/2 (+ 1 (* x 1/4)))) (* -1/2 (- (sqrt (/ 1 x)) (sqrt x))))
(+.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* (sqrt (/ 1 (* x (* x x)))) (* 1/2 (+ 1 (* x 1/4))))
(*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))))
(sqrt (/ 1 (* x (* x x))))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))
(/ 1 (* x (* x x)))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
1
#s(literal 1 binary64)
(* x (* x x))
(*.f64 x (*.f64 x x))
x
(* x x)
(*.f64 x x)
(* 1/2 (+ 1 (* x 1/4)))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1 (* x 1/4))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64)))
(* x 1/4)
(*.f64 x #s(literal 1/4 binary64))
1/4
#s(literal 1/4 binary64)
(* -1/2 (- (sqrt (/ 1 x)) (sqrt x)))
(*.f64 #s(literal 1/2 binary64) (-.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
-1/2
#s(literal -1/2 binary64)
(- (sqrt (/ 1 x)) (sqrt x))
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(sqrt x)
(sqrt.f64 x)
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(- (pow x -1/2) (pow (+ 1 x) -1/2))
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(pow x -1/2)
(pow.f64 x #s(literal -1/2 binary64))
x
-1/2
#s(literal -1/2 binary64)
(pow (+ 1 x) -1/2)
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
(* (- (sqrt (/ 1 x)) (sqrt x)) (/ -1/2 (* x x)))
(*.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(- (sqrt (/ 1 x)) (sqrt x))
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(sqrt x)
(sqrt.f64 x)
(/ -1/2 (* x x))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
-1/2
#s(literal -1/2 binary64)
(* x x)
(*.f64 x x)
(/ (/ (- (+ 1 x) x) (+ x (sqrt (* x (+ 1 x))))) (pow (+ 1 x) 1/2))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(/ (- (+ 1 x) x) (+ x (sqrt (* x (+ 1 x)))))
(/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(- (+ 1 x) x)
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(+ x (sqrt (* x (+ 1 x))))
(+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))
(sqrt (* x (+ 1 x)))
(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))
(* x (+ 1 x))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(pow (+ 1 x) 1/2)
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)

localize415.0ms (3.9%)

Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
✓accuracy99.6%
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
✓accuracy53.8%
(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))
✓accuracy8.8%
(-.f64 (+.f64 #s(literal 1 binary64) x) x)
✓accuracy100.0%
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
✓accuracy99.8%
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓accuracy98.8%
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
✓accuracy82.7%
(*.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))
✓accuracy100.0%
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
✓accuracy100.0%
(pow.f64 x #s(literal -1/2 binary64))
✓accuracy100.0%
(+.f64 #s(literal 1 binary64) x)
✓accuracy37.0%
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓accuracy100.0%
(/.f64 #s(literal 1 binary64) x)
✓accuracy99.8%
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓accuracy99.4%
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))
✓accuracy81.5%
(/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64))))) (*.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (*.f64 x x))
✓accuracy71.7%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64)))))
✓accuracy71.2%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))
Results
250.0ms201×1valid
96.0ms48×2valid
4.0ms7×0valid
Compiler

Compiled 283 to 34 computations (88% saved)

Precisions
Click to see histograms. Total time spent on operations: 185.0ms
ival-pow: 59.0ms (31.9% of total)
backward-pass: 39.0ms (21.1% of total)
ival-mult: 27.0ms (14.6% of total)
ival-div: 23.0ms (12.4% of total)
ival-sqrt: 15.0ms (8.1% of total)
ival-add: 11.0ms (5.9% of total)
ival-sub: 8.0ms (4.3% of total)
const: 1.0ms (0.5% of total)

series21.0ms (0.2%)

Counts
19 → 228
Calls
Call 1
Inputs
#<alt (* 1/2 (+ 1 (* x 1/4)))>
#<alt (/ (+ (* (sqrt (/ 1 (* x (* x x)))) (* 1/2 (+ 1 (* x 1/4)))) (* -1/2 (- (sqrt (/ 1 x)) (sqrt x)))) (* x x))>
#<alt (+ (* (sqrt (/ 1 (* x (* x x)))) (* 1/2 (+ 1 (* x 1/4)))) (* -1/2 (- (sqrt (/ 1 x)) (sqrt x))))>
#<alt (* (sqrt (/ 1 (* x (* x x)))) (* 1/2 (+ 1 (* x 1/4))))>
#<alt (sqrt (/ 1 x))>
#<alt (/ 1 x)>
#<alt (- (pow x -1/2) (pow (+ 1 x) -1/2))>
#<alt (pow x -1/2)>
#<alt (pow (+ 1 x) -1/2)>
#<alt (+ 1 x)>
#<alt (* (- (sqrt (/ 1 x)) (sqrt x)) (/ -1/2 (* x x)))>
#<alt (- (sqrt (/ 1 x)) (sqrt x))>
#<alt (- (+ 1 x) x)>
#<alt (/ (/ (- (+ 1 x) x) (+ x (sqrt (* x (+ 1 x))))) (pow (+ 1 x) 1/2))>
#<alt (/ (- (+ 1 x) x) (+ x (sqrt (* x (+ 1 x)))))>
#<alt (sqrt (/ 1 (* x (* x x))))>
#<alt (/ 1 (* x (* x x)))>
#<alt (/ -1/2 (* x x))>
#<alt (sqrt (* x (+ 1 x)))>
Outputs
#<alt 1/2>
#<alt (+ 1/2 (* 1/8 x))>
#<alt (+ 1/2 (* 1/8 x))>
#<alt (+ 1/2 (* 1/8 x))>
#<alt (* 1/8 x)>
#<alt (* x (+ 1/8 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/8 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/8 (* 1/2 (/ 1 x))))>
#<alt (* 1/8 x)>
#<alt (* x (+ 1/8 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/8 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/8 (* 1/2 (/ 1 x))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 7))))>
#<alt (/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (* 1/8 (sqrt x))))) (pow x 4))>
#<alt (/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (+ (* 1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))) (pow x 4))>
#<alt (/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (+ (* 1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))) (pow x 4))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) x)>
#<alt (/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 5))))))) x)>
#<alt (/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 5))))))) x)>
#<alt (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (* 1/8 (sqrt x))))) (pow x 2))>
#<alt (/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (+ (* 1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))) (pow x 2))>
#<alt (/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (+ (* 1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))) (pow x 2))>
#<alt (* 1/2 (sqrt x))>
#<alt (* x (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))))>
#<alt (* x (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 5))))))))>
#<alt (* x (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 5))))))))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* 1/8 (sqrt (pow x 3))) (* 1/2 (sqrt x))) (pow x 2))>
#<alt (/ (+ (* 1/8 (sqrt (pow x 3))) (* 1/2 (sqrt x))) (pow x 2))>
#<alt (/ (+ (* 1/8 (sqrt (pow x 3))) (* 1/2 (sqrt x))) (pow x 2))>
#<alt (* 1/8 (sqrt (/ 1 x)))>
#<alt (+ (* 1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 3)))))>
#<alt (+ (* 1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 3)))))>
#<alt (+ (* 1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 3)))))>
#<alt (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (sqrt (/ 1 x))>
#<alt (/ (+ (sqrt x) (* -1 x)) x)>
#<alt (/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)>
#<alt (/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))>
#<alt (/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))>
#<alt (/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))>
#<alt (/ (- (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) x)) (* -1/2 (sqrt x))) (pow x 2))>
#<alt (/ (- (* -1 (/ (- (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/2 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (* (sqrt x) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) x)) (* -1/2 (sqrt x))) x)) (* -1/2 (sqrt x))) (pow x 2))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* 3/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))>
#<alt (sqrt (/ 1 x))>
#<alt (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))>
#<alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))>
#<alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* -1/2 (sqrt (/ 1 (pow x 5))))>
#<alt (/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))>
#<alt (/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))>
#<alt (/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))>
#<alt (sqrt (/ 1 x))>
#<alt (/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)>
#<alt (* -1 (sqrt x))>
#<alt (* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))>
#<alt (* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))>
#<alt (* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))>
#<alt (* (sqrt x) (pow (sqrt -1) 2))>
#<alt (* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt (sqrt (/ 1 x))>
#<alt (+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x))))>
#<alt (+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x))))>
#<alt (+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1))))>
#<alt (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2))))) x)) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/16 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 3)))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3)))) (- (pow (sqrt -1) 2) 1))) (* 1/16 (/ 1 (* (pow (sqrt -1) 4) (pow (- (pow (sqrt -1) 2) 1) 2))))))))) (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* 1/4 (* (sqrt x) (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))))) x)) (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3)))))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2))))) x)) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))>
#<alt (sqrt (/ 1 x))>
#<alt (- (sqrt (/ 1 x)) 1)>
#<alt (+ (sqrt (/ 1 x)) (* x (- (* -1 (* x (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x))))>
#<alt (+ (sqrt (/ 1 x)) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (pow x 2))) (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x))))>
#<alt (/ 1/2 x)>
#<alt (/ (- 1/2 (* 1/8 (/ 1 x))) x)>
#<alt (/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)>
#<alt (/ (- (+ 1/2 (/ 1/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3))))) x)>
#<alt (/ -1 (* x (- (pow (sqrt -1) 2) 1)))>
#<alt (* -1 (/ (+ (* 1/2 (/ 1 (* x (pow (- (pow (sqrt -1) 2) 1) 2)))) (/ 1 (- (pow (sqrt -1) 2) 1))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3)))) x)) (* 1/2 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) x)) (/ 1 (- (pow (sqrt -1) 2) 1))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3)))) (* x (- (pow (sqrt -1) 2) 1)))) (+ (/ 1/16 (* x (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 3)))) (/ 1/16 (* x (* (pow (sqrt -1) 4) (pow (- (pow (sqrt -1) 2) 1) 2)))))))) x)) (* 1/2 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) x)) (/ 1 (- (pow (sqrt -1) 2) 1))) x))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (sqrt x)>
#<alt (+ (sqrt x) (* 1/2 (sqrt (pow x 3))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))>
#<alt (* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))>
#<alt (* -1 (* x (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (- (pow (sqrt -1) 2) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))>
Calls

57 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
(/ (/ (- (+ 1 x) x) (+ x (sqrt (* x (+ 1 x))))) (pow (+ 1 x) 1/2))
1.0ms
x
@-inf
(* (sqrt (/ 1 (* x (* x x)))) (* 1/2 (+ 1 (* x 1/4))))
1.0ms
x
@0
(/ (/ (- (+ 1 x) x) (+ x (sqrt (* x (+ 1 x))))) (pow (+ 1 x) 1/2))
1.0ms
x
@-inf
(/ (+ (* (sqrt (/ 1 (* x (* x x)))) (* 1/2 (+ 1 (* x 1/4)))) (* -1/2 (- (sqrt (/ 1 x)) (sqrt x)))) (* x x))
1.0ms
x
@0
(/ (+ (* (sqrt (/ 1 (* x (* x x)))) (* 1/2 (+ 1 (* x 1/4)))) (* -1/2 (- (sqrt (/ 1 x)) (sqrt x)))) (* x x))

rewrite289.0ms (2.7%)

Algorithm
1×batch-egg-rewrite
Rules
3184×*-lowering-*.f32
3184×*-lowering-*.f64
2096×fma-lowering-fma.f32
2096×fma-lowering-fma.f64
1950×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
033164
1227120
22070113
08372113
Stop Event
1×iter limit
1×node limit
Counts
19 → 602
Calls
Call 1
Inputs
(* 1/2 (+ 1 (* x 1/4)))
(/ (+ (* (sqrt (/ 1 (* x (* x x)))) (* 1/2 (+ 1 (* x 1/4)))) (* -1/2 (- (sqrt (/ 1 x)) (sqrt x)))) (* x x))
(+ (* (sqrt (/ 1 (* x (* x x)))) (* 1/2 (+ 1 (* x 1/4)))) (* -1/2 (- (sqrt (/ 1 x)) (sqrt x))))
(* (sqrt (/ 1 (* x (* x x)))) (* 1/2 (+ 1 (* x 1/4))))
(sqrt (/ 1 x))
(/ 1 x)
(- (pow x -1/2) (pow (+ 1 x) -1/2))
(pow x -1/2)
(pow (+ 1 x) -1/2)
(+ 1 x)
(* (- (sqrt (/ 1 x)) (sqrt x)) (/ -1/2 (* x x)))
(- (sqrt (/ 1 x)) (sqrt x))
(- (+ 1 x) x)
(/ (/ (- (+ 1 x) x) (+ x (sqrt (* x (+ 1 x))))) (pow (+ 1 x) 1/2))
(/ (- (+ 1 x) x) (+ x (sqrt (* x (+ 1 x)))))
(sqrt (/ 1 (* x (* x x))))
(/ 1 (* x (* x x)))
(/ -1/2 (* x x))
(sqrt (* x (+ 1 x)))
Outputs
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64)))
(+.f64 (*.f64 x #s(literal 1/8 binary64)) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64))
(fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/8 binary64) x #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1/4 binary64) #s(literal 1/2 binary64))
(/.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/512 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 x #s(literal 1/8 binary64)) (*.f64 x #s(literal 1/8 binary64))) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x #s(literal 1/8 binary64)) (*.f64 x #s(literal 1/8 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/64 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x #s(literal 1/4 binary64)) (-.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1/16 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64))))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/64 binary64))) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x #s(literal 1/4 binary64)) (-.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1/16 binary64))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64))))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64))))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64))) #s(literal 1/2 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 x x) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))) (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))))) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))) x)))
(/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))) (*.f64 x x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x x) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))))) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (+.f64 (/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))))) (pow.f64 x #s(literal 9/2 binary64))) (pow.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) #s(literal 3 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))))) (*.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) (-.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))))))))
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))))) (pow.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) #s(literal 2 binary64))) (*.f64 (*.f64 x x) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal 1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))))))
(/.f64 (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))) x) x)
(/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))))) (pow.f64 x #s(literal 9/2 binary64))) (pow.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) #s(literal 3 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))))) (*.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) (-.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64)))))) (*.f64 x x)))
(/.f64 (*.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))))) (pow.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) #s(literal 2 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal 1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))) (*.f64 x x)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))))) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))))
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(*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x))))))
(*.f64 (pow.f64 x #s(literal -3/4 binary64)) (pow.f64 x #s(literal -3/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -3/2 binary64)) (pow.f64 x #s(literal -3/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 x #s(literal -3/4 binary64)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal -3/4 binary64)) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal -3/2 binary64))) (sqrt.f64 (pow.f64 x #s(literal -3/2 binary64))))
(exp.f64 (*.f64 #s(literal -3 binary64) (log.f64 x)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -3 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64)))
(exp.f64 (+.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 x)) #s(literal 3 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 x)) #s(literal 3 binary64))))
(exp.f64 (+.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 x)) #s(literal 3 binary64)) (*.f64 (*.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (+.f64 (*.f64 (*.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 x)) #s(literal 3 binary64))))
(exp.f64 (+.f64 (*.f64 (*.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64)) (*.f64 (*.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (-.f64 (log.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x x))))
(neg.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 3 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) #s(literal 3 binary64)))
(/.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 x x))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x))))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(pow.f64 x #s(literal -3 binary64))
(pow.f64 (*.f64 x x) #s(literal -3/2 binary64))
(pow.f64 (*.f64 x (*.f64 x x)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 6 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -6 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 3/2 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1 binary64))
(pow.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 x #s(literal -3/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))))
(*.f64 #s(literal -1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) #s(literal 3 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (pow.f64 x #s(literal -3/4 binary64)) (pow.f64 (pow.f64 x #s(literal -3/4 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal -3/4 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal -3/4 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal -1/2 binary64) x)))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x x) #s(literal -1/2 binary64))))
(/.f64 (/.f64 #s(literal -1/2 binary64) x) x)
(/.f64 (neg.f64 (/.f64 #s(literal -1/2 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(pow.f64 (/.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 x (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1/2 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(*.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) x))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(exp.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)) (*.f64 #s(literal 1/2 binary64) (log1p.f64 x))))
(exp.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x)) (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
(hypot.f64 x (sqrt.f64 x))
(hypot.f64 (sqrt.f64 x) x)
(fabs.f64 (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))
(/.f64 (sqrt.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x (*.f64 x x))))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (sqrt.f64 (-.f64 x (*.f64 x x))))
(/.f64 (sqrt.f64 (*.f64 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 (sqrt.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(pow.f64 (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) (*.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(*.f64 (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 #s(literal 1 binary64) x)))) #s(literal 1/2 binary64)))
(*.f64 (*.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) x)) #s(literal 1/2 binary64)) (pow.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 #s(literal 1 binary64) x))))))
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) x))) (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))

simplify315.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
3528×*-lowering-*.f32
3528×*-lowering-*.f64
2310×+-lowering-+.f64
2310×+-lowering-+.f32
1426×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04312795
114031990
257841966
083381966
Stop Event
1×iter limit
1×node limit
Counts
228 → 228
Calls
Call 1
Inputs
1/2
(+ 1/2 (* 1/8 x))
(+ 1/2 (* 1/8 x))
(+ 1/2 (* 1/8 x))
(* 1/8 x)
(* x (+ 1/8 (* 1/2 (/ 1 x))))
(* x (+ 1/8 (* 1/2 (/ 1 x))))
(* x (+ 1/8 (* 1/2 (/ 1 x))))
(* 1/8 x)
(* x (+ 1/8 (* 1/2 (/ 1 x))))
(* x (+ 1/8 (* 1/2 (/ 1 x))))
(* x (+ 1/8 (* 1/2 (/ 1 x))))
(* 1/2 (sqrt (/ 1 (pow x 7))))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (* 1/8 (sqrt x))))) (pow x 4))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (+ (* 1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))) (pow x 4))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (+ (* 1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))) (pow x 4))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) x)
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 5))))))) x)
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 5))))))) x)
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (* 1/8 (sqrt x))))) (pow x 2))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (+ (* 1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))) (pow x 2))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (+ (* 1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))) (pow x 2))
(* 1/2 (sqrt x))
(* x (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))))
(* x (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 5))))))))
(* x (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 5))))))))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* 1/8 (sqrt (pow x 3))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* 1/8 (sqrt (pow x 3))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* 1/8 (sqrt (pow x 3))) (* 1/2 (sqrt x))) (pow x 2))
(* 1/8 (sqrt (/ 1 x)))
(+ (* 1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 3)))))
(+ (* 1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 3)))))
(+ (* 1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 3)))))
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) x)) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* -1 (/ (- (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/2 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (* (sqrt x) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) x)) (* -1/2 (sqrt x))) x)) (* -1/2 (sqrt x))) (pow x 2))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* -1/2 (sqrt (/ 1 (pow x 5))))
(/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)
(* -1 (sqrt x))
(* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))
(* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))
(* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))
(* (sqrt x) (pow (sqrt -1) 2))
(* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
1
1
1
1
1
1
1
1
1
1
1
1
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)
(* -1 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1))))
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2))))) x)) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/16 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 3)))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3)))) (- (pow (sqrt -1) 2) 1))) (* 1/16 (/ 1 (* (pow (sqrt -1) 4) (pow (- (pow (sqrt -1) 2) 1) 2))))))))) (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* 1/4 (* (sqrt x) (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))))) x)) (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3)))))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2))))) x)) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))
(sqrt (/ 1 x))
(- (sqrt (/ 1 x)) 1)
(+ (sqrt (/ 1 x)) (* x (- (* -1 (* x (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (pow x 2))) (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x))))
(/ 1/2 x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3))))) x)
(/ -1 (* x (- (pow (sqrt -1) 2) 1)))
(* -1 (/ (+ (* 1/2 (/ 1 (* x (pow (- (pow (sqrt -1) 2) 1) 2)))) (/ 1 (- (pow (sqrt -1) 2) 1))) x))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3)))) x)) (* 1/2 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) x)) (/ 1 (- (pow (sqrt -1) 2) 1))) x))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3)))) (* x (- (pow (sqrt -1) 2) 1)))) (+ (/ 1/16 (* x (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 3)))) (/ 1/16 (* x (* (pow (sqrt -1) 4) (pow (- (pow (sqrt -1) 2) 1) 2)))))))) x)) (* 1/2 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) x)) (/ 1 (- (pow (sqrt -1) 2) 1))) x))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(sqrt x)
(+ (sqrt x) (* 1/2 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (- (pow (sqrt -1) 2) (* 1/2 (/ 1 x)))))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/8 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) x))
(+ 1/2 (* 1/8 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) x))
(+ 1/2 (* 1/8 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) x))
(* 1/8 x)
(*.f64 #s(literal 1/8 binary64) x)
(* x (+ 1/8 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) x))
(* x (+ 1/8 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) x))
(* x (+ 1/8 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) x))
(* 1/8 x)
(*.f64 #s(literal 1/8 binary64) x)
(* x (+ 1/8 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) x))
(* x (+ 1/8 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) x))
(* x (+ 1/8 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) x))
(* 1/2 (sqrt (/ 1 (pow x 7))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (* 1/8 (sqrt x))))) (pow x 4))
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 (*.f64 x (sqrt.f64 x)) #s(literal -3/8 binary64))) (*.f64 (*.f64 x x) (*.f64 x x)))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (+ (* 1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))) (pow x 4))
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 x (+.f64 (*.f64 (sqrt.f64 x) #s(literal -3/8 binary64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 x (*.f64 x x))))))) (*.f64 (*.f64 x x) (*.f64 x x)))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (+ (* 1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))) (pow x 4))
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 x (+.f64 (*.f64 (sqrt.f64 x) #s(literal -3/8 binary64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 x (*.f64 x x))))))) (*.f64 (*.f64 x x) (*.f64 x x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)))
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) x)
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -3/8 binary64))) x)
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 5))))))) x)
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -3/8 binary64))) x)
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 5))))))) x)
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -3/8 binary64))) x)
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 5/8 binary64)) x)) x)
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/.f64 (-.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)) (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 5/8 binary64))) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/.f64 (-.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)) (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 5/8 binary64))) x)) (-.f64 #s(literal 0 binary64) x))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (* 1/8 (sqrt x))))) (pow x 2))
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 (*.f64 x (sqrt.f64 x)) #s(literal -3/8 binary64))) (*.f64 x x))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (+ (* 1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))) (pow x 2))
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 x (+.f64 (*.f64 (sqrt.f64 x) #s(literal -3/8 binary64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 x (*.f64 x x))))))) (*.f64 x x))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (+ (* 1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))) (pow x 2))
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 x (+.f64 (*.f64 (sqrt.f64 x) #s(literal -3/8 binary64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 x (*.f64 x x))))))) (*.f64 x x))
(* 1/2 (sqrt x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* x (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))))
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -3/8 binary64))))
(* x (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 5))))))))
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -3/8 binary64))))
(* x (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 5))))))))
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -3/8 binary64))))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* -1 (* x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 5/8 binary64)) x)))
(* -1 (* x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 x (-.f64 #s(literal 0 binary64) (-.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)) (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 5/8 binary64))) x))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 x (-.f64 #s(literal 0 binary64) (-.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)) (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 5/8 binary64))) x))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)))
(/ (+ (* 1/8 (sqrt (pow x 3))) (* 1/2 (sqrt x))) (pow x 2))
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 x (*.f64 x x))))) (*.f64 x x))
(/ (+ (* 1/8 (sqrt (pow x 3))) (* 1/2 (sqrt x))) (pow x 2))
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 x (*.f64 x x))))) (*.f64 x x))
(/ (+ (* 1/8 (sqrt (pow x 3))) (* 1/2 (sqrt x))) (pow x 2))
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (*.f64 x (*.f64 x x))))) (*.f64 x x))
(* 1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* 1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 3)))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* 1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 3)))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* 1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 3)))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
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(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/.f64 (+.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -3/8 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/16 binary64))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)
(/.f64 (+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal -5/128 binary64)) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 3/8 binary64)))) (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -3/8 binary64))) x)
(* -1 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1))))
(/.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -2 binary64))
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -1/8 binary64))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2))))) x)) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))
(/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (-.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (/.f64 (sqrt.f64 x) #s(literal 4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/16 binary64))) x)) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/16 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 3)))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3)))) (- (pow (sqrt -1) 2) 1))) (* 1/16 (/ 1 (* (pow (sqrt -1) 4) (pow (- (pow (sqrt -1) 2) 1) 2))))))))) (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* 1/4 (* (sqrt x) (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))))) x)) (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3)))))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2))))) x)) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))
(/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (-.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 x) #s(literal 4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/16 binary64))) (/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 3/128 binary64))) (+.f64 (/.f64 (sqrt.f64 x) #s(literal 4 binary64)) (*.f64 (sqrt.f64 x) #s(literal 1/16 binary64)))) x)) x)) x)) (-.f64 #s(literal 0 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(- (sqrt (/ 1 x)) 1)
(+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(+ (sqrt (/ 1 x)) (* x (- (* -1 (* x (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x))))
(+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (*.f64 x (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (*.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64)))
(+ (sqrt (/ 1 x)) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (pow x 2))) (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x))))
(+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (*.f64 x (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)))))))) #s(literal -1 binary64)))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3))))) x)
(/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) (/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))) x)
(/ -1 (* x (- (pow (sqrt -1) 2) 1)))
(/.f64 #s(literal 1/2 binary64) x)
(* -1 (/ (+ (* 1/2 (/ 1 (* x (pow (- (pow (sqrt -1) 2) 1) 2)))) (/ 1 (- (pow (sqrt -1) 2) 1))) x))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3)))) x)) (* 1/2 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) x)) (/ 1 (- (pow (sqrt -1) 2) 1))) x))
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3)))) (* x (- (pow (sqrt -1) 2) 1)))) (+ (/ 1/16 (* x (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 3)))) (/ 1/16 (* x (* (pow (sqrt -1) 4) (pow (- (pow (sqrt -1) 2) 1) 2)))))))) x)) (* 1/2 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) x)) (/ 1 (- (pow (sqrt -1) 2) 1))) x))
(/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal -1/16 binary64) (+.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) x) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (/.f64 #s(literal 1/128 binary64) x)))) x) #s(literal 1/8 binary64)) x)) (-.f64 #s(literal 0 binary64) x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))
(/ 1 (pow x 3))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(/ 1 (pow x 3))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(/ 1 (pow x 3))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(/ 1 (pow x 3))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(/ 1 (pow x 3))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(/ 1 (pow x 3))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(/ 1 (pow x 3))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(/ 1 (pow x 3))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(/ 1 (pow x 3))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(/ 1 (pow x 3))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(/ 1 (pow x 3))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(/ 1 (pow x 3))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (sqrt (pow x 3))))
(+.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 x (*.f64 x x)))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))
(+.f64 (sqrt.f64 x) (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal -1/8 binary64)))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))
(+.f64 (sqrt.f64 x) (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 x (*.f64 x (+.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -1/8 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/16 binary64))))))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) x)
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) x) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))))
(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (- (pow (sqrt -1) 2) (* 1/2 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) x)
(* -1 (* x (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
(+.f64 x (*.f64 x (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (/.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) x)))

eval179.0ms (1.7%)

Compiler

Compiled 28537 to 3041 computations (89.3% saved)

prune136.0ms (1.3%)

Pruning

21 alts after pruning (19 fresh and 2 done)

PrunedKeptTotal
New1151181169
Fresh819
Picked325
Done000
Total1162211183
Accuracy
100.0%
Counts
1183 → 21
Alt Table
Click to see full alt table
StatusAccuracyProgram
35.0%
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
35.0%
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
▶5.8%
(pow.f64 x #s(literal -1/2 binary64))
▶81.6%
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
39.1%
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
38.5%
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) x) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
▶98.9%
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) (/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
▶98.8%
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
98.4%
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
97.2%
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
97.0%
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 5/8 binary64)) x)) x)
98.4%
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -3/8 binary64))) x)
97.1%
(/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) x)
74.2%
(/.f64 (*.f64 (+.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (*.f64 (*.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x (+.f64 #s(literal 1 binary64) x))))
80.1%
(/.f64 (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -3/8 binary64)))) (*.f64 x x))
▶78.9%
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 x x))
5.8%
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓37.0%
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
97.1%
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)) x) (/.f64 #s(literal -1/2 binary64) x))
68.0%
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))
✓5.8%
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
Compiler

Compiled 611 to 387 computations (36.7% saved)

simplify215.0ms (2%)

Algorithm
1×egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))
✓cost-diff0
(+.f64 #s(literal 1 binary64) x)
✓cost-diff0
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
✓cost-diff0
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x))
✓cost-diff0
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x)
✓cost-diff0
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
✓cost-diff64
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
✓cost-diff0
(*.f64 x x)
✓cost-diff0
(sqrt.f64 x)
✓cost-diff0
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓cost-diff0
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 x x))
✓cost-diff0
(pow.f64 x #s(literal -1/2 binary64))
✓cost-diff0
(-.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) (/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x))))
✓cost-diff0
(/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) (/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))) x)
✓cost-diff0
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) (/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
✓cost-diff64
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
Rules
2546×*-lowering-*.f32
2546×*-lowering-*.f64
1306×/-lowering-/.f32
1306×/-lowering-/.f64
1302×div-sub
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
030230
169223
2139223
3369223
4927223
52593223
67022223
08103223
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ (/ (- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x)))) x) (pow (+ 1 x) 1/2))
(/ (- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x)))) x)
(- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x))))
(+ 1/2 (/ (- -1/8 (/ -1/16 x)) x))
1/2
(/ (- -1/8 (/ -1/16 x)) x)
(- -1/8 (/ -1/16 x))
-1/8
(/ -1/16 x)
-1/16
x
(/ 5/128 (* x (* x x)))
5/128
(* x (* x x))
(* x x)
(pow (+ 1 x) 1/2)
(+ 1 x)
1
(pow x -1/2)
x
-1/2
(/ (* 1/2 (sqrt x)) (* x x))
(* 1/2 (sqrt x))
1/2
(sqrt x)
x
(* x x)
(/ (/ (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) x) (pow (+ 1 x) 1/2))
(/ (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) x)
(+ 1/2 (/ (- -1/8 (/ -1/16 x)) x))
1/2
(/ (- -1/8 (/ -1/16 x)) x)
(- -1/8 (/ -1/16 x))
-1/8
(/ -1/16 x)
-1/16
x
(pow (+ 1 x) 1/2)
(+ 1 x)
1
(/ (pow (+ 1 x) -1/2) (+ x (sqrt (* x (+ 1 x)))))
(pow (+ 1 x) -1/2)
(+ 1 x)
1
x
-1/2
(+ x (sqrt (* x (+ 1 x))))
(sqrt (* x (+ 1 x)))
(* x (+ 1 x))
Outputs
(/ (/ (- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x)))) x) (pow (+ 1 x) 1/2))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x) (/.f64 #s(literal -5/128 binary64) (*.f64 x (*.f64 x x))))) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/ (- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x)))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x) (/.f64 #s(literal -5/128 binary64) (*.f64 x (*.f64 x x))))) x)
(- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x))))
(+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x) (/.f64 #s(literal -5/128 binary64) (*.f64 x (*.f64 x x)))))
(+ 1/2 (/ (- -1/8 (/ -1/16 x)) x))
(+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x))
1/2
#s(literal 1/2 binary64)
(/ (- -1/8 (/ -1/16 x)) x)
(/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)
(- -1/8 (/ -1/16 x))
(-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))
-1/8
#s(literal -1/8 binary64)
(/ -1/16 x)
(/.f64 #s(literal -1/16 binary64) x)
-1/16
#s(literal -1/16 binary64)
x
(/ 5/128 (* x (* x x)))
(/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))
5/128
#s(literal 5/128 binary64)
(* x (* x x))
(*.f64 x (*.f64 x x))
(* x x)
(*.f64 x x)
(pow (+ 1 x) 1/2)
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(pow x -1/2)
(pow.f64 x #s(literal -1/2 binary64))
x
-1/2
#s(literal -1/2 binary64)
(/ (* 1/2 (sqrt x)) (* x x))
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 x x))
(* 1/2 (sqrt x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
1/2
#s(literal 1/2 binary64)
(sqrt x)
(sqrt.f64 x)
x
(* x x)
(*.f64 x x)
(/ (/ (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) x) (pow (+ 1 x) 1/2))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) (*.f64 x (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/ (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x)
(+ 1/2 (/ (- -1/8 (/ -1/16 x)) x))
(+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x))
1/2
#s(literal 1/2 binary64)
(/ (- -1/8 (/ -1/16 x)) x)
(/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)
(- -1/8 (/ -1/16 x))
(-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))
-1/8
#s(literal -1/8 binary64)
(/ -1/16 x)
(/.f64 #s(literal -1/16 binary64) x)
-1/16
#s(literal -1/16 binary64)
x
(pow (+ 1 x) 1/2)
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(/ (pow (+ 1 x) -1/2) (+ x (sqrt (* x (+ 1 x)))))
(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))))
(pow (+ 1 x) -1/2)
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
1
#s(literal 1 binary64)
x
-1/2
#s(literal -1/2 binary64)
(+ x (sqrt (* x (+ 1 x))))
(+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))
(sqrt (* x (+ 1 x)))
(sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))
(* x (+ 1 x))
(*.f64 x (+.f64 x #s(literal 1 binary64)))

localize192.0ms (1.8%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 x (+.f64 #s(literal 1 binary64) x))
✓accuracy100.0%
(+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))
✓accuracy99.7%
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
✓accuracy53.8%
(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))
✓accuracy100.0%
(+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x))
✓accuracy100.0%
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x)
✓accuracy100.0%
(/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)
✓accuracy99.6%
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
✓accuracy100.0%
(*.f64 x x)
✓accuracy100.0%
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓accuracy100.0%
(sqrt.f64 x)
✓accuracy81.5%
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 x x))
✓accuracy100.0%
(pow.f64 x #s(literal -1/2 binary64))
✓accuracy100.0%
(/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)
✓accuracy99.8%
(*.f64 x (*.f64 x x))
✓accuracy99.6%
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) (/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
✓accuracy99.4%
(/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))
Results
135.0ms255×0valid
1.0ms1×1valid
Compiler

Compiled 249 to 31 computations (87.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 53.0ms
ival-pow: 20.0ms (37.7% of total)
ival-div: 15.0ms (28.3% of total)
ival-mult: 7.0ms (13.2% of total)
ival-add: 4.0ms (7.5% of total)
ival-sqrt: 4.0ms (7.5% of total)
ival-sub: 3.0ms (5.7% of total)
const: 1.0ms (1.9% of total)
backward-pass: 0.0ms (0% of total)

series22.0ms (0.2%)

Counts
21 → 252
Calls
Call 1
Inputs
#<alt (pow (+ 1 x) 1/2)>
#<alt (/ (/ (- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x)))) x) (pow (+ 1 x) 1/2))>
#<alt (/ (- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x)))) x)>
#<alt (- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x))))>
#<alt (pow x -1/2)>
#<alt (/ (* 1/2 (sqrt x)) (* x x))>
#<alt (* 1/2 (sqrt x))>
#<alt (sqrt x)>
#<alt (* x x)>
#<alt (/ (/ (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) x) (pow (+ 1 x) 1/2))>
#<alt (/ (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) x)>
#<alt (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x))>
#<alt (/ (pow (+ 1 x) -1/2) (+ x (sqrt (* x (+ 1 x)))))>
#<alt (pow (+ 1 x) -1/2)>
#<alt (+ 1 x)>
#<alt (+ x (sqrt (* x (+ 1 x))))>
#<alt (/ 5/128 (* x (* x x)))>
#<alt (* x (* x x))>
#<alt (/ (- -1/8 (/ -1/16 x)) x)>
#<alt (sqrt (* x (+ 1 x)))>
#<alt (* x (+ 1 x))>
Outputs
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (/ -5/128 (pow x 4))>
#<alt (/ (- (* 21/256 x) 5/128) (pow x 4))>
#<alt (/ (- (* x (+ 21/256 (* -175/1024 x))) 5/128) (pow x 4))>
#<alt (/ (- (* x (+ 21/256 (* x (- (* 1225/2048 x) 175/1024)))) 5/128) (pow x 4))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)>
#<alt (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/16 (sqrt (/ 1 x))) (* 5/128 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (/ -5/128 (pow x 4))>
#<alt (/ (- (* 1/16 x) 5/128) (pow x 4))>
#<alt (/ (- (* x (+ 1/16 (* -1/8 x))) 5/128) (pow x 4))>
#<alt (/ (- (* x (+ 1/16 (* x (- (* 1/2 x) 1/8)))) 5/128) (pow x 4))>
#<alt (/ 1/2 x)>
#<alt (/ (- 1/2 (* 1/8 (/ 1 x))) x)>
#<alt (/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)>
#<alt (/ (- (+ 1/2 (/ 1/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3))))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 5/128 (/ 1 x)) 1/16) x)) 1/8) x)) 1/2) x))>
#<alt (/ -5/128 (pow x 3))>
#<alt (/ (- (* 1/16 x) 5/128) (pow x 3))>
#<alt (/ (- (* x (+ 1/16 (* -1/8 x))) 5/128) (pow x 3))>
#<alt (/ (- (* x (+ 1/16 (* x (- (* 1/2 x) 1/8)))) 5/128) (pow x 3))>
#<alt 1/2>
#<alt (- 1/2 (* 1/8 (/ 1 x)))>
#<alt (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x)))>
#<alt (- (+ 1/2 (/ 1/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3)))))>
#<alt 1/2>
#<alt (- 1/2 (* 1/8 (/ 1 x)))>
#<alt (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x)))>
#<alt (+ 1/2 (* -1 (/ (+ 1/8 (* -1 (/ (- 1/16 (* 5/128 (/ 1 x))) x))) x)))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ (+ 1/16 (* -5/32 x)) (pow x 3))>
#<alt (/ (+ 1/16 (* x (- (* 75/128 x) 5/32))) (pow x 3))>
#<alt (/ (+ 1/16 (* x (- (* x (+ 75/128 (* -81/256 x))) 5/32))) (pow x 3))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))) x)>
#<alt (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/4 (sqrt (/ 1 x))) (* -1/16 (sqrt (/ 1 x))))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ (+ 1/16 (* -1/8 x)) (pow x 3))>
#<alt (/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 3))>
#<alt (/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 3))>
#<alt (/ 1/2 x)>
#<alt (/ (- 1/2 (* 1/8 (/ 1 x))) x)>
#<alt (/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)>
#<alt (/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))>
#<alt (/ 1/16 (pow x 2))>
#<alt (/ (+ 1/16 (* -1/8 x)) (pow x 2))>
#<alt (/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 2))>
#<alt (/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 2))>
#<alt 1/2>
#<alt (- 1/2 (* 1/8 (/ 1 x)))>
#<alt (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x)))>
#<alt (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x)))>
#<alt 1/2>
#<alt (- 1/2 (* 1/8 (/ 1 x)))>
#<alt (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x)))>
#<alt (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x)))>
#<alt (sqrt (/ 1 x))>
#<alt (+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x))))>
#<alt (+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x))))>
#<alt (+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1))))>
#<alt (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2))))) x)) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/16 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 3)))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3)))) (- (pow (sqrt -1) 2) 1))) (* 1/16 (/ 1 (* (pow (sqrt -1) 4) (pow (- (pow (sqrt -1) 2) 1) 2))))))))) (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* 1/4 (* (sqrt x) (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))))) x)) (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3)))))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2))))) x)) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* 3/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))>
#<alt (sqrt (/ 1 x))>
#<alt (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))>
#<alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))>
#<alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (sqrt x)>
#<alt (+ x (sqrt x))>
#<alt (+ (sqrt x) (* x (+ 1 (* 1/2 (sqrt x)))))>
#<alt (+ (sqrt x) (* x (+ 1 (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* 1/2 (/ 1 x))))>
#<alt (* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))>
#<alt (* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))>
#<alt (* -1 (* x (- (pow (sqrt -1) 2) 1)))>
#<alt (* -1 (* x (- (pow (sqrt -1) 2) (+ 1 (* 1/2 (/ 1 x))))))>
#<alt (* -1 (* x (- (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2)) 1)))>
#<alt (* -1 (* x (- (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2)) 1)))>
#<alt (/ 5/128 (pow x 3))>
#<alt (/ 5/128 (pow x 3))>
#<alt (/ 5/128 (pow x 3))>
#<alt (/ 5/128 (pow x 3))>
#<alt (/ 5/128 (pow x 3))>
#<alt (/ 5/128 (pow x 3))>
#<alt (/ 5/128 (pow x 3))>
#<alt (/ 5/128 (pow x 3))>
#<alt (/ 5/128 (pow x 3))>
#<alt (/ 5/128 (pow x 3))>
#<alt (/ 5/128 (pow x 3))>
#<alt (/ 5/128 (pow x 3))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (/ 1/16 (pow x 2))>
#<alt (/ (+ 1/16 (* -1/8 x)) (pow x 2))>
#<alt (/ (+ 1/16 (* -1/8 x)) (pow x 2))>
#<alt (/ (+ 1/16 (* -1/8 x)) (pow x 2))>
#<alt (/ -1/8 x)>
#<alt (/ (- (* 1/16 (/ 1 x)) 1/8) x)>
#<alt (/ (- (* 1/16 (/ 1 x)) 1/8) x)>
#<alt (/ (- (* 1/16 (/ 1 x)) 1/8) x)>
#<alt (/ -1/8 x)>
#<alt (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))>
#<alt (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))>
#<alt (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))>
#<alt (sqrt x)>
#<alt (+ (sqrt x) (* 1/2 (sqrt (pow x 3))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))>
#<alt (* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))>
#<alt (* -1 (* x (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (- (pow (sqrt -1) 2) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))>
#<alt x>
#<alt (* x (+ 1 x))>
#<alt (* x (+ 1 x))>
#<alt (* x (+ 1 x))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
Calls

63 calls:

TimeVariablePointExpression
7.0ms
x
@-inf
(* x (+ 1 x))
3.0ms
x
@-inf
(pow (+ 1 x) 1/2)
2.0ms
x
@-inf
(/ (/ (- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x)))) x) (pow (+ 1 x) 1/2))
0.0ms
x
@inf
(pow (+ 1 x) 1/2)
0.0ms
x
@0
(/ (/ (- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x)))) x) (pow (+ 1 x) 1/2))

rewrite378.0ms (3.5%)

Algorithm
1×batch-egg-rewrite
Rules
4422×/-lowering-/.f32
4422×/-lowering-/.f64
3340×*-lowering-*.f32
3340×*-lowering-*.f64
1634×pow-lowering-pow.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
030168
1207157
21929157
08838157
Stop Event
1×iter limit
1×node limit
Counts
21 → 833
Calls
Call 1
Inputs
(pow (+ 1 x) 1/2)
(/ (/ (- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x)))) x) (pow (+ 1 x) 1/2))
(/ (- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x)))) x)
(- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x))))
(pow x -1/2)
(/ (* 1/2 (sqrt x)) (* x x))
(* 1/2 (sqrt x))
(sqrt x)
(* x x)
(/ (/ (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) x) (pow (+ 1 x) 1/2))
(/ (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) x)
(+ 1/2 (/ (- -1/8 (/ -1/16 x)) x))
(/ (pow (+ 1 x) -1/2) (+ x (sqrt (* x (+ 1 x)))))
(pow (+ 1 x) -1/2)
(+ 1 x)
(+ x (sqrt (* x (+ 1 x))))
(/ 5/128 (* x (* x x)))
(* x (* x x))
(/ (- -1/8 (/ -1/16 x)) x)
(sqrt (* x (+ 1 x)))
(* x (+ 1 x))
Outputs
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (*.f64 (log1p.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (*.f64 (log1p.f64 x) #s(literal 1/4 binary64)) (*.f64 (log1p.f64 x) #s(literal 1/4 binary64))))
(exp.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) (log1p.f64 x))))
(exp.f64 (neg.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x)))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(/.f64 (sqrt.f64 (+.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 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64)))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (neg.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) #s(literal -2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log1p.f64 x))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64)))))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (/.f64 (/.f64 #s(literal 5/128 binary64) x) x)) x)) x))) #s(literal -1 binary64)))
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (*.f64 x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) (/.f64 (/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x))) (*.f64 x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (*.f64 x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) (/.f64 (/.f64 (/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (*.f64 x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) (/.f64 (/.f64 (/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x))) x) (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))
(-.f64 (/.f64 (/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))) (+.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))) (*.f64 (/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))))))) (*.f64 x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) (/.f64 (/.f64 (/.f64 (/.f64 #s(literal 125/2097152 binary64) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (+.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))) (*.f64 (/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))))))) (*.f64 x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) (/.f64 (/.f64 (/.f64 #s(literal 25/16384 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
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(/.f64 (neg.f64 (*.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (*.f64 (+.f64 #s(literal -1/512 binary64) (/.f64 #s(literal 1/4096 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1 binary64))) (neg.f64 (*.f64 (+.f64 #s(literal 1/64 binary64) (*.f64 (/.f64 #s(literal -1/16 binary64) x) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))) x)))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (*.f64 x x))) #s(literal 1 binary64))) (neg.f64 (*.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)))
(/.f64 (neg.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x))))
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(/.f64 (neg.f64 (*.f64 (+.f64 #s(literal -1/512 binary64) (/.f64 #s(literal 1/4096 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) x))) (neg.f64 (+.f64 #s(literal 1/64 binary64) (*.f64 (/.f64 #s(literal -1/16 binary64) x) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))))))
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(pow.f64 (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 x (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(*.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal 1 binary64))
(*.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))
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(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 x (+.f64 #s(literal -1/512 binary64) (/.f64 #s(literal 1/4096 binary64) (*.f64 x (*.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (*.f64 (/.f64 #s(literal -1/16 binary64) x) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))))))
(*.f64 (pow.f64 (/.f64 x (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (*.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))))
(*.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (+.f64 #s(literal -1/512 binary64) (/.f64 #s(literal 1/4096 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (*.f64 (/.f64 #s(literal -1/16 binary64) x) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))))) x))
(*.f64 (/.f64 (+.f64 #s(literal -1/512 binary64) (/.f64 #s(literal 1/4096 binary64) (*.f64 x (*.f64 x x)))) x) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (*.f64 (/.f64 #s(literal -1/16 binary64) x) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))))) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (*.f64 x x))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) x))
(*.f64 (/.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (*.f64 x x))) x) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) #s(literal 1 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(exp.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x)) (*.f64 (log.f64 x) #s(literal 1/2 binary64))))
(exp.f64 (+.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (log1p.f64 x))))
(fabs.f64 (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))
(/.f64 (sqrt.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x (*.f64 x x))))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (sqrt.f64 (-.f64 x (*.f64 x x))))
(/.f64 (sqrt.f64 (*.f64 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 (sqrt.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(pow.f64 (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) (*.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 #s(literal 1 binary64) x)))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) x)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 #s(literal 1 binary64) x))))))
(*.f64 (sqrt.f64 (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (sqrt.f64 (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) x))) (sqrt.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(+.f64 x (*.f64 x x))
(+.f64 (*.f64 x x) x)
(exp.f64 (log.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))
(exp.f64 (*.f64 (log.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) (*.f64 x (+.f64 #s(literal 1 binary64) x)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64)))
(fabs.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (*.f64 x x))) (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 x (*.f64 x x))))
(sqrt.f64 (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) (*.f64 x (+.f64 #s(literal 1 binary64) x))))
(fma.f64 #s(literal 1 binary64) x (*.f64 x x))
(fma.f64 x #s(literal 1 binary64) (*.f64 x x))
(fma.f64 x x x)
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (+.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x (*.f64 x x)))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 x (*.f64 x x)))
(/.f64 (*.f64 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 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))) x) (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) x) (-.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))))) (neg.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x (*.f64 x x))))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (neg.f64 (-.f64 x (*.f64 x x))))
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(/.f64 (neg.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (neg.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) x)) (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64))))))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (neg.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (+.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 (*.f64 x x) (*.f64 x (*.f64 x x)))))
(pow.f64 (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(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)) (*.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(*.f64 (+.f64 #s(literal 1 binary64) x) x)
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) #s(literal 2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) x)) #s(literal 1 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))

simplify308.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
3838×*-lowering-*.f32
3838×*-lowering-*.f64
2426×+-lowering-+.f64
2426×+-lowering-+.f32
1676×sum5-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04692684
114862058
257842038
090052038
Stop Event
1×iter limit
1×node limit
Counts
252 → 252
Calls
Call 1
Inputs
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(/ -5/128 (pow x 4))
(/ (- (* 21/256 x) 5/128) (pow x 4))
(/ (- (* x (+ 21/256 (* -175/1024 x))) 5/128) (pow x 4))
(/ (- (* x (+ 21/256 (* x (- (* 1225/2048 x) 175/1024)))) 5/128) (pow x 4))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/16 (sqrt (/ 1 x))) (* 5/128 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/ -5/128 (pow x 4))
(/ (- (* 1/16 x) 5/128) (pow x 4))
(/ (- (* x (+ 1/16 (* -1/8 x))) 5/128) (pow x 4))
(/ (- (* x (+ 1/16 (* x (- (* 1/2 x) 1/8)))) 5/128) (pow x 4))
(/ 1/2 x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3))))) x)
(/ 1/2 x)
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 5/128 (/ 1 x)) 1/16) x)) 1/8) x)) 1/2) x))
(/ -5/128 (pow x 3))
(/ (- (* 1/16 x) 5/128) (pow x 3))
(/ (- (* x (+ 1/16 (* -1/8 x))) 5/128) (pow x 3))
(/ (- (* x (+ 1/16 (* x (- (* 1/2 x) 1/8)))) 5/128) (pow x 3))
1/2
(- 1/2 (* 1/8 (/ 1 x)))
(- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x)))
(- (+ 1/2 (/ 1/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3)))))
1/2
(- 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x)))
(+ 1/2 (* -1 (/ (+ 1/8 (* -1 (/ (- 1/16 (* 5/128 (/ 1 x))) x))) x)))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ 1/16 (pow x 3))
(/ (+ 1/16 (* -5/32 x)) (pow x 3))
(/ (+ 1/16 (* x (- (* 75/128 x) 5/32))) (pow x 3))
(/ (+ 1/16 (* x (- (* x (+ 75/128 (* -81/256 x))) 5/32))) (pow x 3))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))) x)
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/4 (sqrt (/ 1 x))) (* -1/16 (sqrt (/ 1 x))))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/ 1/16 (pow x 3))
(/ (+ 1/16 (* -1/8 x)) (pow x 3))
(/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 3))
(/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 3))
(/ 1/2 x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)
(/ 1/2 x)
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))
(* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))
(/ 1/16 (pow x 2))
(/ (+ 1/16 (* -1/8 x)) (pow x 2))
(/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 2))
(/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 2))
1/2
(- 1/2 (* 1/8 (/ 1 x)))
(- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x)))
(- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x)))
1/2
(- 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x)))
(+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x)))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)
(* -1 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1))))
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2))))) x)) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/16 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 3)))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3)))) (- (pow (sqrt -1) 2) 1))) (* 1/16 (/ 1 (* (pow (sqrt -1) 4) (pow (- (pow (sqrt -1) 2) 1) 2))))))))) (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* 1/4 (* (sqrt x) (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))))) x)) (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3)))))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2))))) x)) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(sqrt x)
(+ x (sqrt x))
(+ (sqrt x) (* x (+ 1 (* 1/2 (sqrt x)))))
(+ (sqrt x) (* x (+ 1 (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))))
(* 2 x)
(* x (+ 2 (* 1/2 (/ 1 x))))
(* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(* -1 (* x (- (pow (sqrt -1) 2) 1)))
(* -1 (* x (- (pow (sqrt -1) 2) (+ 1 (* 1/2 (/ 1 x))))))
(* -1 (* x (- (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2)) 1)))
(* -1 (* x (- (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2)) 1)))
(/ 5/128 (pow x 3))
(/ 5/128 (pow x 3))
(/ 5/128 (pow x 3))
(/ 5/128 (pow x 3))
(/ 5/128 (pow x 3))
(/ 5/128 (pow x 3))
(/ 5/128 (pow x 3))
(/ 5/128 (pow x 3))
(/ 5/128 (pow x 3))
(/ 5/128 (pow x 3))
(/ 5/128 (pow x 3))
(/ 5/128 (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)
(pow x 3)
(/ 1/16 (pow x 2))
(/ (+ 1/16 (* -1/8 x)) (pow x 2))
(/ (+ 1/16 (* -1/8 x)) (pow x 2))
(/ (+ 1/16 (* -1/8 x)) (pow x 2))
(/ -1/8 x)
(/ (- (* 1/16 (/ 1 x)) 1/8) x)
(/ (- (* 1/16 (/ 1 x)) 1/8) x)
(/ (- (* 1/16 (/ 1 x)) 1/8) x)
(/ -1/8 x)
(* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))
(* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))
(* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))
(sqrt x)
(+ (sqrt x) (* 1/2 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (- (pow (sqrt -1) 2) (* 1/2 (/ 1 x)))))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
x
(* x (+ 1 x))
(* x (+ 1 x))
(* x (+ 1 x))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
Outputs
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(-.f64 #s(literal 0 binary64) (*.f64 x (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (+.f64 (+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (/.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (neg.f64 x))
(/ -5/128 (pow x 4))
(/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 4 binary64)))
(/ (- (* 21/256 x) 5/128) (pow x 4))
(/.f64 (+.f64 #s(literal -5/128 binary64) (*.f64 x #s(literal 21/256 binary64))) (pow.f64 x #s(literal 4 binary64)))
(/ (- (* x (+ 21/256 (* -175/1024 x))) 5/128) (pow x 4))
(/.f64 (+.f64 #s(literal -5/128 binary64) (*.f64 x (+.f64 #s(literal 21/256 binary64) (*.f64 x #s(literal -175/1024 binary64))))) (pow.f64 x #s(literal 4 binary64)))
(/ (- (* x (+ 21/256 (* x (- (* 1225/2048 x) 175/1024)))) 5/128) (pow x 4))
(/.f64 (+.f64 #s(literal -5/128 binary64) (*.f64 x (+.f64 #s(literal 21/256 binary64) (*.f64 x (+.f64 #s(literal -175/1024 binary64) (*.f64 x #s(literal 1225/2048 binary64))))))) (pow.f64 x #s(literal 4 binary64)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/.f64 (+.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -3/8 binary64))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)
(/.f64 (+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -3/8 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal -5/128 binary64))) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 3/8 binary64)))) x)
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -1/2 binary64))
(* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64)) (+.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -1/16 binary64)))) x)) (neg.f64 x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/16 (sqrt (/ 1 x))) (* 5/128 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (-.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (+.f64 (/.f64 (sqrt.f64 x) #s(literal 4 binary64)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (+.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -5/128 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -5/16 binary64)))) x)) x)) (neg.f64 x))
(/ -5/128 (pow x 4))
(/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 4 binary64)))
(/ (- (* 1/16 x) 5/128) (pow x 4))
(/.f64 (+.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -5/128 binary64)) (pow.f64 x #s(literal 4 binary64)))
(/ (- (* x (+ 1/16 (* -1/8 x))) 5/128) (pow x 4))
(/.f64 (+.f64 #s(literal -5/128 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal -1/8 binary64)) #s(literal 1/16 binary64)))) (pow.f64 x #s(literal 4 binary64)))
(/ (- (* x (+ 1/16 (* x (- (* 1/2 x) 1/8)))) 5/128) (pow x 4))
(/.f64 (+.f64 #s(literal -5/128 binary64) (*.f64 x (+.f64 #s(literal 1/16 binary64) (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal -1/8 binary64)))))) (pow.f64 x #s(literal 4 binary64)))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3))))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -5/128 binary64) x)) x)) x)) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
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(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))
(/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2))))) x)) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))
(/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (-.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (/.f64 (sqrt.f64 x) #s(literal 4 binary64)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)) x)) (neg.f64 x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/16 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 3)))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3)))) (- (pow (sqrt -1) 2) 1))) (* 1/16 (/ 1 (* (pow (sqrt -1) 4) (pow (- (pow (sqrt -1) 2) 1) 2))))))))) (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* 1/4 (* (sqrt x) (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))))) x)) (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3)))))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2))))) x)) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))
(/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (-.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 x) #s(literal 4 binary64)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (/.f64 (-.f64 (+.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x)) (/.f64 (sqrt.f64 x) #s(literal 4 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -3/128 binary64) (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/64 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))))) x)) x)) x)) (neg.f64 x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 3/8 binary64)))))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 #s(literal 3/8 binary64) (*.f64 x #s(literal -5/16 binary64)))))))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))
(+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -1/2 binary64)))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))
(+.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -1/2 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64)))))) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(-.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (-.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(-.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (/.f64 (sqrt.f64 x) #s(literal -2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/4 binary64) (/.f64 x #s(literal -1 binary64))))))) (*.f64 x (*.f64 x x))))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(sqrt x)
(sqrt.f64 x)
(+ x (sqrt x))
(+.f64 x (sqrt.f64 x))
(+ (sqrt x) (* x (+ 1 (* 1/2 (sqrt x)))))
(+.f64 (sqrt.f64 x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))))
(+ (sqrt x) (* x (+ 1 (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))))
(+.f64 (sqrt.f64 x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))
(* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))
(* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(*.f64 x (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) x)))
(* -1 (* x (- (pow (sqrt -1) 2) 1)))
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (pow (sqrt -1) 2) (+ 1 (* 1/2 (/ 1 x))))))
(*.f64 (*.f64 #s(literal -1 binary64) (+.f64 #s(literal -2 binary64) (/.f64 #s(literal -1/2 binary64) x))) x)
(* -1 (* x (- (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2)) 1)))
(*.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))) (neg.f64 x))
(* -1 (* x (- (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2)) 1)))
(*.f64 (+.f64 #s(literal -2 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) x) x))) (neg.f64 x))) (neg.f64 x))
(/ 5/128 (pow x 3))
(/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))
(/ 5/128 (pow x 3))
(/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))
(/ 5/128 (pow x 3))
(/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))
(/ 5/128 (pow x 3))
(/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))
(/ 5/128 (pow x 3))
(/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))
(/ 5/128 (pow x 3))
(/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))
(/ 5/128 (pow x 3))
(/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))
(/ 5/128 (pow x 3))
(/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))
(/ 5/128 (pow x 3))
(/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))
(/ 5/128 (pow x 3))
(/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))
(/ 5/128 (pow x 3))
(/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))
(/ 5/128 (pow x 3))
(/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(/ (+ 1/16 (* -1/8 x)) (pow x 2))
(/.f64 (+.f64 (*.f64 x #s(literal -1/8 binary64)) #s(literal 1/16 binary64)) (*.f64 x x))
(/ (+ 1/16 (* -1/8 x)) (pow x 2))
(/.f64 (+.f64 (*.f64 x #s(literal -1/8 binary64)) #s(literal 1/16 binary64)) (*.f64 x x))
(/ (+ 1/16 (* -1/8 x)) (pow x 2))
(/.f64 (+.f64 (*.f64 x #s(literal -1/8 binary64)) #s(literal 1/16 binary64)) (*.f64 x x))
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ (- (* 1/16 (/ 1 x)) 1/8) x)
(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ (- (* 1/16 (/ 1 x)) 1/8) x)
(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ (- (* 1/16 (/ 1 x)) 1/8) x)
(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (sqrt (pow x 3))))
(+.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 x (*.f64 x x)))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))
(+.f64 (sqrt.f64 x) (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))
(+.f64 (sqrt.f64 x) (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 x (*.f64 x (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) x)
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) x)))
(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (- (pow (sqrt -1) 2) (* 1/2 (/ 1 x)))))
(*.f64 (*.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x))) x)
(* -1 (* x (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)) (neg.f64 x))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) x) x))) x)) (neg.f64 x))
x
(* x (+ 1 x))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(* x (+ 1 x))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(* x (+ 1 x))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) x))

eval172.0ms (1.6%)

Compiler

Compiled 41708 to 3814 computations (90.9% saved)

prune215.0ms (2%)

Pruning

21 alts after pruning (19 fresh and 2 done)

PrunedKeptTotal
New1389161405
Fresh11314
Picked415
Done112
Total1405211426
Accuracy
100.0%
Counts
1426 → 21
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.5%
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (+.f64 #s(literal 1/2 binary64) x)))
98.9%
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))))
81.6%
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) x))))
97.3%
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x x))
▶99.0%
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (*.f64 x (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) x))))
98.9%
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))))
38.5%
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) x) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
98.9%
(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -5/128 binary64) x)) x)) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
35.9%
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
98.8%
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
8.0%
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) #s(literal 1 binary64))
98.8%
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) x)
▶98.4%
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
97.2%
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
97.8%
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (/.f64 (/.f64 #s(literal 5/128 binary64) x) x)) x)) (*.f64 x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
✓78.9%
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 x x))
▶34.7%
(/.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x x)))
✓37.0%
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
▶97.1%
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1/2 binary64) x))
97.4%
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
▶98.7%
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
Compiler

Compiled 643 to 457 computations (28.9% saved)

simplify230.0ms (2.1%)

Algorithm
1×egg-herbie
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
✓cost-diff64
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
✓cost-diff128
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
✓cost-diff0
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
✓cost-diff0
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
✓cost-diff64
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
✓cost-diff0
(/.f64 #s(literal 1/2 binary64) x)
✓cost-diff0
(pow.f64 x #s(literal -1/2 binary64))
✓cost-diff0
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1/2 binary64) x))
✓cost-diff0
(*.f64 x x)
✓cost-diff0
(*.f64 x (*.f64 x x))
✓cost-diff0
(/.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x x)))
✓cost-diff0
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
✓cost-diff0
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (*.f64 x (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) x))))
✓cost-diff128
(+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) x))
✓cost-diff128
(*.f64 x (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) x)))
Rules
2944×*-lowering-*.f32
2944×*-lowering-*.f64
2560×/-lowering-/.f32
2560×/-lowering-/.f64
1914×fma-define
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
032223
169223
2131221
3260215
4494215
5884215
62571215
76870215
87431215
97507215
107567215
117600215
127633215
08554215
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ (pow (+ 1 x) -1/2) (* x (+ (+ 2 (/ 1/2 x)) (/ (/ (+ -1/8 (/ 1/16 x)) x) x))))
(pow (+ 1 x) -1/2)
(+ 1 x)
1
x
-1/2
(* x (+ (+ 2 (/ 1/2 x)) (/ (/ (+ -1/8 (/ 1/16 x)) x) x)))
(+ (+ 2 (/ 1/2 x)) (/ (/ (+ -1/8 (/ 1/16 x)) x) x))
(+ 2 (/ 1/2 x))
2
(/ 1/2 x)
1/2
(/ (/ (+ -1/8 (/ 1/16 x)) x) x)
(/ (+ -1/8 (/ 1/16 x)) x)
(+ -1/8 (/ 1/16 x))
-1/8
(/ 1/16 x)
1/16
(/ 1/16 (* x (* x x)))
1/16
(* x (* x x))
x
(* x x)
(* (pow x -1/2) (/ 1/2 x))
(pow x -1/2)
x
-1/2
(/ 1/2 x)
1/2
(/ (/ (+ 1/2 (/ -1/8 x)) x) (pow (+ 1 x) 1/2))
(/ (+ 1/2 (/ -1/8 x)) x)
(+ 1/2 (/ -1/8 x))
1/2
(/ -1/8 x)
-1/8
x
(pow (+ 1 x) 1/2)
(+ 1 x)
1
(* (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) (/ (/ 1 x) (pow (+ 1 x) 1/2)))
(+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x))
1/2
(/ (+ -1/8 (/ 1/16 x)) x)
(+ -1/8 (/ 1/16 x))
-1/8
(/ 1/16 x)
1/16
x
(/ (/ 1 x) (pow (+ 1 x) 1/2))
(/ 1 x)
1
(pow (+ 1 x) 1/2)
(+ 1 x)
Outputs
(/ (pow (+ 1 x) -1/2) (* x (+ (+ 2 (/ 1/2 x)) (/ (/ (+ -1/8 (/ 1/16 x)) x) x))))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (+.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(pow (+ 1 x) -1/2)
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
-1/2
#s(literal -1/2 binary64)
(* x (+ (+ 2 (/ 1/2 x)) (/ (/ (+ -1/8 (/ 1/16 x)) x) x)))
(+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (+.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(+ (+ 2 (/ 1/2 x)) (/ (/ (+ -1/8 (/ 1/16 x)) x) x))
(+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal 1/2 binary64)) x))
(+ 2 (/ 1/2 x))
(+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))
2
#s(literal 2 binary64)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
1/2
#s(literal 1/2 binary64)
(/ (/ (+ -1/8 (/ 1/16 x)) x) x)
(/.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) x)
(/ (+ -1/8 (/ 1/16 x)) x)
(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(+ -1/8 (/ 1/16 x))
(+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
-1/8
#s(literal -1/8 binary64)
(/ 1/16 x)
(/.f64 #s(literal 1/16 binary64) x)
1/16
#s(literal 1/16 binary64)
(/ 1/16 (* x (* x x)))
(/.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x x)))
1/16
#s(literal 1/16 binary64)
(* x (* x x))
(*.f64 x (*.f64 x x))
x
(* x x)
(*.f64 x x)
(* (pow x -1/2) (/ 1/2 x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 x #s(literal -1/2 binary64)))
(pow x -1/2)
(pow.f64 x #s(literal -1/2 binary64))
x
-1/2
#s(literal -1/2 binary64)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
1/2
#s(literal 1/2 binary64)
(/ (/ (+ 1/2 (/ -1/8 x)) x) (pow (+ 1 x) 1/2))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/ (+ 1/2 (/ -1/8 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(+ 1/2 (/ -1/8 x))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
1/2
#s(literal 1/2 binary64)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
-1/8
#s(literal -1/8 binary64)
x
(pow (+ 1 x) 1/2)
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
(* (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) (/ (/ 1 x) (pow (+ 1 x) 1/2)))
(/.f64 (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal 1/2 binary64)) (*.f64 x (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x))
(+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(/ (+ -1/8 (/ 1/16 x)) x)
(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(+ -1/8 (/ 1/16 x))
(+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
-1/8
#s(literal -1/8 binary64)
(/ 1/16 x)
(/.f64 #s(literal 1/16 binary64) x)
1/16
#s(literal 1/16 binary64)
x
(/ (/ 1 x) (pow (+ 1 x) 1/2))
(/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
(pow (+ 1 x) 1/2)
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)

localize232.0ms (2.2%)

Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
✓accuracy100.0%
(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
✓accuracy100.0%
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
✓accuracy99.6%
(/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
✓accuracy100.0%
(+.f64 #s(literal 1 binary64) x)
✓accuracy100.0%
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
✓accuracy100.0%
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
✓accuracy99.6%
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
✓accuracy100.0%
(pow.f64 x #s(literal -1/2 binary64))
✓accuracy100.0%
(/.f64 #s(literal 1/2 binary64) x)
✓accuracy99.7%
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1/2 binary64) x))
✓accuracy100.0%
(*.f64 x x)
✓accuracy99.8%
(*.f64 x (*.f64 x x))
✓accuracy99.5%
(/.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x x)))
✓accuracy100.0%
(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
✓accuracy100.0%
(*.f64 x (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) x)))
✓accuracy99.8%
(/.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) x)
✓accuracy99.7%
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (*.f64 x (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) x))))
Results
176.0ms255×0valid
1.0ms1×1valid
Compiler

Compiled 245 to 33 computations (86.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 75.0ms
ival-div: 41.0ms (55% of total)
ival-pow: 16.0ms (21.4% of total)
ival-mult: 9.0ms (12.1% of total)
ival-add: 8.0ms (10.7% of total)
const: 1.0ms (1.3% of total)
backward-pass: 0.0ms (0% of total)

series10.0ms (0.1%)

Counts
21 → 252
Calls
Call 1
Inputs
#<alt (* x (+ (+ 2 (/ 1/2 x)) (/ (/ (+ -1/8 (/ 1/16 x)) x) x)))>
#<alt (+ (+ 2 (/ 1/2 x)) (/ (/ (+ -1/8 (/ 1/16 x)) x) x))>
#<alt (/ (pow (+ 1 x) -1/2) (* x (+ (+ 2 (/ 1/2 x)) (/ (/ (+ -1/8 (/ 1/16 x)) x) x))))>
#<alt (pow (+ 1 x) -1/2)>
#<alt (/ 1/16 (* x (* x x)))>
#<alt (* x (* x x))>
#<alt (* x x)>
#<alt (* (pow x -1/2) (/ 1/2 x))>
#<alt (pow x -1/2)>
#<alt (/ 1/2 x)>
#<alt (pow (+ 1 x) 1/2)>
#<alt (/ (/ (+ 1/2 (/ -1/8 x)) x) (pow (+ 1 x) 1/2))>
#<alt (/ (+ 1/2 (/ -1/8 x)) x)>
#<alt (+ 1/2 (/ -1/8 x))>
#<alt (* (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) (/ (/ 1 x) (pow (+ 1 x) 1/2)))>
#<alt (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x))>
#<alt (/ (+ -1/8 (/ 1/16 x)) x)>
#<alt (/ (/ (+ -1/8 (/ 1/16 x)) x) x)>
#<alt (+ 1 x)>
#<alt (/ (/ 1 x) (pow (+ 1 x) 1/2))>
#<alt (+ -1/8 (/ 1/16 x))>
Outputs
#<alt (/ 1/16 (pow x 2))>
#<alt (/ (+ 1/16 (* -1/8 x)) (pow x 2))>
#<alt (/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 2))>
#<alt (/ (+ 1/16 (* x (- (* x (+ 1/2 (* 2 x))) 1/8))) (pow x 2))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* 1/2 (/ 1 x))))>
#<alt (* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))>
#<alt (* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* x (- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) x)) 2)))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ (+ 1/16 (* -1/8 x)) (pow x 3))>
#<alt (/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 3))>
#<alt (/ (+ 1/16 (* x (- (* x (+ 1/2 (* 2 x))) 1/8))) (pow x 3))>
#<alt 2>
#<alt (+ 2 (* 1/2 (/ 1 x)))>
#<alt (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))>
#<alt (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))>
#<alt 2>
#<alt (+ 2 (* 1/2 (/ 1 x)))>
#<alt (+ 2 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x)))>
#<alt (+ 2 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x)))>
#<alt (* 16 (pow x 2))>
#<alt (* (pow x 2) (+ 16 (* 24 x)))>
#<alt (* (pow x 2) (+ 16 (* x (+ 24 (* -74 x)))))>
#<alt (* (pow x 2) (+ 16 (* x (+ 24 (* x (- (* -857 x) 74))))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)>
#<alt (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/16 (sqrt (/ 1 x))) (* 5/128 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* 3/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))>
#<alt (sqrt (/ 1 x))>
#<alt (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))>
#<alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))>
#<alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ 1/16 (pow x 3))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<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>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ (- (* 9/16 x) 1/8) (pow x 2))>
#<alt (/ (- (* x (+ 9/16 (* -19/64 x))) 1/8) (pow x 2))>
#<alt (/ (- (* x (+ 9/16 (* x (- (* 29/128 x) 19/64)))) 1/8) (pow x 2))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))) x)>
#<alt (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/16 (sqrt (/ 1 x))) (* 1/4 (sqrt x)))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ (- (* 1/2 x) 1/8) (pow x 2))>
#<alt (/ (- (* 1/2 x) 1/8) (pow x 2))>
#<alt (/ (- (* 1/2 x) 1/8) (pow x 2))>
#<alt (/ 1/2 x)>
#<alt (/ (- 1/2 (* 1/8 (/ 1 x))) x)>
#<alt (/ (- 1/2 (* 1/8 (/ 1 x))) x)>
#<alt (/ (- 1/2 (* 1/8 (/ 1 x))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))>
#<alt (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))>
#<alt (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))>
#<alt (/ -1/8 x)>
#<alt (/ (- (* 1/2 x) 1/8) x)>
#<alt (/ (- (* 1/2 x) 1/8) x)>
#<alt (/ (- (* 1/2 x) 1/8) x)>
#<alt 1/2>
#<alt (- 1/2 (* 1/8 (/ 1 x)))>
#<alt (- 1/2 (* 1/8 (/ 1 x)))>
#<alt (- 1/2 (* 1/8 (/ 1 x)))>
#<alt 1/2>
#<alt (- 1/2 (* 1/8 (/ 1 x)))>
#<alt (- 1/2 (* 1/8 (/ 1 x)))>
#<alt (- 1/2 (* 1/8 (/ 1 x)))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ (+ 1/16 (* -5/32 x)) (pow x 3))>
#<alt (/ (+ 1/16 (* x (- (* 75/128 x) 5/32))) (pow x 3))>
#<alt (/ (+ 1/16 (* x (- (* x (+ 75/128 (* -81/256 x))) 5/32))) (pow x 3))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))) x)>
#<alt (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/4 (sqrt (/ 1 x))) (* -1/16 (sqrt (/ 1 x))))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (/ 1/16 (pow x 2))>
#<alt (/ (+ 1/16 (* -1/8 x)) (pow x 2))>
#<alt (/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 2))>
#<alt (/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 2))>
#<alt 1/2>
#<alt (- 1/2 (* 1/8 (/ 1 x)))>
#<alt (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x)))>
#<alt (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x)))>
#<alt 1/2>
#<alt (- 1/2 (* 1/8 (/ 1 x)))>
#<alt (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x)))>
#<alt (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x)))>
#<alt (/ 1/16 (pow x 2))>
#<alt (/ (+ 1/16 (* -1/8 x)) (pow x 2))>
#<alt (/ (+ 1/16 (* -1/8 x)) (pow x 2))>
#<alt (/ (+ 1/16 (* -1/8 x)) (pow x 2))>
#<alt (/ -1/8 x)>
#<alt (/ (- (* 1/16 (/ 1 x)) 1/8) x)>
#<alt (/ (- (* 1/16 (/ 1 x)) 1/8) x)>
#<alt (/ (- (* 1/16 (/ 1 x)) 1/8) x)>
#<alt (/ -1/8 x)>
#<alt (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))>
#<alt (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))>
#<alt (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ (+ 1/16 (* -1/8 x)) (pow x 3))>
#<alt (/ (+ 1/16 (* -1/8 x)) (pow x 3))>
#<alt (/ (+ 1/16 (* -1/8 x)) (pow x 3))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ (- (* 1/16 (/ 1 x)) 1/8) (pow x 2))>
#<alt (/ (- (* 1/16 (/ 1 x)) 1/8) (pow x 2))>
#<alt (/ (- (* 1/16 (/ 1 x)) 1/8) (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ (- (* 1/16 (/ 1 x)) 1/8) (pow x 2))>
#<alt (/ (- (* 1/16 (/ 1 x)) 1/8) (pow x 2))>
#<alt (/ (- (* 1/16 (/ 1 x)) 1/8) (pow x 2))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* -1/2 x)) x)>
#<alt (/ (+ 1 (* x (- (* 3/8 x) 1/2))) x)>
#<alt (/ (+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2))) x)>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (/ (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))) x)>
#<alt (/ (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))) x)>
#<alt (/ (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))) x)>
#<alt (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))>
#<alt (* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (sqrt (/ 1 (pow x 3))))) x))>
#<alt (* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) x))>
#<alt (* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* 1/2 (sqrt x))) (pow x 3))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) x))>
#<alt (/ 1/16 x)>
#<alt (/ (+ 1/16 (* -1/8 x)) x)>
#<alt (/ (+ 1/16 (* -1/8 x)) x)>
#<alt (/ (+ 1/16 (* -1/8 x)) x)>
#<alt -1/8>
#<alt (- (* 1/16 (/ 1 x)) 1/8)>
#<alt (- (* 1/16 (/ 1 x)) 1/8)>
#<alt (- (* 1/16 (/ 1 x)) 1/8)>
#<alt -1/8>
#<alt (- (* 1/16 (/ 1 x)) 1/8)>
#<alt (- (* 1/16 (/ 1 x)) 1/8)>
#<alt (- (* 1/16 (/ 1 x)) 1/8)>
Calls

63 calls:

TimeVariablePointExpression
0.0ms
x
@-inf
(/ (/ 1 x) (pow (+ 1 x) 1/2))
0.0ms
x
@-inf
(/ (+ 1/2 (/ -1/8 x)) x)
0.0ms
x
@-inf
(/ (/ (+ 1/2 (/ -1/8 x)) x) (pow (+ 1 x) 1/2))
0.0ms
x
@-inf
(* (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) (/ (/ 1 x) (pow (+ 1 x) 1/2)))
0.0ms
x
@inf
(/ (/ (+ 1/2 (/ -1/8 x)) x) (pow (+ 1 x) 1/2))

rewrite425.0ms (3.9%)

Algorithm
1×batch-egg-rewrite
Rules
4540×/-lowering-/.f32
4540×/-lowering-/.f64
3186×*-lowering-*.f32
3186×*-lowering-*.f64
1332×neg-lowering-neg.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
032161
1225157
22204153
08170153
Stop Event
1×iter limit
1×node limit
Counts
21 → 904
Calls
Call 1
Inputs
(* x (+ (+ 2 (/ 1/2 x)) (/ (/ (+ -1/8 (/ 1/16 x)) x) x)))
(+ (+ 2 (/ 1/2 x)) (/ (/ (+ -1/8 (/ 1/16 x)) x) x))
(/ (pow (+ 1 x) -1/2) (* x (+ (+ 2 (/ 1/2 x)) (/ (/ (+ -1/8 (/ 1/16 x)) x) x))))
(pow (+ 1 x) -1/2)
(/ 1/16 (* x (* x x)))
(* x (* x x))
(* x x)
(* (pow x -1/2) (/ 1/2 x))
(pow x -1/2)
(/ 1/2 x)
(pow (+ 1 x) 1/2)
(/ (/ (+ 1/2 (/ -1/8 x)) x) (pow (+ 1 x) 1/2))
(/ (+ 1/2 (/ -1/8 x)) x)
(+ 1/2 (/ -1/8 x))
(* (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) (/ (/ 1 x) (pow (+ 1 x) 1/2)))
(+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x))
(/ (+ -1/8 (/ 1/16 x)) x)
(/ (/ (+ -1/8 (/ 1/16 x)) x) x)
(+ 1 x)
(/ (/ 1 x) (pow (+ 1 x) 1/2))
(+ -1/8 (/ 1/16 x))
Outputs
(+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(+.f64 (/.f64 x #s(literal 1/2 binary64)) (*.f64 x (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)))
(+.f64 (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(+.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x) x))
(-.f64 (/.f64 (*.f64 (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)))) (-.f64 (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))) (/.f64 (*.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (-.f64 (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))))
(fma.f64 x #s(literal 2 binary64) (*.f64 x (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)))
(fma.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(fma.f64 x (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (*.f64 x x)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(fma.f64 #s(literal 2 binary64) x (*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x) x))
(fma.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)) x (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(fma.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(fma.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (*.f64 x x)) x (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(fma.f64 (*.f64 x (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (/.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(/.f64 (+.f64 (*.f64 (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (*.f64 (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))))) (/.f64 (*.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (*.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)))) (-.f64 (*.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (*.f64 (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))))
(/.f64 (-.f64 (*.f64 (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)))) (*.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))) (-.f64 (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
(/.f64 (*.f64 x (+.f64 (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)))) (/.f64 (/.f64 (*.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (*.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (/.f64 (-.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (*.f64 x x)) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (/.f64 x (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))))
(/.f64 (*.f64 x (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)) (+.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)))) (+.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)))
(/.f64 (*.f64 (+.f64 (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)))) (/.f64 (/.f64 (*.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (*.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))) (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x x)))) x) (+.f64 (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (/.f64 (-.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (*.f64 x x)) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (/.f64 x (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))))
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 (+.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 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64))))))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (+.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))
(/.f64 (exp.f64 (log1p.f64 (*.f64 x (*.f64 x x)))) (exp.f64 (log1p.f64 (*.f64 x (-.f64 x #s(literal 1 binary64))))))
(/.f64 (exp.f64 (log1p.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) x))) (exp.f64 (log.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))) (neg.f64 (-.f64 x #s(literal 1 binary64))))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x 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 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(exp.f64 (*.f64 (log.f64 (*.f64 x (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))) #s(literal -1 binary64)))
(exp.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (log1p.f64 x)) (*.f64 (log.f64 x) #s(literal -1 binary64))))
(exp.f64 (+.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x))) (*.f64 (log.f64 x) #s(literal -1 binary64))))
(exp.f64 (+.f64 (*.f64 (log.f64 x) #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) (log1p.f64 x))))
(exp.f64 (+.f64 (*.f64 (log.f64 x) #s(literal -1 binary64)) (neg.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x)))))
(exp.f64 (-.f64 (*.f64 (log.f64 x) #s(literal -1 binary64)) (*.f64 #s(literal 1/2 binary64) (log1p.f64 x))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) x)))
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(pow.f64 (*.f64 x (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 x (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) x))
(*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x))
(*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (pow.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (pow.f64 (*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) x) #s(literal -1 binary64)))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)))
(*.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x) (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (/.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) x) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)))))
(*.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) #s(literal -1 binary64)) (/.f64 (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64))) x))
(*.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (/.f64 #s(literal 2 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)))) (/.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x))
(*.f64 (/.f64 (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64))) #s(literal -1 binary64)) (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x))
(+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
(+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))
(-.f64 (/.f64 #s(literal 1/64 binary64) (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))) (/.f64 (/.f64 #s(literal 1/256 binary64) (*.f64 x x)) (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
(-.f64 (/.f64 (/.f64 #s(literal 1/256 binary64) (*.f64 x x)) (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))) (/.f64 #s(literal 1/64 binary64) (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))))
(fma.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1 binary64) x) #s(literal -1/8 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/16 binary64) #s(literal -1/8 binary64))
(fma.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -1 binary64) x) #s(literal -1/8 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/64 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) (/.f64 x #s(literal 1/16 binary64)))) (+.f64 #s(literal -1/512 binary64) (/.f64 #s(literal 1/4096 binary64) (*.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (*.f64 x x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1/64 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) (/.f64 x #s(literal 1/16 binary64)))) (+.f64 #s(literal -1/512 binary64) (/.f64 #s(literal 1/4096 binary64) (*.f64 x (*.f64 x x)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (*.f64 x x))))))
(/.f64 (+.f64 #s(literal -1/512 binary64) (/.f64 #s(literal 1/4096 binary64) (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1/64 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) (/.f64 x #s(literal 1/16 binary64)))))
(/.f64 (+.f64 #s(literal -1/512 binary64) (/.f64 #s(literal 1/4096 binary64) (*.f64 x (*.f64 x x)))) (+.f64 (/.f64 #s(literal 1/256 binary64) (*.f64 x x)) (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal -1/128 binary64) x))))
(/.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (*.f64 x x))) (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))
(/.f64 (neg.f64 (+.f64 #s(literal -1/512 binary64) (/.f64 #s(literal 1/4096 binary64) (*.f64 x (*.f64 x x))))) (neg.f64 (+.f64 #s(literal 1/64 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) (/.f64 x #s(literal 1/16 binary64))))))
(/.f64 (neg.f64 (+.f64 #s(literal -1/512 binary64) (/.f64 #s(literal 1/4096 binary64) (*.f64 x (*.f64 x x))))) (neg.f64 (+.f64 (/.f64 #s(literal 1/256 binary64) (*.f64 x x)) (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal -1/128 binary64) x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (*.f64 x x)))) (neg.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
(/.f64 (-.f64 (/.f64 #s(literal 1/256 binary64) (*.f64 x x)) #s(literal 1/64 binary64)) (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)))
(/.f64 (neg.f64 (neg.f64 (+.f64 #s(literal -1/512 binary64) (/.f64 #s(literal 1/4096 binary64) (*.f64 x (*.f64 x x)))))) (neg.f64 (neg.f64 (+.f64 #s(literal 1/64 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) (/.f64 x #s(literal 1/16 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (*.f64 x x))))) (neg.f64 (neg.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))
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(pow.f64 (/.f64 (+.f64 #s(literal 1/64 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) (/.f64 x #s(literal 1/16 binary64)))) (+.f64 #s(literal -1/512 binary64) (/.f64 #s(literal 1/4096 binary64) (*.f64 x (*.f64 x x))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (*.f64 x x)))) #s(literal -1 binary64))
(*.f64 (+.f64 #s(literal -1/512 binary64) (/.f64 #s(literal 1/4096 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) (/.f64 x #s(literal 1/16 binary64))))))
(*.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))

simplify294.0ms (2.7%)

Algorithm
1×egg-herbie
Rules
4164×+-lowering-+.f64
4164×+-lowering-+.f32
3736×*-lowering-*.f32
3736×*-lowering-*.f64
1316×sum3-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03582393
110421948
234651897
088611897
Stop Event
1×iter limit
1×node limit
Counts
252 → 252
Calls
Call 1
Inputs
(/ 1/16 (pow x 2))
(/ (+ 1/16 (* -1/8 x)) (pow x 2))
(/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 2))
(/ (+ 1/16 (* x (- (* x (+ 1/2 (* 2 x))) 1/8))) (pow x 2))
(* 2 x)
(* x (+ 2 (* 1/2 (/ 1 x))))
(* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(* 2 x)
(* x (+ 2 (* 1/2 (/ 1 x))))
(* -1 (* x (- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2)))
(* -1 (* x (- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) x)) 2)))
(/ 1/16 (pow x 3))
(/ (+ 1/16 (* -1/8 x)) (pow x 3))
(/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 3))
(/ (+ 1/16 (* x (- (* x (+ 1/2 (* 2 x))) 1/8))) (pow x 3))
2
(+ 2 (* 1/2 (/ 1 x)))
(- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))
(- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))
2
(+ 2 (* 1/2 (/ 1 x)))
(+ 2 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x)))
(+ 2 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x)))
(* 16 (pow x 2))
(* (pow x 2) (+ 16 (* 24 x)))
(* (pow x 2) (+ 16 (* x (+ 24 (* -74 x)))))
(* (pow x 2) (+ 16 (* x (+ 24 (* x (- (* -857 x) 74))))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/16 (sqrt (/ 1 x))) (* 5/128 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(/ 1/16 (pow x 3))
(/ 1/16 (pow x 3))
(/ 1/16 (pow x 3))
(/ 1/16 (pow x 3))
(/ 1/16 (pow x 3))
(/ 1/16 (pow x 3))
(/ 1/16 (pow x 3))
(/ 1/16 (pow x 3))
(/ 1/16 (pow x 3))
(/ 1/16 (pow x 3))
(/ 1/16 (pow x 3))
(/ 1/16 (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)
(pow x 3)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(/ 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
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(/ -1/8 (pow x 2))
(/ (- (* 9/16 x) 1/8) (pow x 2))
(/ (- (* x (+ 9/16 (* -19/64 x))) 1/8) (pow x 2))
(/ (- (* x (+ 9/16 (* x (- (* 29/128 x) 19/64)))) 1/8) (pow x 2))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))) x)
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/16 (sqrt (/ 1 x))) (* 1/4 (sqrt x)))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/ -1/8 (pow x 2))
(/ (- (* 1/2 x) 1/8) (pow x 2))
(/ (- (* 1/2 x) 1/8) (pow x 2))
(/ (- (* 1/2 x) 1/8) (pow x 2))
(/ 1/2 x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ 1/2 x)
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(/ -1/8 x)
(/ (- (* 1/2 x) 1/8) x)
(/ (- (* 1/2 x) 1/8) x)
(/ (- (* 1/2 x) 1/8) x)
1/2
(- 1/2 (* 1/8 (/ 1 x)))
(- 1/2 (* 1/8 (/ 1 x)))
(- 1/2 (* 1/8 (/ 1 x)))
1/2
(- 1/2 (* 1/8 (/ 1 x)))
(- 1/2 (* 1/8 (/ 1 x)))
(- 1/2 (* 1/8 (/ 1 x)))
(/ 1/16 (pow x 3))
(/ (+ 1/16 (* -5/32 x)) (pow x 3))
(/ (+ 1/16 (* x (- (* 75/128 x) 5/32))) (pow x 3))
(/ (+ 1/16 (* x (- (* x (+ 75/128 (* -81/256 x))) 5/32))) (pow x 3))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))) x)
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/4 (sqrt (/ 1 x))) (* -1/16 (sqrt (/ 1 x))))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/ 1/16 (pow x 2))
(/ (+ 1/16 (* -1/8 x)) (pow x 2))
(/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 2))
(/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 2))
1/2
(- 1/2 (* 1/8 (/ 1 x)))
(- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x)))
(- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x)))
1/2
(- 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x)))
(+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x)))
(/ 1/16 (pow x 2))
(/ (+ 1/16 (* -1/8 x)) (pow x 2))
(/ (+ 1/16 (* -1/8 x)) (pow x 2))
(/ (+ 1/16 (* -1/8 x)) (pow x 2))
(/ -1/8 x)
(/ (- (* 1/16 (/ 1 x)) 1/8) x)
(/ (- (* 1/16 (/ 1 x)) 1/8) x)
(/ (- (* 1/16 (/ 1 x)) 1/8) x)
(/ -1/8 x)
(* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))
(* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))
(* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))
(/ 1/16 (pow x 3))
(/ (+ 1/16 (* -1/8 x)) (pow x 3))
(/ (+ 1/16 (* -1/8 x)) (pow x 3))
(/ (+ 1/16 (* -1/8 x)) (pow x 3))
(/ -1/8 (pow x 2))
(/ (- (* 1/16 (/ 1 x)) 1/8) (pow x 2))
(/ (- (* 1/16 (/ 1 x)) 1/8) (pow x 2))
(/ (- (* 1/16 (/ 1 x)) 1/8) (pow x 2))
(/ -1/8 (pow x 2))
(/ (- (* 1/16 (/ 1 x)) 1/8) (pow x 2))
(/ (- (* 1/16 (/ 1 x)) 1/8) (pow x 2))
(/ (- (* 1/16 (/ 1 x)) 1/8) (pow x 2))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(/ 1 x)
(/ (+ 1 (* -1/2 x)) x)
(/ (+ 1 (* x (- (* 3/8 x) 1/2))) x)
(/ (+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2))) x)
(sqrt (/ 1 (pow x 3)))
(/ (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))) x)
(/ (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))) x)
(/ (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))) x)
(* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))
(* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (sqrt (/ 1 (pow x 3))))) x))
(* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) x))
(* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* 1/2 (sqrt x))) (pow x 3))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) x))
(/ 1/16 x)
(/ (+ 1/16 (* -1/8 x)) x)
(/ (+ 1/16 (* -1/8 x)) x)
(/ (+ 1/16 (* -1/8 x)) x)
-1/8
(- (* 1/16 (/ 1 x)) 1/8)
(- (* 1/16 (/ 1 x)) 1/8)
(- (* 1/16 (/ 1 x)) 1/8)
-1/8
(- (* 1/16 (/ 1 x)) 1/8)
(- (* 1/16 (/ 1 x)) 1/8)
(- (* 1/16 (/ 1 x)) 1/8)
Outputs
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(/ (+ 1/16 (* -1/8 x)) (pow x 2))
(/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))) (*.f64 x x))
(/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64))))) (*.f64 x x))
(/ (+ 1/16 (* x (- (* x (+ 1/2 (* 2 x))) 1/8))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))))) (*.f64 x x))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))
(* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))
(* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(*.f64 x (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (*.f64 x x))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))
(* -1 (* x (- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) x)) 2)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)))
(/ 1/16 (pow x 3))
(/.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x x)))
(/ (+ 1/16 (* -1/8 x)) (pow x 3))
(/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))) (*.f64 x (*.f64 x x)))
(/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 3))
(/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64))))) (*.f64 x (*.f64 x x)))
(/ (+ 1/16 (* x (- (* x (+ 1/2 (* 2 x))) 1/8))) (pow x 3))
(/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))))) (*.f64 x (*.f64 x x)))
2
#s(literal 2 binary64)
(+ 2 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))
(+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))
(- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))
(+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (*.f64 x x)))
2
#s(literal 2 binary64)
(+ 2 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(+ 2 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x)))
(+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))
(+ 2 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x)))
(+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x))
(* 16 (pow x 2))
(*.f64 x (*.f64 x #s(literal 16 binary64)))
(* (pow x 2) (+ 16 (* 24 x)))
(*.f64 (*.f64 x x) (+.f64 #s(literal 16 binary64) (*.f64 x #s(literal 24 binary64))))
(* (pow x 2) (+ 16 (* x (+ 24 (* -74 x)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 16 binary64) (*.f64 x (+.f64 #s(literal 24 binary64) (*.f64 x #s(literal -74 binary64))))))
(* (pow x 2) (+ 16 (* x (+ 24 (* x (- (* -857 x) 74))))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 16 binary64) (*.f64 x (+.f64 #s(literal 24 binary64) (*.f64 x (+.f64 #s(literal -74 binary64) (*.f64 x #s(literal -857 binary64))))))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/.f64 (+.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -3/8 binary64)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)
(/.f64 (+.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 3/8 binary64))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -3/8 binary64)) (*.f64 #s(literal -5/128 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))) x)
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64))
(* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) x)
(* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/16 binary64)) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/16 (sqrt (/ 1 x))) (* 5/128 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (-.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -5/128 binary64)) (+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64)))) x)) x)) (-.f64 #s(literal 0 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 3/8 binary64)))))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 #s(literal 3/8 binary64) (*.f64 x #s(literal -5/16 binary64)))))))
(sqrt (/ 1 x))
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(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/.f64 (+.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -3/8 binary64)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))) x)
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 3/8 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -3/8 binary64)))) x)
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64))
(* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) x)
(* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/16 binary64)) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/4 (sqrt (/ 1 x))) (* -1/16 (sqrt (/ 1 x))))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)) x)) (-.f64 #s(literal 0 binary64) x))
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(/ (+ 1/16 (* -1/8 x)) (pow x 2))
(/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))) (*.f64 x x))
(/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64))))) (*.f64 x x))
(/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64))))) (*.f64 x x))
1/2
#s(literal 1/2 binary64)
(- 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
(- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
1/2
#s(literal 1/2 binary64)
(- 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
(+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(/ (+ 1/16 (* -1/8 x)) (pow x 2))
(/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))) (*.f64 x x))
(/ (+ 1/16 (* -1/8 x)) (pow x 2))
(/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))) (*.f64 x x))
(/ (+ 1/16 (* -1/8 x)) (pow x 2))
(/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))) (*.f64 x x))
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ (- (* 1/16 (/ 1 x)) 1/8) x)
(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ (- (* 1/16 (/ 1 x)) 1/8) x)
(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ (- (* 1/16 (/ 1 x)) 1/8) x)
(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))
(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))
(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))
(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ 1/16 (pow x 3))
(/.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x x)))
(/ (+ 1/16 (* -1/8 x)) (pow x 3))
(/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))) (*.f64 x (*.f64 x x)))
(/ (+ 1/16 (* -1/8 x)) (pow x 3))
(/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))) (*.f64 x (*.f64 x x)))
(/ (+ 1/16 (* -1/8 x)) (pow x 3))
(/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))) (*.f64 x (*.f64 x x)))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ (- (* 1/16 (/ 1 x)) 1/8) (pow x 2))
(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (*.f64 x x))
(/ (- (* 1/16 (/ 1 x)) 1/8) (pow x 2))
(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (*.f64 x x))
(/ (- (* 1/16 (/ 1 x)) 1/8) (pow x 2))
(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ (- (* 1/16 (/ 1 x)) 1/8) (pow x 2))
(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (*.f64 x x))
(/ (- (* 1/16 (/ 1 x)) 1/8) (pow x 2))
(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (*.f64 x x))
(/ (- (* 1/16 (/ 1 x)) 1/8) (pow x 2))
(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* -1/2 x)) x)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64))) x)
(/ (+ 1 (* x (- (* 3/8 x) 1/2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 3/8 binary64))))) x)
(/ (+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 #s(literal 3/8 binary64) (*.f64 x #s(literal -5/16 binary64))))))) x)
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))
(/ (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))) x)
(/.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64))) x)
(/ (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))) x)
(/.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) x)
(/ (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))) x)
(/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64)))))) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))
(* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (sqrt (/ 1 (pow x 3))))) x))
(/.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) x))
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/2 binary64)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* 1/2 (sqrt x))) (pow x 3))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) x))
(/.f64 (+.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal -1/4 binary64)) #s(literal -1 binary64))) #s(literal -1/2 binary64))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (*.f64 x (*.f64 x x)))) x)
(/ 1/16 x)
(/.f64 #s(literal 1/16 binary64) x)
(/ (+ 1/16 (* -1/8 x)) x)
(/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))) x)
(/ (+ 1/16 (* -1/8 x)) x)
(/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))) x)
(/ (+ 1/16 (* -1/8 x)) x)
(/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))) x)
-1/8
#s(literal -1/8 binary64)
(- (* 1/16 (/ 1 x)) 1/8)
(+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
(- (* 1/16 (/ 1 x)) 1/8)
(+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
(- (* 1/16 (/ 1 x)) 1/8)
(+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
-1/8
#s(literal -1/8 binary64)
(- (* 1/16 (/ 1 x)) 1/8)
(+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
(- (* 1/16 (/ 1 x)) 1/8)
(+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
(- (* 1/16 (/ 1 x)) 1/8)
(+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))

eval231.0ms (2.2%)

Compiler

Compiled 37275 to 3923 computations (89.5% saved)

prune193.0ms (1.8%)

Pruning

26 alts after pruning (23 fresh and 3 done)

PrunedKeptTotal
New1422131435
Fresh41014
Picked415
Done022
Total1430261456
Accuracy
100.0%
Counts
1456 → 26
Alt Table
Click to see full alt table
StatusAccuracyProgram
38.4%
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))))) (*.f64 x x)))
98.5%
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (+.f64 #s(literal 1/2 binary64) x)))
98.9%
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))))
81.6%
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) x))))
97.3%
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x x))
99.0%
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)) x))
37.8%
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (*.f64 x (/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))))) (*.f64 x (*.f64 x x)))))
98.9%
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))))
35.9%
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
98.8%
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
98.4%
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) x)
35.9%
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
98.4%
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
8.0%
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) #s(literal 1 binary64))
97.2%
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
8.0%
(/.f64 (-.f64 #s(literal 9/16 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)
97.8%
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (/.f64 (/.f64 #s(literal 5/128 binary64) x) x)) x)) (*.f64 x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
✓78.9%
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 x x))
97.8%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64))))
32.9%
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
✓37.0%
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓97.1%
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1/2 binary64) x))
97.4%
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
35.9%
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))
98.4%
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
3.0%
(*.f64 x (*.f64 x #s(literal 16 binary64)))
Compiler

Compiled 1318 to 496 computations (62.4% saved)

regimes35.0ms (0.3%)

Counts
62 → 1
Calls
Call 1
Inputs
(*.f64 x (*.f64 x #s(literal 16 binary64)))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x x)))
(/.f64 (-.f64 #s(literal 9/16 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) #s(literal 1 binary64))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) #s(literal 1 binary64))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(pow.f64 x #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1/2 binary64) x))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 x x))
(/.f64 (/.f64 #s(literal 1/2 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)) (+.f64 x x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (+.f64 #s(literal 1/2 binary64) x)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) x)
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) x)
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) 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)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))))
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (/.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)) (+.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))))
(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -5/128 binary64) x)) x)) x)) 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)) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)) x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64))))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (/.f64 (/.f64 #s(literal 5/128 binary64) x) x)) x)) (*.f64 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)) (*.f64 x (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) x))))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))))) (*.f64 x x)))
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) (/.f64 #s(literal 5/128 binary64) (*.f64 x (*.f64 x x)))) 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)) (*.f64 x (/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))))) (*.f64 x (*.f64 x x)))))
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) x) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)) x) (/.f64 #s(literal -1/2 binary64) x))
(/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) x)
(*.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) x))))
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 5/8 binary64)) x)) x)
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -3/8 binary64))) x)
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x))) (+.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -3/8 binary64)))) (*.f64 x x))
(/.f64 (*.f64 (+.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (*.f64 (*.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (*.f64 (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))))
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64))))) (*.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (*.f64 x x))
(/.f64 (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (*.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)))
Outputs
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)) x))
Calls

2 calls:

18.0ms
x
13.0ms
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Results
AccuracySegmentsBranch
99.0%1x
99.0%1(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes25.0ms (0.2%)

Counts
32 → 1
Calls
Call 1
Inputs
(*.f64 x (*.f64 x #s(literal 16 binary64)))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x x)))
(/.f64 (-.f64 #s(literal 9/16 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) #s(literal 1 binary64))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) #s(literal 1 binary64))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(pow.f64 x #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1/2 binary64) x))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 x x))
(/.f64 (/.f64 #s(literal 1/2 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)) (+.f64 x x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (+.f64 #s(literal 1/2 binary64) x)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) x)
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) x)
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) 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)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))))
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (/.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)) (+.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))))
(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -5/128 binary64) x)) x)) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
Outputs
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))))
Calls

1 calls:

23.0ms
x
Results
AccuracySegmentsBranch
98.9%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes10.0ms (0.1%)

Counts
28 → 1
Calls
Call 1
Inputs
(*.f64 x (*.f64 x #s(literal 16 binary64)))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x x)))
(/.f64 (-.f64 #s(literal 9/16 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) #s(literal 1 binary64))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) #s(literal 1 binary64))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(pow.f64 x #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1/2 binary64) x))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 x x))
(/.f64 (/.f64 #s(literal 1/2 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)) (+.f64 x x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (+.f64 #s(literal 1/2 binary64) x)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) x)
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) x)
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
Outputs
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
Calls

1 calls:

8.0ms
x
Results
AccuracySegmentsBranch
98.8%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes9.0ms (0.1%)

Counts
25 → 1
Calls
Call 1
Inputs
(*.f64 x (*.f64 x #s(literal 16 binary64)))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x x)))
(/.f64 (-.f64 #s(literal 9/16 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) #s(literal 1 binary64))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) #s(literal 1 binary64))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(pow.f64 x #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1/2 binary64) x))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 x x))
(/.f64 (/.f64 #s(literal 1/2 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)) (+.f64 x x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (+.f64 #s(literal 1/2 binary64) x)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) x)
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
Outputs
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (+.f64 #s(literal 1/2 binary64) x)))
Calls

1 calls:

8.0ms
x
Results
AccuracySegmentsBranch
98.5%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes17.0ms (0.2%)

Counts
20 → 1
Calls
Call 1
Inputs
(*.f64 x (*.f64 x #s(literal 16 binary64)))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x x)))
(/.f64 (-.f64 #s(literal 9/16 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) #s(literal 1 binary64))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) #s(literal 1 binary64))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(pow.f64 x #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1/2 binary64) x))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 x x))
(/.f64 (/.f64 #s(literal 1/2 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)) (+.f64 x x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))
Outputs
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
Calls

1 calls:

16.0ms
x
Results
AccuracySegmentsBranch
97.4%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0%)

Counts
12 → 1
Calls
Call 1
Inputs
(*.f64 x (*.f64 x #s(literal 16 binary64)))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x x)))
(/.f64 (-.f64 #s(literal 9/16 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) #s(literal 1 binary64))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) #s(literal 1 binary64))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(pow.f64 x #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
Outputs
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
Calls

1 calls:

4.0ms
x
Results
AccuracySegmentsBranch
35.9%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Counts
7 → 1
Calls
Call 1
Inputs
(*.f64 x (*.f64 x #s(literal 16 binary64)))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x x)))
(/.f64 (-.f64 #s(literal 9/16 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) #s(literal 1 binary64))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) #s(literal 1 binary64))
Outputs
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
Calls

1 calls:

3.0ms
x
Results
AccuracySegmentsBranch
35.9%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Counts
5 → 1
Calls
Call 1
Inputs
(*.f64 x (*.f64 x #s(literal 16 binary64)))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x x)))
(/.f64 (-.f64 #s(literal 9/16 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) #s(literal 1 binary64))
Outputs
(/.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x x)))
Calls

1 calls:

2.0ms
x
Results
AccuracySegmentsBranch
34.7%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts
2 → 1
Calls
Call 1
Inputs
(*.f64 x (*.f64 x #s(literal 16 binary64)))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
Outputs
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
Calls

1 calls:

2.0ms
x
Results
AccuracySegmentsBranch
32.9%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 x (*.f64 x #s(literal 16 binary64)))
Outputs
(*.f64 x (*.f64 x #s(literal 16 binary64)))
Calls

1 calls:

1.0ms
x
Results
AccuracySegmentsBranch
3.0%1x
Compiler

Compiled 2 to 1 computations (50% saved)

simplify19.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
30×+-commutative_binary64
20×*-commutative_binary64
8×sub-neg_binary64
6×neg-sub0_binary64
6×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
050117
173117
281117
387117
492117
594117
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)) x))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (+.f64 #s(literal 1/2 binary64) x)))
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x x)))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(*.f64 x (*.f64 x #s(literal 16 binary64)))
Outputs
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)) x))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x))))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (+.f64 #s(literal 1/2 binary64) x)))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (+.f64 x #s(literal 1/2 binary64))))
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -3/2 binary64)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))
(/.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x x)))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(*.f64 x (*.f64 x #s(literal 16 binary64)))

soundness2.7s (24.9%)

Rules
4540×/-lowering-/.f32
4540×/-lowering-/.f64
4422×/-lowering-/.f32
4422×/-lowering-/.f64
4164×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04312795
114031990
257841966
083381966
04692684
114862058
257842038
090052038
0114458
1334394
21141371
34906370
08253370
030168
1207157
21929157
08838157
0815
16415
260115
3727915
0816015
03582393
110421948
234651897
088611897
032161
1225157
22204153
08170153
033164
1227120
22070113
08372113
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
1×iter limit
1×node limit
Compiler

Compiled 301 to 175 computations (41.9% saved)

preprocess65.0ms (0.6%)

Compiler

Compiled 292 to 130 computations (55.5% saved)

end0.0ms (0%)

Profiling

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