Falkner and Boettcher, Appendix B, 2

Time bar (total: 6.9s)

analyze5.0ms (0.1%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
0%0%50%0%0%50%0%3
50%25%25%0%0%50%0%4
75%37.5%12.5%0%0%50%0%5
87.5%43.7%6.2%0%0%50%0%6
93.8%46.9%3.1%0%0%50%0%7
96.9%48.4%1.6%0%0%50%0%8
98.4%49.2%0.8%0%0%50%0%9
99.2%49.6%0.4%0%0%50%0%10
99.6%49.8%0.2%0%0%50%0%11
99.8%49.9%0.1%0%0%50%0%12
Compiler

Compiled 21 to 15 computations (28.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-mult: 1.0ms (40% of total)
ival-sqrt: 1.0ms (40% of total)
ival-div: 0.0ms (0% of total)
ival-sub: 0.0ms (0% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample1.2s (17.2%)

Results
904.0ms8256×0valid
1.0ms10×0invalid
Precisions
Click to see histograms. Total time spent on operations: 617.0ms
ival-mult: 264.0ms (42.8% of total)
ival-sqrt: 136.0ms (22.1% of total)
ival-sub: 114.0ms (18.5% of total)
ival-div: 76.0ms (12.3% of total)
const: 23.0ms (3.7% of total)
backward-pass: 3.0ms (0.5% of total)
Bogosity

preprocess228.0ms (3.3%)

Algorithm
2×egg-herbie
Rules
2030×fma-lowering-fma.f32
2030×fma-lowering-fma.f64
1914×*-lowering-*.f32
1914×*-lowering-*.f64
1702×fma-define
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
02352
17551
219248
364248
4211948
5589245
01417
13717
28916
324416
473716
5178215
6306215
7546115
8753115
0809415
Stop Event
1×iter limit
1×node limit
1×node limit
Calls
Call 1
Inputs
(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))
Outputs
(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64)))) (-.f64 #s(literal 1/4 binary64) (*.f64 v (/.f64 v #s(literal 4 binary64))))))
Call 2
Inputs
(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))
(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (neg v) (neg v)))))) (- 1 (* (neg v) (neg v))))
(neg (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (neg v) (neg v)))))) (- 1 (* (neg v) (neg v)))))
Outputs
(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))
(* (* (sqrt 2) (sqrt (fnmsub 3 (square v) -1))) (fnmsub (square v) 1/4 -1/4))
(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (neg v) (neg v)))))) (- 1 (* (neg v) (neg v))))
(* (* (sqrt 2) (sqrt (fnmsub 3 (square v) -1))) (fnmsub (square v) 1/4 -1/4))
(neg (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (neg v) (neg v)))))) (- 1 (* (neg v) (neg v)))))
(* (* (sqrt 2) (sqrt (fnmsub 3 (square v) -1))) (fnmsub (square v) -1/4 1/4))
Symmetry

(abs v)

explain175.0ms (2.5%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(-.f64 #s(literal 1 binary64) (*.f64 v v))
00-0-#s(literal 2 binary64)
00-0-v
00-0-(*.f64 #s(literal 3 binary64) (*.f64 v v))
00-0-#s(literal 4 binary64)
00-0-(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v)))
00-0-(sqrt.f64 #s(literal 2 binary64))
00-0-(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64))
00-0-#s(literal 1 binary64)
00-0-#s(literal 3 binary64)
00-0-(*.f64 v v)
00-0-(*.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
00-0-(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v)))))
00-0-(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v))))
Results
116.0ms512×0valid
Compiler

Compiled 166 to 44 computations (73.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 32.0ms
ival-mult: 13.0ms (40.7% of total)
ival-sqrt: 8.0ms (25.1% of total)
ival-sub: 5.0ms (15.7% of total)
ival-div: 4.0ms (12.5% of total)
const: 1.0ms (3.1% of total)
backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 20 to 16 computations (20% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(*.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
Compiler

Compiled 20 to 14 computations (30% saved)

simplify193.0ms (2.8%)

Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64))
✓cost-diff0
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v)))))
✓cost-diff0
(*.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
Rules
2030×fma-lowering-fma.f32
2030×fma-lowering-fma.f64
1914×*-lowering-*.f32
1914×*-lowering-*.f64
1516×fma-define
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01463
13763
28959
324459
473759
5178258
6306258
7546158
8753158
0809458
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))
(* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))
(/ (sqrt 2) 4)
(sqrt 2)
2
4
(sqrt (- 1 (* 3 (* v v))))
(- 1 (* 3 (* v v)))
1
(* 3 (* v v))
3
(* v v)
v
(- 1 (* v v))
Outputs
(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64)))) (-.f64 #s(literal 1/4 binary64) (*.f64 v (/.f64 v #s(literal 4 binary64))))))
(* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64)))))
(/ (sqrt 2) 4)
(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
4
#s(literal 4 binary64)
(sqrt (- 1 (* 3 (* v v))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64))))
(- 1 (* 3 (* v v)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64)))
1
#s(literal 1 binary64)
(* 3 (* v v))
(*.f64 #s(literal 3 binary64) (*.f64 v v))
3
#s(literal 3 binary64)
(* v v)
(*.f64 v v)
v
(- 1 (* v v))
(-.f64 #s(literal 1 binary64) (*.f64 v v))

localize69.0ms (1%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 v v)
✓accuracy100.0%
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v))))
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy99.7%
(*.f64 #s(literal 3 binary64) (*.f64 v v))
Results
46.0ms256×0valid
Compiler

Compiled 73 to 15 computations (79.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 19.0ms
ival-mult: 6.0ms (32.3% of total)
ival-div: 5.0ms (26.9% of total)
ival-sqrt: 4.0ms (21.5% of total)
ival-sub: 3.0ms (16.1% of total)
const: 1.0ms (5.4% of total)
backward-pass: 0.0ms (0% of total)

series35.0ms (0.5%)

Counts
7 → 60
Calls
Call 1
Inputs
#<alt (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))>
#<alt (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))>
#<alt (/ (sqrt 2) 4)>
#<alt (sqrt 2)>
#<alt (* 3 (* v v))>
#<alt (sqrt (- 1 (* 3 (* v v))))>
#<alt (* v v)>
Outputs
#<alt (* 1/4 (sqrt 2))>
#<alt (+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))>
#<alt (* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))>
#<alt (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))>
#<alt (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))>
#<alt (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))>
#<alt (* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))>
#<alt (* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))))))>
#<alt (* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))>
#<alt (* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))))>
#<alt (* 1/4 (sqrt 2))>
#<alt (+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2))))))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* (pow v 2) (+ (* -27/64 (* (pow v 2) (sqrt 2))) (* -9/32 (sqrt 2)))))))>
#<alt (* 1/4 (* v (* (sqrt -3) (sqrt 2))))>
#<alt (* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))>
#<alt (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))>
#<alt (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))>
#<alt (* -1/4 (* v (* (sqrt -3) (sqrt 2))))>
#<alt (* -1 (* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))>
#<alt (* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))>
#<alt (* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))))>
#<alt (* 3 (pow v 2))>
#<alt (* 3 (pow v 2))>
#<alt (* 3 (pow v 2))>
#<alt (* 3 (pow v 2))>
#<alt (* 3 (pow v 2))>
#<alt (* 3 (pow v 2))>
#<alt (* 3 (pow v 2))>
#<alt (* 3 (pow v 2))>
#<alt (* 3 (pow v 2))>
#<alt (* 3 (pow v 2))>
#<alt (* 3 (pow v 2))>
#<alt (* 3 (pow v 2))>
#<alt 1>
#<alt (+ 1 (* -3/2 (pow v 2)))>
#<alt (+ 1 (* (pow v 2) (- (* -9/8 (pow v 2)) 3/2)))>
#<alt (+ 1 (* (pow v 2) (- (* (pow v 2) (- (* -27/16 (pow v 2)) 9/8)) 3/2)))>
#<alt (* v (sqrt -3))>
#<alt (* v (+ (sqrt -3) (* 1/2 (/ 1 (* (pow v 2) (sqrt -3))))))>
#<alt (* v (- (+ (sqrt -3) (/ 1/2 (* (pow v 2) (sqrt -3)))) (/ 1/8 (* (pow v 4) (pow (sqrt -3) 3)))))>
#<alt (* v (- (+ (sqrt -3) (+ (/ 1/2 (* (pow v 2) (sqrt -3))) (* 1/16 (/ 1 (* (pow v 6) (pow (sqrt -3) 5)))))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -3) 3))))))>
#<alt (* -1 (* v (sqrt -3)))>
#<alt (* -1 (* v (+ (sqrt -3) (* 1/2 (/ 1 (* (pow v 2) (sqrt -3)))))))>
#<alt (* -1 (* v (- (+ (sqrt -3) (/ 1/2 (* (pow v 2) (sqrt -3)))) (/ 1/8 (* (pow v 4) (pow (sqrt -3) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -3) (+ (/ 1/2 (* (pow v 2) (sqrt -3))) (* 1/16 (/ 1 (* (pow v 6) (pow (sqrt -3) 5)))))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -3) 3)))))))>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
Calls

15 calls:

TimeVariablePointExpression
28.0ms
v
@0
(* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))
1.0ms
v
@inf
(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))
1.0ms
v
@0
(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))
1.0ms
v
@inf
(* 3 (* v v))
1.0ms
v
@inf
(* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))

rewrite279.0ms (4%)

Algorithm
1×batch-egg-rewrite
Rules
3004×*-lowering-*.f32
3004×*-lowering-*.f64
1870×/-lowering-/.f32
1870×/-lowering-/.f64
1754×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01448
17246
249143
3541243
0843943
Stop Event
1×iter limit
1×node limit
Counts
7 → 277
Calls
Call 1
Inputs
(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))
(* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))
(/ (sqrt 2) 4)
(sqrt 2)
(* 3 (* v v))
(sqrt (- 1 (* 3 (* v v))))
(* v v)
Outputs
(+.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) #s(literal 4 binary64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 0 binary64) (*.f64 v v)))))
(+.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 0 binary64) (*.f64 v v)))) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) #s(literal 4 binary64)))
(-.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) #s(literal 4 binary64)) (*.f64 (*.f64 v v) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) #s(literal 4 binary64))))
(-.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) #s(literal 4 binary64)) (*.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) #s(literal 4 binary64)) (*.f64 v v)))
(fma.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) #s(literal 4 binary64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 0 binary64) (*.f64 v v)))))
(fma.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) #s(literal 4 binary64)) #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 0 binary64) (*.f64 v v)))))
(neg.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -4 binary64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(neg.f64 (*.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -4 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (/.f64 #s(literal 4 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 4 binary64) (*.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v))))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v))))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 4 binary64) (*.f64 #s(literal 4 binary64) (*.f64 v v))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 v v)) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) (/.f64 #s(literal 4 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64))))))))
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(*.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64))) #s(literal 1/4 binary64)) #s(literal 4 binary64)) (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64))) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(*.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64))) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64))) #s(literal 1/4 binary64)))
(*.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64)))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)))
(*.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64)))) #s(literal -4 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -4 binary64)))
(neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -4 binary64)))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -4 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 4 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -4 binary64))
(/.f64 #s(literal 1/4 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -4 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -4 binary64))
(pow.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/4 binary64))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal 1/4 binary64) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -4 binary64)))
(*.f64 #s(literal -1/4 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 4 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64))
(*.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(*.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 #s(literal 2 binary64))
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(*.f64 #s(literal 1 binary64) (*.f64 v (*.f64 #s(literal 3 binary64) v)))
(*.f64 #s(literal 3 binary64) (*.f64 v v))
(*.f64 v (*.f64 #s(literal 3 binary64) v))
(*.f64 (*.f64 v v) #s(literal 3 binary64))
(*.f64 (*.f64 v (*.f64 #s(literal 3 binary64) v)) #s(literal 1 binary64))
(*.f64 (*.f64 #s(literal 3 binary64) v) v)
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 3 binary64) (*.f64 (*.f64 v v) #s(literal 9 binary64)))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 27 binary64) (*.f64 v (*.f64 v v))) (*.f64 v (*.f64 v v)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 #s(literal 3 binary64) v)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 (*.f64 v (*.f64 v v)) #s(literal 9 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 27 binary64) (*.f64 v (*.f64 v v))) (*.f64 v (*.f64 v v))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 3 binary64) (*.f64 (*.f64 v v) #s(literal 9 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 (*.f64 v (*.f64 v v)) #s(literal 9 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 #s(literal 3 binary64) v)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 27 binary64) (*.f64 v (*.f64 v v))) (*.f64 v (*.f64 v v)))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 3 binary64) (*.f64 (*.f64 v v) #s(literal 9 binary64))))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (*.f64 v (*.f64 (*.f64 v (*.f64 v v)) #s(literal 9 binary64))))) (sqrt.f64 (+.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal -1 binary64))))
(/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 27 binary64) (*.f64 v (*.f64 v v))) (*.f64 v (*.f64 v v))))) #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 3 binary64) (*.f64 (*.f64 v v) #s(literal 9 binary64)))))))
(/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 (*.f64 v (*.f64 v v)) #s(literal 9 binary64))))) #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 #s(literal 3 binary64) v)))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 27 binary64) (*.f64 v (*.f64 v v))) (*.f64 v (*.f64 v v)))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 3 binary64) (*.f64 (*.f64 v v) #s(literal 9 binary64)))))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 (*.f64 v (*.f64 v v)) #s(literal 9 binary64)))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 #s(literal 3 binary64) v)))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 27 binary64) (*.f64 v (*.f64 v v))) (*.f64 v (*.f64 v v)))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 3 binary64) (*.f64 (*.f64 v v) #s(literal 9 binary64))))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 (*.f64 v (*.f64 v v)) #s(literal 9 binary64)))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 #s(literal 3 binary64) v))))))
(pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64)))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log1p.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64)))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64)))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 27 binary64) (*.f64 v (*.f64 v v))) (*.f64 v (*.f64 v v))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 3 binary64) (*.f64 (*.f64 v v) #s(literal 9 binary64)))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 27 binary64) (*.f64 v (*.f64 v v))) (*.f64 v (*.f64 v v))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 3 binary64) (*.f64 (*.f64 v v) #s(literal 9 binary64))))))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 27 binary64) (*.f64 v (*.f64 v v))) (*.f64 v (*.f64 v v))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 3 binary64) (*.f64 (*.f64 v v) #s(literal 9 binary64))))))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 (*.f64 v (*.f64 v v)) #s(literal 9 binary64))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 #s(literal 3 binary64) v)))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 (*.f64 v (*.f64 v v)) #s(literal 9 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 #s(literal 3 binary64) v))))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 (*.f64 v (*.f64 v v)) #s(literal 9 binary64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 #s(literal 3 binary64) v))))))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64))) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64))) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64))) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64))) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64))) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 v)))
(pow.f64 v #s(literal 2 binary64))
(pow.f64 (*.f64 v v) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 v)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 v v))
(*.f64 v v)
(*.f64 (*.f64 v v) #s(literal 1 binary64))
(*.f64 (exp.f64 (log.f64 v)) (exp.f64 (log.f64 v)))

simplify272.0ms (3.9%)

Algorithm
1×egg-herbie
Rules
4446×*-lowering-*.f32
4446×*-lowering-*.f64
2750×+-lowering-+.f64
2750×+-lowering-+.f32
1222×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0169976
1566883
22318833
36891833
08430833
Stop Event
1×iter limit
1×node limit
Counts
60 → 60
Calls
Call 1
Inputs
(* 1/4 (sqrt 2))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))))
(* 1/4 (sqrt 2))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* (pow v 2) (+ (* -27/64 (* (pow v 2) (sqrt 2))) (* -9/32 (sqrt 2)))))))
(* 1/4 (* v (* (sqrt -3) (sqrt 2))))
(* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))
(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
(* -1/4 (* v (* (sqrt -3) (sqrt 2))))
(* -1 (* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
1
(+ 1 (* -3/2 (pow v 2)))
(+ 1 (* (pow v 2) (- (* -9/8 (pow v 2)) 3/2)))
(+ 1 (* (pow v 2) (- (* (pow v 2) (- (* -27/16 (pow v 2)) 9/8)) 3/2)))
(* v (sqrt -3))
(* v (+ (sqrt -3) (* 1/2 (/ 1 (* (pow v 2) (sqrt -3))))))
(* v (- (+ (sqrt -3) (/ 1/2 (* (pow v 2) (sqrt -3)))) (/ 1/8 (* (pow v 4) (pow (sqrt -3) 3)))))
(* v (- (+ (sqrt -3) (+ (/ 1/2 (* (pow v 2) (sqrt -3))) (* 1/16 (/ 1 (* (pow v 6) (pow (sqrt -3) 5)))))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -3) 3))))))
(* -1 (* v (sqrt -3)))
(* -1 (* v (+ (sqrt -3) (* 1/2 (/ 1 (* (pow v 2) (sqrt -3)))))))
(* -1 (* v (- (+ (sqrt -3) (/ 1/2 (* (pow v 2) (sqrt -3)))) (/ 1/8 (* (pow v 4) (pow (sqrt -3) 3))))))
(* -1 (* v (- (+ (sqrt -3) (+ (/ 1/2 (* (pow v 2) (sqrt -3))) (* 1/16 (/ 1 (* (pow v 6) (pow (sqrt -3) 5)))))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -3) 3)))))))
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
Outputs
(* 1/4 (sqrt 2))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 v v) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(*.f64 #s(literal 1/4 binary64) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 v v) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal -5/2 binary64) (*.f64 (*.f64 v v) #s(literal 3/8 binary64)))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 v v) (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/8 binary64) (*.f64 (*.f64 v v) #s(literal -9/16 binary64)))) (*.f64 #s(literal 1/4 binary64) (*.f64 v v))))))
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal -3 binary64)) (*.f64 #s(literal -1/4 binary64) (*.f64 v (*.f64 v v)))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))
(*.f64 (*.f64 v (*.f64 v v)) (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))) (/.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -3 binary64))))) (*.f64 v v))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))
(*.f64 (*.f64 v (*.f64 v v)) (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))) (*.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (*.f64 v v)) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -3 binary64))))) (/.f64 #s(literal 11/24 binary64) (*.f64 v v)))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(*.f64 v (*.f64 (*.f64 v v) (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))) (*.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (+.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/24 binary64)) (sqrt.f64 #s(literal -3 binary64))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64)))) (pow.f64 v #s(literal 6 binary64))) (+.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (*.f64 v v)) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -3 binary64))))) (/.f64 #s(literal 11/24 binary64) (*.f64 v v)))))))))
(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal -3 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v v)))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))))))
(*.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))) (/.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -3 binary64))))) (*.f64 v v))) (-.f64 #s(literal 0 binary64) (*.f64 v (*.f64 v v))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(*.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))) (*.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (*.f64 v v)) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -3 binary64))))) (/.f64 #s(literal 11/24 binary64) (*.f64 v v)))))) (-.f64 #s(literal 0 binary64) (*.f64 v (*.f64 v v))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))))
(*.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))) (*.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (+.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/24 binary64)) (sqrt.f64 #s(literal -3 binary64))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64)))) (pow.f64 v #s(literal 6 binary64))) (+.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (*.f64 v v)) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -3 binary64))))) (/.f64 #s(literal 11/24 binary64) (*.f64 v v))))))) (-.f64 #s(literal 0 binary64) (*.f64 v (*.f64 v v))))
(* 1/4 (sqrt 2))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -3/8 binary64))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2))))))
(+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v v)) (+.f64 #s(literal -3/8 binary64) (*.f64 (*.f64 v v) #s(literal -9/32 binary64)))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* (pow v 2) (+ (* -27/64 (* (pow v 2) (sqrt 2))) (* -9/32 (sqrt 2)))))))
(+.f64 (*.f64 v (*.f64 v (*.f64 (*.f64 v v) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal -9/32 binary64) (*.f64 (*.f64 v v) #s(literal -27/64 binary64))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -3/8 binary64)))))
(* 1/4 (* v (* (sqrt -3) (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))))
(* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))
(*.f64 v (+.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -3 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64))))))
(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
(*.f64 v (+.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -3 binary64))))) (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1/96 binary64) (sqrt.f64 #s(literal -3 binary64)))) (*.f64 (*.f64 v v) (*.f64 v v))))))
(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
(*.f64 v (+.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1/96 binary64) (sqrt.f64 #s(literal -3 binary64)))) (*.f64 (*.f64 v v) (*.f64 v v))) (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))) (+.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -3 binary64))))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/64 binary64)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64)) (pow.f64 v #s(literal 6 binary64))))))))
(* -1/4 (* v (* (sqrt -3) (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/4 binary64) (*.f64 v (sqrt.f64 #s(literal -3 binary64)))))
(* -1 (* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
(*.f64 (+.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -3 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64))))) (-.f64 #s(literal 0 binary64) v))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
(-.f64 #s(literal 0 binary64) (*.f64 v (+.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -3 binary64))))) (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1/96 binary64) (sqrt.f64 #s(literal -3 binary64)))) (*.f64 (*.f64 v v) (*.f64 v v)))))))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))))
(*.f64 (+.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1/96 binary64) (sqrt.f64 #s(literal -3 binary64)))) (*.f64 (*.f64 v v) (*.f64 v v))) (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))) (+.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -3 binary64))))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/64 binary64)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64)) (pow.f64 v #s(literal 6 binary64))))))) (-.f64 #s(literal 0 binary64) v))
(* 3 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 3 binary64))
(* 3 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 3 binary64))
(* 3 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 3 binary64))
(* 3 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 3 binary64))
(* 3 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 3 binary64))
(* 3 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 3 binary64))
(* 3 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 3 binary64))
(* 3 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 3 binary64))
(* 3 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 3 binary64))
(* 3 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 3 binary64))
(* 3 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 3 binary64))
(* 3 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 3 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -3/2 (pow v 2)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3/2 binary64)))
(+ 1 (* (pow v 2) (- (* -9/8 (pow v 2)) 3/2)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal -3/2 binary64) (*.f64 v (*.f64 v #s(literal -9/8 binary64))))))
(+ 1 (* (pow v 2) (- (* (pow v 2) (- (* -27/16 (pow v 2)) 9/8)) 3/2)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal -3/2 binary64) (*.f64 v (*.f64 v (+.f64 #s(literal -9/8 binary64) (*.f64 (*.f64 v v) #s(literal -27/16 binary64))))))))
(* v (sqrt -3))
(*.f64 v (sqrt.f64 #s(literal -3 binary64)))
(* v (+ (sqrt -3) (* 1/2 (/ 1 (* (pow v 2) (sqrt -3))))))
(*.f64 v (+.f64 (sqrt.f64 #s(literal -3 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -3 binary64)))))
(* v (- (+ (sqrt -3) (/ 1/2 (* (pow v 2) (sqrt -3)))) (/ 1/8 (* (pow v 4) (pow (sqrt -3) 3)))))
(*.f64 v (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -3 binary64))) (-.f64 (sqrt.f64 #s(literal -3 binary64)) (/.f64 (/.f64 #s(literal -1/24 binary64) (sqrt.f64 #s(literal -3 binary64))) (*.f64 (*.f64 v v) (*.f64 v v))))))
(* v (- (+ (sqrt -3) (+ (/ 1/2 (* (pow v 2) (sqrt -3))) (* 1/16 (/ 1 (* (pow v 6) (pow (sqrt -3) 5)))))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -3) 3))))))
(*.f64 v (+.f64 (+.f64 (sqrt.f64 #s(literal -3 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -3 binary64)))) (-.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 v #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (/.f64 (/.f64 #s(literal -1/24 binary64) (sqrt.f64 #s(literal -3 binary64))) (*.f64 (*.f64 v v) (*.f64 v v))))))
(* -1 (* v (sqrt -3)))
(-.f64 #s(literal 0 binary64) (*.f64 v (sqrt.f64 #s(literal -3 binary64))))
(* -1 (* v (+ (sqrt -3) (* 1/2 (/ 1 (* (pow v 2) (sqrt -3)))))))
(*.f64 (+.f64 (sqrt.f64 #s(literal -3 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -3 binary64)))) (-.f64 #s(literal 0 binary64) v))
(* -1 (* v (- (+ (sqrt -3) (/ 1/2 (* (pow v 2) (sqrt -3)))) (/ 1/8 (* (pow v 4) (pow (sqrt -3) 3))))))
(*.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -3 binary64))) (-.f64 (sqrt.f64 #s(literal -3 binary64)) (/.f64 (/.f64 #s(literal -1/24 binary64) (sqrt.f64 #s(literal -3 binary64))) (*.f64 (*.f64 v v) (*.f64 v v))))) (-.f64 #s(literal 0 binary64) v))
(* -1 (* v (- (+ (sqrt -3) (+ (/ 1/2 (* (pow v 2) (sqrt -3))) (* 1/16 (/ 1 (* (pow v 6) (pow (sqrt -3) 5)))))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -3) 3)))))))
(*.f64 (+.f64 (+.f64 (sqrt.f64 #s(literal -3 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -3 binary64)))) (-.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 v #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (/.f64 (/.f64 #s(literal -1/24 binary64) (sqrt.f64 #s(literal -3 binary64))) (*.f64 (*.f64 v v) (*.f64 v v))))) (-.f64 #s(literal 0 binary64) v))
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)

eval57.0ms (0.8%)

Compiler

Compiled 9949 to 1081 computations (89.1% saved)

prune41.0ms (0.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New3534357
Fresh000
Picked101
Done000
Total3544358
Accuracy
100.0%
Counts
358 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64))))) #s(literal 4 binary64))
▶99.8%
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -3/8 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
▶99.4%
(*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
▶99.4%
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
Compiler

Compiled 52 to 39 computations (25% saved)

simplify179.0ms (2.6%)

Algorithm
1×egg-herbie
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(-.f64 #s(literal 1 binary64) (*.f64 v v))
✓cost-diff0
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))))
✓cost-diff0
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64))))) #s(literal 4 binary64))
✓cost-diff128
(*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64))
✓cost-diff0
(+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -3/8 binary64)))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -3/8 binary64))))
✓cost-diff0
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -3/8 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓cost-diff0
(-.f64 #s(literal 1 binary64) (*.f64 v v))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
Rules
2518×*-lowering-*.f32
2518×*-lowering-*.f64
2122×sum3-define
1906×fnmadd-define
1156×fma-lowering-fma.f32
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
022137
160130
2168130
3502130
41796129
54184129
08297129
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* 1/4 (sqrt 2))
1/4
(sqrt 2)
2
(* (* 1/4 (sqrt 2)) (- 1 (* v v)))
(* 1/4 (sqrt 2))
1/4
(sqrt 2)
2
(- 1 (* v v))
1
(* v v)
v
(* (* (sqrt 2) (+ 1/4 (* (* v v) -3/8))) (- 1 (* v v)))
(* (sqrt 2) (+ 1/4 (* (* v v) -3/8)))
(sqrt 2)
2
(+ 1/4 (* (* v v) -3/8))
1/4
(* (* v v) -3/8)
(* v v)
v
-3/8
(- 1 (* v v))
1
(/ (* (- 1 (* v v)) (sqrt (+ 2 (* (* (* v v) -3) 2)))) 4)
(* (- 1 (* v v)) (sqrt (+ 2 (* (* (* v v) -3) 2))))
(- 1 (* v v))
1
(* v v)
v
(sqrt (+ 2 (* (* (* v v) -3) 2)))
(+ 2 (* (* (* v v) -3) 2))
2
(* (* (* v v) -3) 2)
(* (* v v) -3)
-3
4
Outputs
(* 1/4 (sqrt 2))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
1/4
#s(literal 1/4 binary64)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(* (* 1/4 (sqrt 2)) (- 1 (* v v)))
(*.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(* 1/4 (sqrt 2))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
1/4
#s(literal 1/4 binary64)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(- 1 (* v v))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
1
#s(literal 1 binary64)
(* v v)
(*.f64 v v)
v
(* (* (sqrt 2) (+ 1/4 (* (* v v) -3/8))) (- 1 (* v v)))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -3/8 binary64)))))
(* (sqrt 2) (+ 1/4 (* (* v v) -3/8)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -3/8 binary64))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(+ 1/4 (* (* v v) -3/8))
(+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -3/8 binary64)))
1/4
#s(literal 1/4 binary64)
(* (* v v) -3/8)
(*.f64 (*.f64 v v) #s(literal -3/8 binary64))
(* v v)
(*.f64 v v)
v
-3/8
#s(literal -3/8 binary64)
(- 1 (* v v))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
1
#s(literal 1 binary64)
(/ (* (- 1 (* v v)) (sqrt (+ 2 (* (* (* v v) -3) 2)))) 4)
(*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64))))
(* (- 1 (* v v)) (sqrt (+ 2 (* (* (* v v) -3) 2))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
(- 1 (* v v))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
1
#s(literal 1 binary64)
(* v v)
(*.f64 v v)
v
(sqrt (+ 2 (* (* (* v v) -3) 2)))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))
(+ 2 (* (* (* v v) -3) 2))
(+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))
2
#s(literal 2 binary64)
(* (* (* v v) -3) 2)
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* (* v v) -3)
(*.f64 v (*.f64 v #s(literal -3 binary64)))
-3
#s(literal -3 binary64)
4
#s(literal 4 binary64)

localize156.0ms (2.3%)

Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 v v)
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64))))
✓accuracy100.0%
(*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64))
✓accuracy99.7%
(*.f64 (*.f64 v v) #s(literal -3 binary64))
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy100.0%
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -3/8 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓accuracy100.0%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -3/8 binary64))))
✓accuracy99.8%
(*.f64 (*.f64 v v) #s(literal -3/8 binary64))
✓accuracy100.0%
(*.f64 v v)
✓accuracy100.0%
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy100.0%
(*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓accuracy100.0%
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
Results
93.0ms256×0valid
Compiler

Compiled 169 to 23 computations (86.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 25.0ms
ival-mult: 14.0ms (55.4% of total)
ival-sqrt: 4.0ms (15.8% of total)
ival-div: 2.0ms (7.9% of total)
ival-add: 2.0ms (7.9% of total)
ival-sub: 1.0ms (4% of total)
const: 1.0ms (4% of total)
backward-pass: 0.0ms (0% of total)

series13.0ms (0.2%)

Counts
14 → 144
Calls
Call 1
Inputs
#<alt (* 1/4 (sqrt 2))>
#<alt (sqrt 2)>
#<alt (* (* 1/4 (sqrt 2)) (- 1 (* v v)))>
#<alt (- 1 (* v v))>
#<alt (* (* (sqrt 2) (+ 1/4 (* (* v v) -3/8))) (- 1 (* v v)))>
#<alt (* (sqrt 2) (+ 1/4 (* (* v v) -3/8)))>
#<alt (+ 1/4 (* (* v v) -3/8))>
#<alt (* (* (* v v) -3) 2)>
#<alt (/ (* (- 1 (* v v)) (sqrt (+ 2 (* (* (* v v) -3) 2)))) 4)>
#<alt (* (- 1 (* v v)) (sqrt (+ 2 (* (* (* v v) -3) 2))))>
#<alt (* v v)>
#<alt (* (* v v) -3/8)>
#<alt (* (* v v) -3)>
#<alt (sqrt (+ 2 (* (* (* v v) -3) 2)))>
Outputs
#<alt (* 1/4 (sqrt 2))>
#<alt (+ (* -1/4 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (+ (* -1/4 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (+ (* -1/4 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (* -1/4 (* (pow v 2) (sqrt 2)))>
#<alt (* (pow v 2) (+ (* -1/4 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -1/4 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -1/4 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* -1/4 (* (pow v 2) (sqrt 2)))>
#<alt (* (pow v 2) (+ (* -1/4 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -1/4 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -1/4 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt 1>
#<alt (+ 1 (* -1 (pow v 2)))>
#<alt (+ 1 (* -1 (pow v 2)))>
#<alt (+ 1 (* -1 (pow v 2)))>
#<alt (* -1 (pow v 2))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* -1 (pow v 2))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* 1/4 (sqrt 2))>
#<alt (+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 3/8 (* (pow v 2) (sqrt 2))))))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 3/8 (* (pow v 2) (sqrt 2))))))>
#<alt (* 3/8 (* (pow v 4) (sqrt 2)))>
#<alt (* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (* 3/8 (sqrt 2))))>
#<alt (* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (+ (* 1/4 (/ (sqrt 2) (pow v 4))) (* 3/8 (sqrt 2)))))>
#<alt (* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (+ (* 1/4 (/ (sqrt 2) (pow v 4))) (* 3/8 (sqrt 2)))))>
#<alt (* 3/8 (* (pow v 4) (sqrt 2)))>
#<alt (* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (* 3/8 (sqrt 2))))>
#<alt (* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (+ (* 1/4 (/ (sqrt 2) (pow v 4))) (* 3/8 (sqrt 2)))))>
#<alt (* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (+ (* 1/4 (/ (sqrt 2) (pow v 4))) (* 3/8 (sqrt 2)))))>
#<alt (* 1/4 (sqrt 2))>
#<alt (+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (* -3/8 (* (pow v 2) (sqrt 2)))>
#<alt (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* -3/8 (* (pow v 2) (sqrt 2)))>
#<alt (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt 1/4>
#<alt (+ 1/4 (* -3/8 (pow v 2)))>
#<alt (+ 1/4 (* -3/8 (pow v 2)))>
#<alt (+ 1/4 (* -3/8 (pow v 2)))>
#<alt (* -3/8 (pow v 2))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 3/8))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 3/8))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 3/8))>
#<alt (* -3/8 (pow v 2))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 3/8))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 3/8))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 3/8))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* 1/4 (sqrt 2))>
#<alt (+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2)))))))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (- (* 3 (/ 1 (sqrt 2))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 1/4 (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2))))))))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2))))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (- (* 9/2 (/ 1 (pow (sqrt 2) 3))) (* 27/2 (/ 1 (pow (sqrt 2) 5)))))) (* 1/4 (- (* 3 (/ 1 (sqrt 2))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))))))))>
#<alt (* -1/4 (* (pow v 3) (sqrt -6)))>
#<alt (* (pow v 3) (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2)))))>
#<alt (* (pow v 3) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (+ (/ 1 (sqrt -6)) (* 1/2 (/ 1 (pow (sqrt -6) 3)))) (pow v 4))) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2))))))>
#<alt (* (pow v 3) (+ (* -1/4 (sqrt -6)) (+ (* -1/4 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* 1/4 (/ (+ (/ 1 (sqrt -6)) (* 1/2 (/ 1 (pow (sqrt -6) 3)))) (pow v 4))) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2)))))))>
#<alt (* 1/4 (* (pow v 3) (sqrt -6)))>
#<alt (* -1 (* (pow v 3) (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2))))))>
#<alt (* -1 (* (pow v 3) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (+ (/ 1 (sqrt -6)) (* 1/2 (/ 1 (pow (sqrt -6) 3)))) (pow v 4))) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2)))))))>
#<alt (* -1 (* (pow v 3) (+ (* -1/4 (sqrt -6)) (+ (* -1/4 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* 1/4 (/ (+ (/ 1 (sqrt -6)) (* 1/2 (/ 1 (pow (sqrt -6) 3)))) (pow v 4))) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2))))))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (+ (* -1 (sqrt 2)) (* (pow v 2) (- (* 3 (/ 1 (sqrt 2))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (+ (* -1 (sqrt 2)) (* (pow v 2) (- (+ (* 3 (/ 1 (sqrt 2))) (* (pow v 2) (- (* 9/2 (/ 1 (pow (sqrt 2) 3))) (* 27/2 (/ 1 (pow (sqrt 2) 5)))))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* -1 (* (pow v 3) (sqrt -6)))>
#<alt (* (pow v 3) (- (+ (* -1 (sqrt -6)) (/ (sqrt -6) (pow v 2))) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2))))) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (* -1 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2)))))) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* (pow v 3) (sqrt -6))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1 (sqrt -6)) (/ (sqrt -6) (pow v 2))) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2))))) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (* -1 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2)))))) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (* -3/8 (pow v 2))>
#<alt (* -3/8 (pow v 2))>
#<alt (* -3/8 (pow v 2))>
#<alt (* -3/8 (pow v 2))>
#<alt (* -3/8 (pow v 2))>
#<alt (* -3/8 (pow v 2))>
#<alt (* -3/8 (pow v 2))>
#<alt (* -3/8 (pow v 2))>
#<alt (* -3/8 (pow v 2))>
#<alt (* -3/8 (pow v 2))>
#<alt (* -3/8 (pow v 2))>
#<alt (* -3/8 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* v (sqrt -6))>
#<alt (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>
Calls

36 calls:

TimeVariablePointExpression
2.0ms
v
@0
(* (sqrt 2) (+ 1/4 (* (* v v) -3/8)))
1.0ms
v
@inf
(* (* (* v v) -3) 2)
1.0ms
v
@inf
(/ (* (- 1 (* v v)) (sqrt (+ 2 (* (* (* v v) -3) 2)))) 4)
1.0ms
v
@0
(/ (* (- 1 (* v v)) (sqrt (+ 2 (* (* (* v v) -3) 2)))) 4)
0.0ms
v
@0
(* (- 1 (* v v)) (sqrt (+ 2 (* (* (* v v) -3) 2))))

rewrite329.0ms (4.8%)

Algorithm
1×batch-egg-rewrite
Rules
5840×*-lowering-*.f32
5840×*-lowering-*.f64
2956×/-lowering-/.f32
2956×/-lowering-/.f64
1476×+-lowering-+.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02295
111289
279889
0844989
Stop Event
1×iter limit
1×node limit
Counts
14 → 635
Calls
Call 1
Inputs
(* 1/4 (sqrt 2))
(sqrt 2)
(* (* 1/4 (sqrt 2)) (- 1 (* v v)))
(- 1 (* v v))
(* (* (sqrt 2) (+ 1/4 (* (* v v) -3/8))) (- 1 (* v v)))
(* (sqrt 2) (+ 1/4 (* (* v v) -3/8)))
(+ 1/4 (* (* v v) -3/8))
(* (* (* v v) -3) 2)
(/ (* (- 1 (* v v)) (sqrt (+ 2 (* (* (* v v) -3) 2)))) 4)
(* (- 1 (* v v)) (sqrt (+ 2 (* (* (* v v) -3) 2))))
(* v v)
(* (* v v) -3/8)
(* (* v v) -3)
(sqrt (+ 2 (* (* (* v v) -3) 2)))
Outputs
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 1/4 binary64)))
(*.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 0 binary64) (*.f64 v v)))))
(+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))))
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(/.f64 (+.f64 (pow.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 3 binary64)) (pow.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) #s(literal 3 binary64))) (+.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (-.f64 (*.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))))))
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(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -216 binary64))))) (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) (-.f64 (*.f64 (*.f64 v v) #s(literal -12 binary64)) #s(literal 4 binary64))))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) (*.f64 #s(literal 36 binary64) (*.f64 v v)))))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))
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(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
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(*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(*.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
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(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 v)))
(pow.f64 v #s(literal 2 binary64))
(pow.f64 (*.f64 v v) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 v)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 v v))
(*.f64 v v)
(*.f64 v (*.f64 v #s(literal 1 binary64)))
(*.f64 (*.f64 v v) #s(literal 1 binary64))
(*.f64 (exp.f64 (log.f64 v)) (exp.f64 (log.f64 v)))
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3/8 binary64)))
(*.f64 v (*.f64 v #s(literal -3/8 binary64)))
(*.f64 (*.f64 v v) #s(literal -3/8 binary64))
(*.f64 #s(literal -3/8 binary64) (*.f64 v v))
(*.f64 (*.f64 (*.f64 v v) #s(literal -3/8 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 v #s(literal -3/8 binary64)) v)
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64)))
(*.f64 v (*.f64 v #s(literal -3 binary64)))
(*.f64 v (*.f64 (*.f64 v #s(literal -3 binary64)) #s(literal 1 binary64)))
(*.f64 (*.f64 v v) #s(literal -3 binary64))
(*.f64 #s(literal -3 binary64) (*.f64 v v))
(*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 v #s(literal -3 binary64)) v)
(*.f64 (*.f64 v #s(literal -3 binary64)) (*.f64 v #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) (-.f64 (*.f64 (*.f64 v v) #s(literal -12 binary64)) #s(literal 4 binary64))))) (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -216 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))) (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) (*.f64 #s(literal 36 binary64) (*.f64 v v)))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -216 binary64)))) (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) (-.f64 (*.f64 (*.f64 v v) #s(literal -12 binary64)) #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -216 binary64)))) (sqrt.f64 (+.f64 (*.f64 (*.f64 v v) (*.f64 #s(literal 36 binary64) (*.f64 v v))) (+.f64 #s(literal 4 binary64) (*.f64 #s(literal 12 binary64) (*.f64 v v))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) (*.f64 #s(literal 36 binary64) (*.f64 v v))))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -216 binary64))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) (-.f64 (*.f64 (*.f64 v v) #s(literal -12 binary64)) #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) (*.f64 #s(literal 36 binary64) (*.f64 v v)))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))))
(/.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 v v) (*.f64 #s(literal 36 binary64) (*.f64 v v))) #s(literal -4 binary64))) (sqrt.f64 (+.f64 (*.f64 v (*.f64 v #s(literal -6 binary64))) #s(literal -2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -216 binary64))))) (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) (-.f64 (*.f64 (*.f64 v v) #s(literal -12 binary64)) #s(literal 4 binary64))))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) (*.f64 #s(literal 36 binary64) (*.f64 v v)))))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -216 binary64))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) (-.f64 (*.f64 (*.f64 v v) #s(literal -12 binary64)) #s(literal 4 binary64)))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) (*.f64 #s(literal 36 binary64) (*.f64 v v)))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))))
(pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64)))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -216 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) (-.f64 (*.f64 (*.f64 v v) #s(literal -12 binary64)) #s(literal 4 binary64))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -216 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) (-.f64 (*.f64 (*.f64 v v) #s(literal -12 binary64)) #s(literal 4 binary64)))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -216 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) (-.f64 (*.f64 (*.f64 v v) #s(literal -12 binary64)) #s(literal 4 binary64)))))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) (*.f64 #s(literal 36 binary64) (*.f64 v v))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) (*.f64 #s(literal 36 binary64) (*.f64 v v))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) (*.f64 #s(literal 36 binary64) (*.f64 v v))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))))
(*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64))))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal 1/4 binary64)))

simplify343.0ms (5%)

Algorithm
1×egg-herbie
Rules
5700×*-lowering-*.f32
5700×*-lowering-*.f64
4118×+-lowering-+.f64
4118×+-lowering-+.f32
1828×fma-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02001714
16341401
223001348
084601348
Stop Event
1×iter limit
1×node limit
Counts
144 → 144
Calls
Call 1
Inputs
(* 1/4 (sqrt 2))
(+ (* -1/4 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* -1/4 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* -1/4 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(* -1/4 (* (pow v 2) (sqrt 2)))
(* (pow v 2) (+ (* -1/4 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -1/4 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -1/4 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* -1/4 (* (pow v 2) (sqrt 2)))
(* (pow v 2) (+ (* -1/4 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -1/4 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -1/4 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
1
(+ 1 (* -1 (pow v 2)))
(+ 1 (* -1 (pow v 2)))
(+ 1 (* -1 (pow v 2)))
(* -1 (pow v 2))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* -1 (pow v 2))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* 1/4 (sqrt 2))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 3/8 (* (pow v 2) (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 3/8 (* (pow v 2) (sqrt 2))))))
(* 3/8 (* (pow v 4) (sqrt 2)))
(* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (* 3/8 (sqrt 2))))
(* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (+ (* 1/4 (/ (sqrt 2) (pow v 4))) (* 3/8 (sqrt 2)))))
(* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (+ (* 1/4 (/ (sqrt 2) (pow v 4))) (* 3/8 (sqrt 2)))))
(* 3/8 (* (pow v 4) (sqrt 2)))
(* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (* 3/8 (sqrt 2))))
(* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (+ (* 1/4 (/ (sqrt 2) (pow v 4))) (* 3/8 (sqrt 2)))))
(* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (+ (* 1/4 (/ (sqrt 2) (pow v 4))) (* 3/8 (sqrt 2)))))
(* 1/4 (sqrt 2))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(* -3/8 (* (pow v 2) (sqrt 2)))
(* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* -3/8 (* (pow v 2) (sqrt 2)))
(* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
1/4
(+ 1/4 (* -3/8 (pow v 2)))
(+ 1/4 (* -3/8 (pow v 2)))
(+ 1/4 (* -3/8 (pow v 2)))
(* -3/8 (pow v 2))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 3/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 3/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 3/8))
(* -3/8 (pow v 2))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 3/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 3/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 3/8))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* 1/4 (sqrt 2))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2)))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (- (* 3 (/ 1 (sqrt 2))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 1/4 (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2))))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2))))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (- (* 9/2 (/ 1 (pow (sqrt 2) 3))) (* 27/2 (/ 1 (pow (sqrt 2) 5)))))) (* 1/4 (- (* 3 (/ 1 (sqrt 2))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))))))))
(* -1/4 (* (pow v 3) (sqrt -6)))
(* (pow v 3) (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2)))))
(* (pow v 3) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (+ (/ 1 (sqrt -6)) (* 1/2 (/ 1 (pow (sqrt -6) 3)))) (pow v 4))) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2))))))
(* (pow v 3) (+ (* -1/4 (sqrt -6)) (+ (* -1/4 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* 1/4 (/ (+ (/ 1 (sqrt -6)) (* 1/2 (/ 1 (pow (sqrt -6) 3)))) (pow v 4))) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2)))))))
(* 1/4 (* (pow v 3) (sqrt -6)))
(* -1 (* (pow v 3) (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (+ (/ 1 (sqrt -6)) (* 1/2 (/ 1 (pow (sqrt -6) 3)))) (pow v 4))) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2)))))))
(* -1 (* (pow v 3) (+ (* -1/4 (sqrt -6)) (+ (* -1/4 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* 1/4 (/ (+ (/ 1 (sqrt -6)) (* 1/2 (/ 1 (pow (sqrt -6) 3)))) (pow v 4))) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2))))))))
(sqrt 2)
(+ (sqrt 2) (* (pow v 2) (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (+ (* -1 (sqrt 2)) (* (pow v 2) (- (* 3 (/ 1 (sqrt 2))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (+ (* -1 (sqrt 2)) (* (pow v 2) (- (+ (* 3 (/ 1 (sqrt 2))) (* (pow v 2) (- (* 9/2 (/ 1 (pow (sqrt 2) 3))) (* 27/2 (/ 1 (pow (sqrt 2) 5)))))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 3 (/ 1 (sqrt 2))))))
(* -1 (* (pow v 3) (sqrt -6)))
(* (pow v 3) (- (+ (* -1 (sqrt -6)) (/ (sqrt -6) (pow v 2))) (/ 1 (* (pow v 2) (sqrt -6)))))
(* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2))))) (/ 1 (* (pow v 2) (sqrt -6)))))
(* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (* -1 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2)))))) (/ 1 (* (pow v 2) (sqrt -6)))))
(* (pow v 3) (sqrt -6))
(* -1 (* (pow v 3) (- (+ (* -1 (sqrt -6)) (/ (sqrt -6) (pow v 2))) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2))))) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (* -1 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2)))))) (/ 1 (* (pow v 2) (sqrt -6))))))
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(* -3/8 (pow v 2))
(* -3/8 (pow v 2))
(* -3/8 (pow v 2))
(* -3/8 (pow v 2))
(* -3/8 (pow v 2))
(* -3/8 (pow v 2))
(* -3/8 (pow v 2))
(* -3/8 (pow v 2))
(* -3/8 (pow v 2))
(* -3/8 (pow v 2))
(* -3/8 (pow v 2))
(* -3/8 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(sqrt 2)
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(* v (sqrt -6))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (sqrt -6)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
Outputs
(* 1/4 (sqrt 2))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/4 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 v v))))
(+ (* -1/4 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 v v))))
(+ (* -1/4 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 v v))))
(* -1/4 (* (pow v 2) (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/4 binary64) (*.f64 v v)))
(* (pow v 2) (+ (* -1/4 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 v v))))
(* (pow v 2) (+ (* -1/4 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 v v))))
(* (pow v 2) (+ (* -1/4 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 v v))))
(* -1/4 (* (pow v 2) (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/4 binary64) (*.f64 v v)))
(* (pow v 2) (+ (* -1/4 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 v v))))
(* (pow v 2) (+ (* -1/4 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 v v))))
(* (pow v 2) (+ (* -1/4 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 v v))))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow v 2)))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(+ 1 (* -1 (pow v 2)))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(+ 1 (* -1 (pow v 2)))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(* -1 (pow v 2))
(-.f64 #s(literal 0 binary64) (*.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(* -1 (pow v 2))
(-.f64 #s(literal 0 binary64) (*.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(* 1/4 (sqrt 2))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -5/8 binary64))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 3/8 (* (pow v 2) (sqrt 2))))))
(+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v v)) (+.f64 #s(literal -5/8 binary64) (*.f64 (*.f64 v v) #s(literal 3/8 binary64)))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 3/8 (* (pow v 2) (sqrt 2))))))
(+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v v)) (+.f64 #s(literal -5/8 binary64) (*.f64 (*.f64 v v) #s(literal 3/8 binary64)))))
(* 3/8 (* (pow v 4) (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 v (*.f64 (*.f64 v v) #s(literal 3/8 binary64)))))
(* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (* 3/8 (sqrt 2))))
(*.f64 (*.f64 v (*.f64 v (*.f64 v v))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal -5/8 binary64) (*.f64 v v)) #s(literal 3/8 binary64))))
(* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (+ (* 1/4 (/ (sqrt 2) (pow v 4))) (* 3/8 (sqrt 2)))))
(*.f64 (*.f64 v (*.f64 v (*.f64 v v))) (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal -5/8 binary64) (*.f64 v v)) #s(literal 3/8 binary64))) (/.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 v (*.f64 v (*.f64 v v))))))
(* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (+ (* 1/4 (/ (sqrt 2) (pow v 4))) (* 3/8 (sqrt 2)))))
(*.f64 (*.f64 v (*.f64 v (*.f64 v v))) (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal -5/8 binary64) (*.f64 v v)) #s(literal 3/8 binary64))) (/.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 v (*.f64 v (*.f64 v v))))))
(* 3/8 (* (pow v 4) (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 v (*.f64 (*.f64 v v) #s(literal 3/8 binary64)))))
(* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (* 3/8 (sqrt 2))))
(*.f64 (*.f64 v (*.f64 v (*.f64 v v))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal -5/8 binary64) (*.f64 v v)) #s(literal 3/8 binary64))))
(* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (+ (* 1/4 (/ (sqrt 2) (pow v 4))) (* 3/8 (sqrt 2)))))
(*.f64 (*.f64 v (*.f64 v (*.f64 v v))) (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal -5/8 binary64) (*.f64 v v)) #s(literal 3/8 binary64))) (/.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 v (*.f64 v (*.f64 v v))))))
(* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (+ (* 1/4 (/ (sqrt 2) (pow v 4))) (* 3/8 (sqrt 2)))))
(*.f64 (*.f64 v (*.f64 v (*.f64 v v))) (+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal -5/8 binary64) (*.f64 v v)) #s(literal 3/8 binary64))) (/.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 v (*.f64 v (*.f64 v v))))))
(* 1/4 (sqrt 2))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -3/8 binary64)))))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -3/8 binary64)))))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -3/8 binary64)))))
(* -3/8 (* (pow v 2) (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 v #s(literal -3/8 binary64))))
(* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -3/8 binary64)))))
(* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -3/8 binary64)))))
(* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -3/8 binary64)))))
(* -3/8 (* (pow v 2) (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 v #s(literal -3/8 binary64))))
(* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -3/8 binary64)))))
(* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -3/8 binary64)))))
(* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -3/8 binary64)))))
1/4
#s(literal 1/4 binary64)
(+ 1/4 (* -3/8 (pow v 2)))
(+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -3/8 binary64))))
(+ 1/4 (* -3/8 (pow v 2)))
(+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -3/8 binary64))))
(+ 1/4 (* -3/8 (pow v 2)))
(+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -3/8 binary64))))
(* -3/8 (pow v 2))
(*.f64 v (*.f64 v #s(literal -3/8 binary64)))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 3/8))
(+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -3/8 binary64))))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 3/8))
(+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -3/8 binary64))))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 3/8))
(+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -3/8 binary64))))
(* -3/8 (pow v 2))
(*.f64 v (*.f64 v #s(literal -3/8 binary64)))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 3/8))
(+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -3/8 binary64))))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 3/8))
(+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -3/8 binary64))))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 3/8))
(+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -3/8 binary64))))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
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eval149.0ms (2.1%)

Compiler

Compiled 29549 to 2389 computations (91.9% saved)

prune97.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New9952997
Fresh000
Picked314
Done000
Total99831001
Accuracy
100.0%
Counts
1001 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) #s(literal 4 binary64))
▶99.9%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -5/8 binary64))))
✓99.4%
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
Compiler

Compiled 33 to 26 computations (21.2% saved)

simplify152.0ms (2.2%)

Algorithm
1×egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 v v)
✓cost-diff0
(-.f64 #s(literal 1 binary64) (*.f64 v v))
✓cost-diff0
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))
✓cost-diff0
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) #s(literal 4 binary64))
✓cost-diff0
(*.f64 (*.f64 v v) #s(literal -5/8 binary64))
✓cost-diff0
(+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -5/8 binary64)))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -5/8 binary64))))
Rules
2242×fnmadd-define
1834×fmsub-define
1814×fma-lowering-fma.f32
1814×fma-lowering-fma.f64
1506×fmm-def
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
01881
14475
28975
316775
432975
558375
6125674
7268874
8486874
0813274
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* (sqrt 2) (+ 1/4 (* (* v v) -5/8)))
(sqrt 2)
2
(+ 1/4 (* (* v v) -5/8))
1/4
(* (* v v) -5/8)
(* v v)
v
-5/8
(/ (* (- 1 (* v v)) (sqrt (+ 2 (* (* v v) -6)))) 4)
(* (- 1 (* v v)) (sqrt (+ 2 (* (* v v) -6))))
(- 1 (* v v))
1
(* v v)
v
(sqrt (+ 2 (* (* v v) -6)))
(+ 2 (* (* v v) -6))
2
(* (* v v) -6)
-6
4
Outputs
(* (sqrt 2) (+ 1/4 (* (* v v) -5/8)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -5/8 binary64))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(+ 1/4 (* (* v v) -5/8))
(+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -5/8 binary64)))
1/4
#s(literal 1/4 binary64)
(* (* v v) -5/8)
(*.f64 (*.f64 v v) #s(literal -5/8 binary64))
(* v v)
(*.f64 v v)
v
-5/8
#s(literal -5/8 binary64)
(/ (* (- 1 (* v v)) (sqrt (+ 2 (* (* v v) -6)))) 4)
(*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64))))
(* (- 1 (* v v)) (sqrt (+ 2 (* (* v v) -6))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))
(- 1 (* v v))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
1
#s(literal 1 binary64)
(* v v)
(*.f64 v v)
v
(sqrt (+ 2 (* (* v v) -6)))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))
(+ 2 (* (* v v) -6))
(+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))
2
#s(literal 2 binary64)
(* (* v v) -6)
(*.f64 (*.f64 v v) #s(literal -6 binary64))
-6
#s(literal -6 binary64)
4
#s(literal 4 binary64)

localize107.0ms (1.5%)

Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))
✓accuracy100.0%
(*.f64 v v)
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))
✓accuracy99.7%
(*.f64 (*.f64 v v) #s(literal -6 binary64))
✓accuracy100.0%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -5/8 binary64))))
✓accuracy100.0%
(*.f64 v v)
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy99.8%
(*.f64 (*.f64 v v) #s(literal -5/8 binary64))
Results
85.0ms256×0valid
Compiler

Compiled 96 to 19 computations (80.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 21.0ms
ival-mult: 9.0ms (43% of total)
ival-sqrt: 4.0ms (19.1% of total)
ival-add: 3.0ms (14.3% of total)
ival-sub: 2.0ms (9.6% of total)
ival-div: 2.0ms (9.6% of total)
const: 1.0ms (4.8% of total)
backward-pass: 0.0ms (0% of total)

series3.0ms (0%)

Counts
10 → 108
Calls
Call 1
Inputs
#<alt (* (sqrt 2) (+ 1/4 (* (* v v) -5/8)))>
#<alt (sqrt 2)>
#<alt (+ 1/4 (* (* v v) -5/8))>
#<alt (* (* v v) -5/8)>
#<alt (/ (* (- 1 (* v v)) (sqrt (+ 2 (* (* v v) -6)))) 4)>
#<alt (* (- 1 (* v v)) (sqrt (+ 2 (* (* v v) -6))))>
#<alt (- 1 (* v v))>
#<alt (* v v)>
#<alt (* (* v v) -6)>
#<alt (sqrt (+ 2 (* (* v v) -6)))>
Outputs
#<alt (* 1/4 (sqrt 2))>
#<alt (+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (* -5/8 (* (pow v 2) (sqrt 2)))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* -5/8 (* (pow v 2) (sqrt 2)))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt 1/4>
#<alt (+ 1/4 (* -5/8 (pow v 2)))>
#<alt (+ 1/4 (* -5/8 (pow v 2)))>
#<alt (+ 1/4 (* -5/8 (pow v 2)))>
#<alt (* -5/8 (pow v 2))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* -5/8 (pow v 2))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* 1/4 (sqrt 2))>
#<alt (+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2)))))))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (- (* 3 (/ 1 (sqrt 2))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 1/4 (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2))))))))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2))))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (- (* 9/2 (/ 1 (pow (sqrt 2) 3))) (* 27/2 (/ 1 (pow (sqrt 2) 5)))))) (* 1/4 (- (* 3 (/ 1 (sqrt 2))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))))))))>
#<alt (* -1/4 (* (pow v 3) (sqrt -6)))>
#<alt (* (pow v 3) (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2)))))>
#<alt (* (pow v 3) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (+ (/ 1 (sqrt -6)) (* 1/2 (/ 1 (pow (sqrt -6) 3)))) (pow v 4))) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2))))))>
#<alt (* (pow v 3) (+ (* -1/4 (sqrt -6)) (+ (* -1/4 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* 1/4 (/ (+ (/ 1 (sqrt -6)) (* 1/2 (/ 1 (pow (sqrt -6) 3)))) (pow v 4))) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2)))))))>
#<alt (* 1/4 (* (pow v 3) (sqrt -6)))>
#<alt (* -1 (* (pow v 3) (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2))))))>
#<alt (* -1 (* (pow v 3) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (+ (/ 1 (sqrt -6)) (* 1/2 (/ 1 (pow (sqrt -6) 3)))) (pow v 4))) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2)))))))>
#<alt (* -1 (* (pow v 3) (+ (* -1/4 (sqrt -6)) (+ (* -1/4 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* 1/4 (/ (+ (/ 1 (sqrt -6)) (* 1/2 (/ 1 (pow (sqrt -6) 3)))) (pow v 4))) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2))))))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (+ (* -1 (sqrt 2)) (* (pow v 2) (- (* 3 (/ 1 (sqrt 2))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (+ (* -1 (sqrt 2)) (* (pow v 2) (- (+ (* 3 (/ 1 (sqrt 2))) (* (pow v 2) (- (* 9/2 (/ 1 (pow (sqrt 2) 3))) (* 27/2 (/ 1 (pow (sqrt 2) 5)))))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* -1 (* (pow v 3) (sqrt -6)))>
#<alt (* (pow v 3) (- (+ (* -1 (sqrt -6)) (/ (sqrt -6) (pow v 2))) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2))))) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (* -1 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2)))))) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* (pow v 3) (sqrt -6))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1 (sqrt -6)) (/ (sqrt -6) (pow v 2))) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2))))) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (* -1 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2)))))) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt 1>
#<alt (+ 1 (* -1 (pow v 2)))>
#<alt (+ 1 (* -1 (pow v 2)))>
#<alt (+ 1 (* -1 (pow v 2)))>
#<alt (* -1 (pow v 2))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* -1 (pow v 2))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* v (sqrt -6))>
#<alt (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>
Calls

27 calls:

TimeVariablePointExpression
0.0ms
v
@inf
(* (sqrt 2) (+ 1/4 (* (* v v) -5/8)))
0.0ms
v
@0
(* (sqrt 2) (+ 1/4 (* (* v v) -5/8)))
0.0ms
v
@inf
(* (* v v) -5/8)
0.0ms
v
@0
(* (* v v) -5/8)
0.0ms
v
@inf
(/ (* (- 1 (* v v)) (sqrt (+ 2 (* (* v v) -6)))) 4)

rewrite429.0ms (6.2%)

Algorithm
1×batch-egg-rewrite
Rules
4220×*-lowering-*.f32
4220×*-lowering-*.f64
2306×/-lowering-/.f32
2306×/-lowering-/.f64
1150×sum3-define
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01864
19659
268059
3676659
0814759
Stop Event
1×iter limit
1×node limit
Counts
10 → 389
Calls
Call 1
Inputs
(* (sqrt 2) (+ 1/4 (* (* v v) -5/8)))
(sqrt 2)
(+ 1/4 (* (* v v) -5/8))
(* (* v v) -5/8)
(/ (* (- 1 (* v v)) (sqrt (+ 2 (* (* v v) -6)))) 4)
(* (- 1 (* v v)) (sqrt (+ 2 (* (* v v) -6))))
(- 1 (* v v))
(* v v)
(* (* v v) -6)
(sqrt (+ 2 (* (* v v) -6)))
Outputs
(+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))))
(+.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(-.f64 (/.f64 (pow.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal 5/8 binary64))))) (/.f64 (pow.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))) #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal 5/8 binary64))))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(fma.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))))
(fma.f64 v (*.f64 v (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(fma.f64 (*.f64 v v) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(fma.f64 #s(literal -5/8 binary64) (*.f64 v (*.f64 (sqrt.f64 #s(literal 2 binary64)) v)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(fma.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) v) (*.f64 v #s(literal -5/8 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(fma.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64)) (*.f64 v v) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(fma.f64 (*.f64 v (*.f64 (sqrt.f64 #s(literal 2 binary64)) v)) #s(literal -5/8 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))) (-.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))) (+.f64 (pow.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 3 binary64)) (*.f64 #s(literal -125/512 binary64) (pow.f64 (*.f64 v (*.f64 (sqrt.f64 #s(literal 2 binary64)) v)) #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal 5/8 binary64)))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal 5/8 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v v) (-.f64 (*.f64 (*.f64 v v) #s(literal 25/64 binary64)) #s(literal -5/32 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v))) #s(literal -125/512 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal 5/8 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) #s(literal -25/64 binary64))))))
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(*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal 1/4 binary64)))

simplify354.0ms (5.1%)

Algorithm
1×egg-herbie
Rules
5460×*-lowering-*.f32
5460×*-lowering-*.f64
3850×+-lowering-+.f64
3850×+-lowering-+.f32
1490×fma-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01751326
15471071
220381040
083941040
Stop Event
1×iter limit
1×node limit
Counts
108 → 108
Calls
Call 1
Inputs
(* 1/4 (sqrt 2))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(* -5/8 (* (pow v 2) (sqrt 2)))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* -5/8 (* (pow v 2) (sqrt 2)))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
1/4
(+ 1/4 (* -5/8 (pow v 2)))
(+ 1/4 (* -5/8 (pow v 2)))
(+ 1/4 (* -5/8 (pow v 2)))
(* -5/8 (pow v 2))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* -5/8 (pow v 2))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* 1/4 (sqrt 2))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2)))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (- (* 3 (/ 1 (sqrt 2))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 1/4 (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2))))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2))))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (- (* 9/2 (/ 1 (pow (sqrt 2) 3))) (* 27/2 (/ 1 (pow (sqrt 2) 5)))))) (* 1/4 (- (* 3 (/ 1 (sqrt 2))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))))))))
(* -1/4 (* (pow v 3) (sqrt -6)))
(* (pow v 3) (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2)))))
(* (pow v 3) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (+ (/ 1 (sqrt -6)) (* 1/2 (/ 1 (pow (sqrt -6) 3)))) (pow v 4))) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2))))))
(* (pow v 3) (+ (* -1/4 (sqrt -6)) (+ (* -1/4 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* 1/4 (/ (+ (/ 1 (sqrt -6)) (* 1/2 (/ 1 (pow (sqrt -6) 3)))) (pow v 4))) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2)))))))
(* 1/4 (* (pow v 3) (sqrt -6)))
(* -1 (* (pow v 3) (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (+ (/ 1 (sqrt -6)) (* 1/2 (/ 1 (pow (sqrt -6) 3)))) (pow v 4))) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2)))))))
(* -1 (* (pow v 3) (+ (* -1/4 (sqrt -6)) (+ (* -1/4 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* 1/4 (/ (+ (/ 1 (sqrt -6)) (* 1/2 (/ 1 (pow (sqrt -6) 3)))) (pow v 4))) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2))))))))
(sqrt 2)
(+ (sqrt 2) (* (pow v 2) (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (+ (* -1 (sqrt 2)) (* (pow v 2) (- (* 3 (/ 1 (sqrt 2))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (+ (* -1 (sqrt 2)) (* (pow v 2) (- (+ (* 3 (/ 1 (sqrt 2))) (* (pow v 2) (- (* 9/2 (/ 1 (pow (sqrt 2) 3))) (* 27/2 (/ 1 (pow (sqrt 2) 5)))))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 3 (/ 1 (sqrt 2))))))
(* -1 (* (pow v 3) (sqrt -6)))
(* (pow v 3) (- (+ (* -1 (sqrt -6)) (/ (sqrt -6) (pow v 2))) (/ 1 (* (pow v 2) (sqrt -6)))))
(* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2))))) (/ 1 (* (pow v 2) (sqrt -6)))))
(* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (* -1 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2)))))) (/ 1 (* (pow v 2) (sqrt -6)))))
(* (pow v 3) (sqrt -6))
(* -1 (* (pow v 3) (- (+ (* -1 (sqrt -6)) (/ (sqrt -6) (pow v 2))) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2))))) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (* -1 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2)))))) (/ 1 (* (pow v 2) (sqrt -6))))))
1
(+ 1 (* -1 (pow v 2)))
(+ 1 (* -1 (pow v 2)))
(+ 1 (* -1 (pow v 2)))
(* -1 (pow v 2))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* -1 (pow v 2))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(sqrt 2)
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(* v (sqrt -6))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (sqrt -6)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
Outputs
(* 1/4 (sqrt 2))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v))))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v))))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v))))
(* -5/8 (* (pow v 2) (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v))))
(* -5/8 (* (pow v 2) (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v))))
1/4
#s(literal 1/4 binary64)
(+ 1/4 (* -5/8 (pow v 2)))
(+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(+ 1/4 (* -5/8 (pow v 2)))
(+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(+ 1/4 (* -5/8 (pow v 2)))
(+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* 1/4 (sqrt 2))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2)))))))
(*.f64 #s(literal 1/4 binary64) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 v (-.f64 (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (- (* 3 (/ 1 (sqrt 2))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 1/4 (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2))))))))
(*.f64 #s(literal 1/4 binary64) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 v (+.f64 (-.f64 (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 v (*.f64 v (+.f64 (/.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64)))))))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2))))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (- (* 9/2 (/ 1 (pow (sqrt 2) 3))) (* 27/2 (/ 1 (pow (sqrt 2) 5)))))) (* 1/4 (- (* 3 (/ 1 (sqrt 2))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))))))))
(+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 v v) (*.f64 #s(literal 1/4 binary64) (+.f64 (-.f64 (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 v v) (+.f64 (/.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 v v) (+.f64 (/.f64 #s(literal 9/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -27/2 binary64) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))))))))))))
(* -1/4 (* (pow v 3) (sqrt -6)))
(*.f64 (*.f64 v v) (*.f64 v (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64)))))
(* (pow v 3) (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2)))))
(*.f64 v (*.f64 v (*.f64 v (+.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v v))))))
(* (pow v 3) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (+ (/ 1 (sqrt -6)) (* 1/2 (/ 1 (pow (sqrt -6) 3)))) (pow v 4))) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2))))))
(*.f64 v (*.f64 (*.f64 v v) (+.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (/.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v v)) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal -1/48 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v (*.f64 v (*.f64 v v))))))))
(* (pow v 3) (+ (* -1/4 (sqrt -6)) (+ (* -1/4 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* 1/4 (/ (+ (/ 1 (sqrt -6)) (* 1/2 (/ 1 (pow (sqrt -6) 3)))) (pow v 4))) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2)))))))
(*.f64 v (*.f64 (*.f64 v v) (+.f64 (+.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (/.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v v)) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal -1/48 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v (*.f64 v (*.f64 v v)))))) (/.f64 (+.f64 (/.f64 #s(literal 1/48 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (pow.f64 v #s(literal 6 binary64))))))
(* 1/4 (* (pow v 3) (sqrt -6)))
(*.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v (*.f64 v (sqrt.f64 #s(literal -6 binary64))))))
(* -1 (* (pow v 3) (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2))))))
(*.f64 (+.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v v))) (*.f64 v (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(* -1 (* (pow v 3) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (+ (/ 1 (sqrt -6)) (* 1/2 (/ 1 (pow (sqrt -6) 3)))) (pow v 4))) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2)))))))
(*.f64 (+.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (/.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v v)) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal -1/48 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v (*.f64 v (*.f64 v v)))))) (*.f64 v (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(* -1 (* (pow v 3) (+ (* -1/4 (sqrt -6)) (+ (* -1/4 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* 1/4 (/ (+ (/ 1 (sqrt -6)) (* 1/2 (/ 1 (pow (sqrt -6) 3)))) (pow v 4))) (* 1/4 (/ (- (sqrt -6) (/ 1 (sqrt -6))) (pow v 2))))))))
(*.f64 (+.f64 (+.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (/.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v v)) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal -1/48 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v (*.f64 v (*.f64 v v)))))) (/.f64 (+.f64 (/.f64 #s(literal 1/48 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (pow.f64 v #s(literal 6 binary64)))) (*.f64 v (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* (pow v 2) (- (* -1 (sqrt 2)) (* 3 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 v (-.f64 (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* (pow v 2) (- (+ (* -1 (sqrt 2)) (* (pow v 2) (- (* 3 (/ 1 (sqrt 2))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 3 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 v (+.f64 (-.f64 (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 v (*.f64 v (+.f64 (/.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64))))))))))
(+ (sqrt 2) (* (pow v 2) (- (+ (* -1 (sqrt 2)) (* (pow v 2) (- (+ (* 3 (/ 1 (sqrt 2))) (* (pow v 2) (- (* 9/2 (/ 1 (pow (sqrt 2) 3))) (* 27/2 (/ 1 (pow (sqrt 2) 5)))))) (* 9/2 (/ 1 (pow (sqrt 2) 3)))))) (* 3 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 v v) (+.f64 (-.f64 (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 v v) (+.f64 (/.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 v v) (+.f64 (/.f64 #s(literal 9/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -27/2 binary64) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64)))))))))))
(* -1 (* (pow v 3) (sqrt -6)))
(-.f64 #s(literal 0 binary64) (*.f64 v (*.f64 v (*.f64 v (sqrt.f64 #s(literal -6 binary64))))))
(* (pow v 3) (- (+ (* -1 (sqrt -6)) (/ (sqrt -6) (pow v 2))) (/ 1 (* (pow v 2) (sqrt -6)))))
(*.f64 (*.f64 v (*.f64 v v)) (-.f64 (/.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))))
(* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2))))) (/ 1 (* (pow v 2) (sqrt -6)))))
(*.f64 (*.f64 v (*.f64 v v)) (+.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -6 binary64))) (*.f64 v (*.f64 v (*.f64 v v)))) (/.f64 (/.f64 #s(literal -1/12 binary64) (sqrt.f64 #s(literal -6 binary64))) (*.f64 v (*.f64 v (*.f64 v v))))) (-.f64 (/.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))))
(* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (* -1 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2)))))) (/ 1 (* (pow v 2) (sqrt -6)))))
(*.f64 (*.f64 v (*.f64 v v)) (+.f64 (+.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -6 binary64))) (*.f64 v (*.f64 v (*.f64 v v)))) (/.f64 (/.f64 #s(literal -1/12 binary64) (sqrt.f64 #s(literal -6 binary64))) (*.f64 v (*.f64 v (*.f64 v v))))) (-.f64 (/.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (pow.f64 v #s(literal 6 binary64)))))
(* (pow v 3) (sqrt -6))
(*.f64 v (*.f64 v (*.f64 v (sqrt.f64 #s(literal -6 binary64)))))
(* -1 (* (pow v 3) (- (+ (* -1 (sqrt -6)) (/ (sqrt -6) (pow v 2))) (/ 1 (* (pow v 2) (sqrt -6))))))
(*.f64 (-.f64 (/.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (*.f64 v (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(* -1 (* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2))))) (/ 1 (* (pow v 2) (sqrt -6))))))
(-.f64 #s(literal 0 binary64) (*.f64 (*.f64 v (*.f64 v v)) (+.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -6 binary64))) (*.f64 v (*.f64 v (*.f64 v v)))) (/.f64 (/.f64 #s(literal -1/12 binary64) (sqrt.f64 #s(literal -6 binary64))) (*.f64 v (*.f64 v (*.f64 v v))))) (-.f64 (/.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))))))
(* -1 (* (pow v 3) (- (+ (* -1 (sqrt -6)) (+ (* -1 (/ (+ (* 1/2 (/ 1 (pow (sqrt -6) 3))) (* 1/2 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (/ 1 (* (pow v 4) (sqrt -6))) (+ (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))) (/ (sqrt -6) (pow v 2)))))) (/ 1 (* (pow v 2) (sqrt -6))))))
(*.f64 (*.f64 v (*.f64 v v)) (-.f64 #s(literal 0 binary64) (+.f64 (+.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -6 binary64))) (*.f64 v (*.f64 v (*.f64 v v)))) (/.f64 (/.f64 #s(literal -1/12 binary64) (sqrt.f64 #s(literal -6 binary64))) (*.f64 v (*.f64 v (*.f64 v v))))) (-.f64 (/.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (pow.f64 v #s(literal 6 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow v 2)))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(+ 1 (* -1 (pow v 2)))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(+ 1 (* -1 (pow v 2)))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(* -1 (pow v 2))
(-.f64 #s(literal 0 binary64) (*.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(* -1 (pow v 2))
(-.f64 #s(literal 0 binary64) (*.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 v (*.f64 v #s(literal -3 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 v (+.f64 (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 v (*.f64 v (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64)))))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 v v) (-.f64 (*.f64 (*.f64 v v) (+.f64 (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 (*.f64 v v) #s(literal -27/2 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))))) (/.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(* v (sqrt -6))
(*.f64 v (sqrt.f64 #s(literal -6 binary64)))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(*.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -6 binary64)))))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(*.f64 v (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -6 binary64))))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal -6 binary64))) (*.f64 v (*.f64 v (*.f64 v v)))))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(*.f64 v (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -6 binary64))))) (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))) (pow.f64 v #s(literal 6 binary64)))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal -6 binary64))) (*.f64 v (*.f64 v (*.f64 v v)))))))
(* -1 (* v (sqrt -6)))
(-.f64 #s(literal 0 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64))))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(*.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (-.f64 #s(literal 0 binary64) v))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -6 binary64))))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal -6 binary64))) (*.f64 v (*.f64 v (*.f64 v v)))))) (-.f64 #s(literal 0 binary64) v))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(*.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -6 binary64))))) (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))) (pow.f64 v #s(literal 6 binary64)))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal -6 binary64))) (*.f64 v (*.f64 v (*.f64 v v)))))) (-.f64 #s(literal 0 binary64) v))

eval63.0ms (0.9%)

Compiler

Compiled 15238 to 1511 computations (90.1% saved)

prune52.0ms (0.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New5361537
Fresh000
Picked022
Done011
Total5364540
Accuracy
100.0%
Counts
540 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) #s(literal 4 binary64))
▶99.9%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))))
✓99.9%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -5/8 binary64))))
✓99.4%
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
Compiler

Compiled 46 to 37 computations (19.6% saved)

simplify8.0ms (0.1%)

Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff128
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))))
Rules
74×*-lowering-*.f32
74×*-lowering-*.f64
40×fma-define
34×*-commutative
32×fma-lowering-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01141
12133
23733
37333
412633
513033
013033
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(/ (sqrt 2) (/ 1 (+ 1/4 (* v (* v -5/8)))))
(sqrt 2)
2
(/ 1 (+ 1/4 (* v (* v -5/8))))
1
(+ 1/4 (* v (* v -5/8)))
1/4
(* v (* v -5/8))
v
(* v -5/8)
-5/8
Outputs
(/ (sqrt 2) (/ 1 (+ 1/4 (* v (* v -5/8)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(/ 1 (+ 1/4 (* v (* v -5/8))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))))
1
#s(literal 1 binary64)
(+ 1/4 (* v (* v -5/8)))
(+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))
1/4
#s(literal 1/4 binary64)
(* v (* v -5/8))
(*.f64 v (*.f64 v #s(literal -5/8 binary64)))
v
(* v -5/8)
(*.f64 v #s(literal -5/8 binary64))
-5/8
#s(literal -5/8 binary64)

localize50.0ms (0.7%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy100.0%
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))))
✓accuracy100.0%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))))
✓accuracy99.8%
(*.f64 v (*.f64 v #s(literal -5/8 binary64)))
Results
33.0ms256×0valid
Compiler

Compiled 45 to 12 computations (73.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-mult: 4.0ms (36% of total)
ival-div: 3.0ms (27% of total)
ival-sqrt: 2.0ms (18% of total)
ival-add: 1.0ms (9% of total)
const: 1.0ms (9% of total)
backward-pass: 0.0ms (0% of total)

series1.0ms (0%)

Counts
5 → 48
Calls
Call 1
Inputs
#<alt (/ (sqrt 2) (/ 1 (+ 1/4 (* v (* v -5/8)))))>
#<alt (sqrt 2)>
#<alt (/ 1 (+ 1/4 (* v (* v -5/8))))>
#<alt (+ 1/4 (* v (* v -5/8)))>
#<alt (* v (* v -5/8))>
Outputs
#<alt (* 1/4 (sqrt 2))>
#<alt (+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (* -5/8 (* (pow v 2) (sqrt 2)))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* -5/8 (* (pow v 2) (sqrt 2)))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt 4>
#<alt (+ 4 (* 10 (pow v 2)))>
#<alt (+ 4 (* (pow v 2) (+ 10 (* 25 (pow v 2)))))>
#<alt (+ 4 (* (pow v 2) (+ 10 (* (pow v 2) (+ 25 (* 125/2 (pow v 2)))))))>
#<alt (/ -8/5 (pow v 2))>
#<alt (* -1 (/ (+ 8/5 (* 16/25 (/ 1 (pow v 2)))) (pow v 2)))>
#<alt (/ (- (* -1 (/ (+ 16/25 (* 32/125 (/ 1 (pow v 2)))) (pow v 2))) 8/5) (pow v 2))>
#<alt (/ (- (* -1 (/ (+ 32/125 (* 64/625 (/ 1 (pow v 2)))) (pow v 4))) (+ 8/5 (* 16/25 (/ 1 (pow v 2))))) (pow v 2))>
#<alt (/ -8/5 (pow v 2))>
#<alt (* -1 (/ (+ 8/5 (* 16/25 (/ 1 (pow v 2)))) (pow v 2)))>
#<alt (/ (- (* -1 (/ (+ 16/25 (* 32/125 (/ 1 (pow v 2)))) (pow v 2))) 8/5) (pow v 2))>
#<alt (/ (- (* -1 (/ (+ 32/125 (* 64/625 (/ 1 (pow v 2)))) (pow v 4))) (+ 8/5 (* 16/25 (/ 1 (pow v 2))))) (pow v 2))>
#<alt 1/4>
#<alt (+ 1/4 (* -5/8 (pow v 2)))>
#<alt (+ 1/4 (* -5/8 (pow v 2)))>
#<alt (+ 1/4 (* -5/8 (pow v 2)))>
#<alt (* -5/8 (pow v 2))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* -5/8 (pow v 2))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
Calls

12 calls:

TimeVariablePointExpression
0.0ms
v
@inf
(/ 1 (+ 1/4 (* v (* v -5/8))))
0.0ms
v
@0
(/ 1 (+ 1/4 (* v (* v -5/8))))
0.0ms
v
@0
(/ (sqrt 2) (/ 1 (+ 1/4 (* v (* v -5/8)))))
0.0ms
v
@-inf
(/ 1 (+ 1/4 (* v (* v -5/8))))
0.0ms
v
@inf
(/ (sqrt 2) (/ 1 (+ 1/4 (* v (* v -5/8)))))

rewrite353.0ms (5.1%)

Algorithm
1×batch-egg-rewrite
Rules
3564×*-lowering-*.f32
3564×*-lowering-*.f64
1938×/-lowering-/.f32
1938×/-lowering-/.f64
1300×pow-lowering-pow.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01133
15325
232625
3311325
0828025
Stop Event
1×iter limit
1×node limit
Counts
5 → 427
Calls
Call 1
Inputs
(/ (sqrt 2) (/ 1 (+ 1/4 (* v (* v -5/8)))))
(sqrt 2)
(/ 1 (+ 1/4 (* v (* v -5/8))))
(+ 1/4 (* v (* v -5/8)))
(* v (* v -5/8))
Outputs
(+.f64 (/.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) (/.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(+.f64 (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))))
(+.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))) (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))))
(+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 v (*.f64 v #s(literal 5/8 binary64)))) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/4 binary64)))
(+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/4 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 v (*.f64 v #s(literal 5/8 binary64)))))
(+.f64 (*.f64 (*.f64 v (*.f64 v #s(literal 5/8 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1/4 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (*.f64 #s(literal -1/4 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 v (*.f64 v #s(literal 5/8 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))))) #s(literal -1 binary64)))
(exp.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))))))
(exp.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) (log.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))))))
(exp.f64 (+.f64 (log.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))) (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))))
(exp.f64 (neg.f64 (log.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))))))
(exp.f64 (-.f64 (log.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))) (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (*.f64 v (*.f64 v #s(literal 5/8 binary64))) #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 v (*.f64 v #s(literal 5/8 binary64))) #s(literal -1/4 binary64)))) (/.f64 (+.f64 (*.f64 v (*.f64 v #s(literal 5/8 binary64))) #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) (/.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (/.f64 #s(literal 1/4 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(fma.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(fma.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(neg.f64 (/.f64 (+.f64 (*.f64 v (*.f64 v #s(literal 5/8 binary64))) #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 (*.f64 v (*.f64 v v)) #s(literal -125/512 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal 5/8 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -25/64 binary64))))))
(/.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))))))
(/.f64 (+.f64 (*.f64 v (*.f64 v #s(literal 5/8 binary64))) #s(literal -1/4 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(/.f64 (+.f64 (*.f64 v (*.f64 v #s(literal 5/8 binary64))) #s(literal -1/4 binary64)) (*.f64 #s(literal -1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 v (*.f64 v #s(literal 5/8 binary64))) #s(literal -1/4 binary64))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 (*.f64 v (*.f64 v v)) #s(literal -125/512 binary64))))) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 (*.f64 v (*.f64 v v)) #s(literal -125/512 binary64))))) (*.f64 #s(literal -1 binary64) (+.f64 (neg.f64 (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)))) #s(literal -1/16 binary64))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -25/64 binary64)))) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal 5/8 binary64)))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -25/64 binary64)))) (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal 5/8 binary64)))))))
(/.f64 (/.f64 (+.f64 (*.f64 v (*.f64 v #s(literal 5/8 binary64))) #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) #s(literal -1 binary64))
(/.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -25/64 binary64)))) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal 5/8 binary64))))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal 125/512 binary64)) #s(literal -1/64 binary64))) (+.f64 (neg.f64 (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)))) #s(literal -1/16 binary64)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal 125/512 binary64)) #s(literal -1/64 binary64))) (*.f64 #s(literal 1 binary64) (+.f64 (neg.f64 (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)))) #s(literal -1/16 binary64))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -25/64 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal 5/8 binary64))))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -25/64 binary64))))) (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal 5/8 binary64)))))))
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 (*.f64 v (*.f64 v v)) #s(literal -125/512 binary64))))) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64))))))
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal 125/512 binary64)) #s(literal -1/64 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (+.f64 (neg.f64 (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)))) #s(literal -1/16 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -25/64 binary64))))) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal 5/8 binary64)))))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 (*.f64 v (*.f64 v v)) #s(literal -125/512 binary64))))) (+.f64 (neg.f64 (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)))) #s(literal -1/16 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -25/64 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal 5/8 binary64))))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal 125/512 binary64)) #s(literal -1/64 binary64))) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal 125/512 binary64)) #s(literal -1/64 binary64))) (*.f64 #s(literal -1 binary64) (+.f64 (neg.f64 (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)))) #s(literal -1/16 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -25/64 binary64))))) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal 5/8 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -25/64 binary64))))) (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal 5/8 binary64)))))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 v (*.f64 v (*.f64 (*.f64 v v) #s(literal 25/64 binary64)))) #s(literal -1/16 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (*.f64 v (*.f64 v (*.f64 (*.f64 v v) #s(literal 25/64 binary64)))) #s(literal -1/16 binary64))) (*.f64 #s(literal 1 binary64) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 (*.f64 v (*.f64 v (*.f64 (*.f64 v v) #s(literal 25/64 binary64)))) #s(literal -1/16 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (*.f64 v (*.f64 v (*.f64 (*.f64 v v) #s(literal 25/64 binary64)))) #s(literal -1/16 binary64))) (*.f64 #s(literal -1 binary64) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 v (*.f64 v #s(literal 5/8 binary64))) #s(literal -1/4 binary64))))
(/.f64 (*.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64))
(/.f64 (*.f64 (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 (*.f64 v (*.f64 v v)) #s(literal -125/512 binary64)))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(/.f64 (*.f64 (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 (*.f64 v (*.f64 v v)) #s(literal -125/512 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)))) #s(literal -1 binary64)))
(/.f64 (*.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -25/64 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal 5/8 binary64)))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(/.f64 (*.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -25/64 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal 5/8 binary64)))) #s(literal -1 binary64)))
(/.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal 125/512 binary64)) #s(literal -1/64 binary64)) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (neg.f64 (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)))) #s(literal -1/16 binary64)))
(/.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal 125/512 binary64)) #s(literal -1/64 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (+.f64 (neg.f64 (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)))) #s(literal -1/16 binary64)) #s(literal 1 binary64)))
(/.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal 125/512 binary64)) #s(literal -1/64 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (neg.f64 (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)))) #s(literal -1/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(/.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal 125/512 binary64)) #s(literal -1/64 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (+.f64 (neg.f64 (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)))) #s(literal -1/16 binary64)) #s(literal -1 binary64)))
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(pow.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))) #s(literal -1/2 binary64)) #s(literal -2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)) (+.f64 (*.f64 v (*.f64 v (*.f64 (*.f64 v v) #s(literal 25/64 binary64)))) #s(literal -1/16 binary64))) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))))))
(*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))))
(*.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (+.f64 (*.f64 v (*.f64 v #s(literal 5/8 binary64))) #s(literal -1/4 binary64)))
(*.f64 (+.f64 (*.f64 v (*.f64 v #s(literal 5/8 binary64))) #s(literal -1/4 binary64)) #s(literal -1 binary64))
(*.f64 (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 (*.f64 v (*.f64 v v)) #s(literal -125/512 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64))))))
(*.f64 (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 (*.f64 v (*.f64 v v)) #s(literal -125/512 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64))))) #s(literal 1 binary64)))
(*.f64 (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 (*.f64 v (*.f64 v v)) #s(literal -125/512 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64))))) #s(literal 1 binary64)))
(*.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -25/64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal 5/8 binary64))))))
(*.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -25/64 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal 5/8 binary64))))) #s(literal 1 binary64)))
(*.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -25/64 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal 5/8 binary64))))) #s(literal 1 binary64)))
(*.f64 (+.f64 (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal 125/512 binary64)) #s(literal -1/64 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (neg.f64 (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)))) #s(literal -1/16 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -25/64 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal 5/8 binary64)))))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64))))) (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 (*.f64 v (*.f64 v v)) #s(literal -125/512 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal 5/8 binary64))))) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -25/64 binary64))))
(*.f64 (+.f64 (*.f64 v (*.f64 v (*.f64 (*.f64 v v) #s(literal 25/64 binary64)))) #s(literal -1/16 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64))))
(*.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -25/64 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal 5/8 binary64))))))
(*.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 (*.f64 v (*.f64 v v)) #s(literal -125/512 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))))
(*.f64 (/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -25/64 binary64))) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -25/64 binary64)))) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))))
(*.f64 (/.f64 (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 (*.f64 v (*.f64 v v)) #s(literal -125/512 binary64)))) (+.f64 #s(literal 1/4096 binary64) (*.f64 (*.f64 (*.f64 v (*.f64 v v)) (*.f64 (*.f64 v (*.f64 v v)) #s(literal -125/512 binary64))) (*.f64 (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)) (*.f64 (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64))))))) (+.f64 #s(literal 1/256 binary64) (*.f64 (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64))) (-.f64 (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64))) #s(literal 1/16 binary64)))))
(*.f64 (/.f64 (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 (*.f64 v (*.f64 v v)) #s(literal -125/512 binary64)))) (-.f64 #s(literal 1/256 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 (*.f64 v v) #s(literal 25/64 binary64)))) (*.f64 (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)))))) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v #s(literal 5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64)))))
(*.f64 (/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -25/64 binary64))) (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal 125/512 binary64)))) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64)))))))
(*.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) (exp.f64 (log.f64 (+.f64 (*.f64 v (*.f64 v #s(literal 5/8 binary64))) #s(literal -1/4 binary64)))))
(*.f64 (exp.f64 (log.f64 (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 (*.f64 v (*.f64 v v)) #s(literal -125/512 binary64)))))) (exp.f64 (-.f64 #s(literal 0 binary64) (log.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal -1/4 binary64))))))))
(*.f64 (exp.f64 (log.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -25/64 binary64))))) (exp.f64 (-.f64 #s(literal 0 binary64) (log.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal 5/8 binary64))))))))
(exp.f64 (log.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64)))) #s(literal 1 binary64)))
(pow.f64 (*.f64 v (*.f64 v #s(literal -5/8 binary64))) #s(literal 1 binary64))
(*.f64 v (*.f64 v #s(literal -5/8 binary64)))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(*.f64 (*.f64 v #s(literal -5/8 binary64)) v)
(*.f64 (*.f64 v v) #s(literal -5/8 binary64))
(*.f64 (*.f64 v v) (exp.f64 (log.f64 #s(literal -5/8 binary64))))
(*.f64 (exp.f64 (log.f64 v)) (exp.f64 (log.f64 (*.f64 v #s(literal -5/8 binary64)))))
(*.f64 (exp.f64 (log.f64 (*.f64 v #s(literal -5/8 binary64)))) (exp.f64 (log.f64 v)))
(*.f64 (exp.f64 (log.f64 #s(literal -5/8 binary64))) (*.f64 v v))

simplify190.0ms (2.7%)

Algorithm
1×egg-herbie
Rules
2304×*-lowering-*.f32
2304×*-lowering-*.f64
1376×fma-lowering-fma.f32
1376×fma-lowering-fma.f64
1318×fma-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
063420
1161320
2475312
31220312
42665312
56170312
08058312
Stop Event
1×iter limit
1×node limit
Counts
48 → 48
Calls
Call 1
Inputs
(* 1/4 (sqrt 2))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(* -5/8 (* (pow v 2) (sqrt 2)))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* -5/8 (* (pow v 2) (sqrt 2)))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
4
(+ 4 (* 10 (pow v 2)))
(+ 4 (* (pow v 2) (+ 10 (* 25 (pow v 2)))))
(+ 4 (* (pow v 2) (+ 10 (* (pow v 2) (+ 25 (* 125/2 (pow v 2)))))))
(/ -8/5 (pow v 2))
(* -1 (/ (+ 8/5 (* 16/25 (/ 1 (pow v 2)))) (pow v 2)))
(/ (- (* -1 (/ (+ 16/25 (* 32/125 (/ 1 (pow v 2)))) (pow v 2))) 8/5) (pow v 2))
(/ (- (* -1 (/ (+ 32/125 (* 64/625 (/ 1 (pow v 2)))) (pow v 4))) (+ 8/5 (* 16/25 (/ 1 (pow v 2))))) (pow v 2))
(/ -8/5 (pow v 2))
(* -1 (/ (+ 8/5 (* 16/25 (/ 1 (pow v 2)))) (pow v 2)))
(/ (- (* -1 (/ (+ 16/25 (* 32/125 (/ 1 (pow v 2)))) (pow v 2))) 8/5) (pow v 2))
(/ (- (* -1 (/ (+ 32/125 (* 64/625 (/ 1 (pow v 2)))) (pow v 4))) (+ 8/5 (* 16/25 (/ 1 (pow v 2))))) (pow v 2))
1/4
(+ 1/4 (* -5/8 (pow v 2)))
(+ 1/4 (* -5/8 (pow v 2)))
(+ 1/4 (* -5/8 (pow v 2)))
(* -5/8 (pow v 2))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* -5/8 (pow v 2))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
Outputs
(* 1/4 (sqrt 2))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v))))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v))))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v))))
(* -5/8 (* (pow v 2) (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v))))
(* -5/8 (* (pow v 2) (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v))))
4
#s(literal 4 binary64)
(+ 4 (* 10 (pow v 2)))
(+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) #s(literal 10 binary64)))
(+ 4 (* (pow v 2) (+ 10 (* 25 (pow v 2)))))
(+.f64 #s(literal 4 binary64) (*.f64 v (*.f64 v (+.f64 #s(literal 10 binary64) (*.f64 (*.f64 v v) #s(literal 25 binary64))))))
(+ 4 (* (pow v 2) (+ 10 (* (pow v 2) (+ 25 (* 125/2 (pow v 2)))))))
(+.f64 #s(literal 4 binary64) (*.f64 v (*.f64 v (+.f64 #s(literal 10 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 25 binary64) (*.f64 (*.f64 v v) #s(literal 125/2 binary64))))))))
(/ -8/5 (pow v 2))
(/.f64 #s(literal -8/5 binary64) (*.f64 v v))
(* -1 (/ (+ 8/5 (* 16/25 (/ 1 (pow v 2)))) (pow v 2)))
(/.f64 (+.f64 #s(literal -8/5 binary64) (/.f64 #s(literal -16/25 binary64) (*.f64 v v))) (*.f64 v v))
(/ (- (* -1 (/ (+ 16/25 (* 32/125 (/ 1 (pow v 2)))) (pow v 2))) 8/5) (pow v 2))
(/.f64 (+.f64 #s(literal -8/5 binary64) (/.f64 (+.f64 #s(literal -16/25 binary64) (/.f64 #s(literal -32/125 binary64) (*.f64 v v))) (*.f64 v v))) (*.f64 v v))
(/ (- (* -1 (/ (+ 32/125 (* 64/625 (/ 1 (pow v 2)))) (pow v 4))) (+ 8/5 (* 16/25 (/ 1 (pow v 2))))) (pow v 2))
(/.f64 (+.f64 #s(literal -8/5 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 v v)) (+.f64 (/.f64 (+.f64 #s(literal 32/125 binary64) (/.f64 #s(literal 64/625 binary64) (*.f64 v v))) (*.f64 v v)) #s(literal 16/25 binary64)))) (*.f64 v v))
(/ -8/5 (pow v 2))
(/.f64 #s(literal -8/5 binary64) (*.f64 v v))
(* -1 (/ (+ 8/5 (* 16/25 (/ 1 (pow v 2)))) (pow v 2)))
(/.f64 (+.f64 #s(literal -8/5 binary64) (/.f64 #s(literal -16/25 binary64) (*.f64 v v))) (*.f64 v v))
(/ (- (* -1 (/ (+ 16/25 (* 32/125 (/ 1 (pow v 2)))) (pow v 2))) 8/5) (pow v 2))
(/.f64 (+.f64 #s(literal -8/5 binary64) (/.f64 (+.f64 #s(literal -16/25 binary64) (/.f64 #s(literal -32/125 binary64) (*.f64 v v))) (*.f64 v v))) (*.f64 v v))
(/ (- (* -1 (/ (+ 32/125 (* 64/625 (/ 1 (pow v 2)))) (pow v 4))) (+ 8/5 (* 16/25 (/ 1 (pow v 2))))) (pow v 2))
(/.f64 (+.f64 #s(literal -8/5 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 v v)) (+.f64 (/.f64 (+.f64 #s(literal 32/125 binary64) (/.f64 #s(literal 64/625 binary64) (*.f64 v v))) (*.f64 v v)) #s(literal 16/25 binary64)))) (*.f64 v v))
1/4
#s(literal 1/4 binary64)
(+ 1/4 (* -5/8 (pow v 2)))
(+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(+ 1/4 (* -5/8 (pow v 2)))
(+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(+ 1/4 (* -5/8 (pow v 2)))
(+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))
(* -5/8 (pow v 2))
(*.f64 #s(literal -5/8 binary64) (*.f64 v v))

eval58.0ms (0.8%)

Compiler

Compiled 13536 to 1475 computations (89.1% saved)

prune53.0ms (0.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New4750475
Fresh000
Picked011
Done033
Total4754479
Accuracy
100.0%
Counts
479 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) #s(literal 4 binary64))
✓99.9%
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))))
✓99.9%
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -5/8 binary64))))
✓99.4%
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
Compiler

Compiled 152 to 81 computations (46.7% saved)

regimes8.0ms (0.1%)

Counts
8 → 1
Calls
Call 1
Inputs
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -5/8 binary64))))
(*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -3/8 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) #s(literal 4 binary64))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64))))) #s(literal 4 binary64))
(*.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
Outputs
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) #s(literal 4 binary64))
Calls

3 calls:

3.0ms
v
2.0ms
(*.f64 v v)
2.0ms
(*.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
Results
AccuracySegmentsBranch
100.0%1v
100.0%1(*.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
100.0%1(*.f64 v v)
Compiler

Compiled 26 to 17 computations (34.6% saved)

regimes4.0ms (0.1%)

Counts
5 → 1
Calls
Call 1
Inputs
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -5/8 binary64))))
(*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 v (*.f64 v #s(literal -5/8 binary64))))))
(*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -3/8 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
Outputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -5/8 binary64))))
Calls

2 calls:

2.0ms
v
2.0ms
(*.f64 v v)
Results
AccuracySegmentsBranch
99.9%1v
99.9%1(*.f64 v v)
Compiler

Compiled 6 to 3 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

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

1 calls:

1.0ms
v
Results
AccuracySegmentsBranch
99.4%1v
Compiler

Compiled 2 to 1 computations (50% saved)

simplify8.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
14×*-commutative_binary64
10×+-commutative_binary64
6×sub-neg_binary64
4×neg-sub0_binary64
4×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01930
13430
24130
34530
44730
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) #s(literal 4 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -5/8 binary64))))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
Outputs
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) #s(literal 4 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 v v) #s(literal -5/8 binary64))))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))

soundness1.2s (17.2%)

Rules
5840×*-lowering-*.f32
5840×*-lowering-*.f64
5700×*-lowering-*.f32
5700×*-lowering-*.f64
4446×*-lowering-*.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0169976
1566883
22318833
36891833
08430833
02001714
16341401
223001348
084601348
02295
111289
279889
0844989
01448
17246
249143
3541243
0843943
Stop Event
1×done
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 82 to 58 computations (29.3% saved)

preprocess27.0ms (0.4%)

Remove

(abs v)

Compiler

Compiled 170 to 114 computations (32.9% saved)

end0.0ms (0%)

Profiling

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