Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B

Time bar (total: 29.7s)

analyze32.0ms (0.1%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%99.9%0.1%0%0%0%2
50%50%50%0.1%0%0%0%3
50%50%50%0.1%0%0%0%4
62.5%62.4%37.5%0.1%0%0%0%5
68.8%68.7%31.2%0.1%0%0%0%6
78.1%78%21.9%0.1%0%0%0%7
82.8%82.7%17.2%0.1%0%0%0%8
88.3%88.2%11.7%0.1%0%0%0%9
91%90.9%9%0.1%0%0%0%10
93.9%93.9%6%0.1%0%0%0%11
95.4%95.3%4.6%0.1%0%0%0%12
Compiler

Compiled 14 to 10 computations (28.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 16.0ms
ival-div: 7.0ms (44.5% of total)
ival-mult: 4.0ms (25.4% of total)
ival-sub: 2.0ms (12.7% of total)
ival-add: 2.0ms (12.7% of total)
const: 1.0ms (6.4% of total)
backward-pass: 0.0ms (0% of total)

sample905.0ms (3%)

Results
665.0ms8253×0valid
0.0ms2×1valid
0.0ms1×3valid
Precisions
Click to see histograms. Total time spent on operations: 403.0ms
ival-div: 200.0ms (49.7% of total)
ival-mult: 95.0ms (23.6% of total)
ival-add: 49.0ms (12.2% of total)
ival-sub: 42.0ms (10.4% of total)
const: 13.0ms (3.2% of total)
backward-pass: 3.0ms (0.7% of total)
Bogosity

preprocess360.0ms (1.2%)

Algorithm
2×egg-herbie
Rules
1168×fnmadd-define
848×fnmsub-define
820×fmsub-define
732×fnmadd-define
714×fma-define
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02874
16566
213862
330260
484960
5216460
6336060
7387660
8391060
9395060
10396660
0911
11710
22910
34710
49610
520910
650710
779610
8125210
9183010
10228510
11234110
12259010
13269710
14270510
0270510
Stop Event
1×iter limit
1×saturated
1×saturated
Calls
Call 1
Inputs
(- x (/ y (+ 1 (/ (* x y) 2))))
Outputs
(- x (/ y (+ 1 (/ (* x y) 2))))
(+.f64 x (/.f64 y (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal -2 binary64)))))
Call 2
Inputs
(- x (/ y (+ 1 (/ (* x y) 2))))
(- (neg x) (/ y (+ 1 (/ (* (neg x) y) 2))))
(- x (/ (neg y) (+ 1 (/ (* x (neg y)) 2))))
(neg (- (neg x) (/ y (+ 1 (/ (* (neg x) y) 2)))))
(neg (- x (/ (neg y) (+ 1 (/ (* x (neg y)) 2)))))
(- y (/ x (+ 1 (/ (* y x) 2))))
Outputs
(- x (/ y (+ 1 (/ (* x y) 2))))
(+ x (/ y (fnmsub x (* y 1/2) 1)))
(- (neg x) (/ y (+ 1 (/ (* (neg x) y) 2))))
(- (/ y (fnmsub x (* y -1/2) 1)) x)
(- x (/ (neg y) (+ 1 (/ (* x (neg y)) 2))))
(+ x (/ y (fnmsub x (* y 1/2) -1)))
(neg (- (neg x) (/ y (+ 1 (/ (* (neg x) y) 2)))))
(+ x (/ y (fnmsub x (* y 1/2) -1)))
(neg (- x (/ (neg y) (+ 1 (/ (* x (neg y)) 2)))))
(- (/ y (fnmsub x (* y -1/2) 1)) x)
(- y (/ x (+ 1 (/ (* y x) 2))))
(+ y (/ x (fnmsub x (* y 1/2) 1)))

explain91.0ms (0.3%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
360-0-(/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))
00-0-x
00-0-#s(literal 2 binary64)
00-0-y
00-0-(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))
00-0-(*.f64 x y)
00-0-(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
00-0-(/.f64 (*.f64 x y) #s(literal 2 binary64))
00-0-#s(literal 1 binary64)
Results
53.0ms512×0valid
Compiler

Compiled 97 to 29 computations (70.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 18.0ms
ival-div: 7.0ms (38.4% of total)
ival-mult: 5.0ms (27.4% of total)
ival-sub: 3.0ms (16.5% of total)
ival-add: 3.0ms (16.5% of total)
const: 1.0ms (5.5% of total)
backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 13 to 9 computations (30.8% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.9%
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify88.0ms (0.3%)

Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 (*.f64 x y) #s(literal 2 binary64))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))
✓cost-diff0
(/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))
✓cost-diff0
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
Rules
732×fnmadd-define
558×fmsub-define
540×fnmsub-define
484×fmm-def
444×sum3-define
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0939
11736
22936
34736
49636
520936
650736
779636
8125236
9183036
10228536
11234136
12259036
13269736
14270536
0270536
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(- x (/ y (+ 1 (/ (* x y) 2))))
x
(/ y (+ 1 (/ (* x y) 2)))
y
(+ 1 (/ (* x y) 2))
1
(/ (* x y) 2)
(* x y)
2
Outputs
(- x (/ y (+ 1 (/ (* x y) 2))))
(+.f64 x (/.f64 y (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal -2 binary64)))))
x
(/ y (+ 1 (/ (* x y) 2)))
(/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))
y
(+ 1 (/ (* x y) 2))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))
1
#s(literal 1 binary64)
(/ (* x y) 2)
(/.f64 (*.f64 x y) #s(literal 2 binary64))
(* x y)
(*.f64 x y)
2
#s(literal 2 binary64)

localize41.0ms (0.1%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))
✓accuracy100.0%
(*.f64 x y)
✓accuracy100.0%
(/.f64 (*.f64 x y) #s(literal 2 binary64))
✓accuracy86.7%
(/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))
Results
20.0ms256×0valid
Compiler

Compiled 42 to 10 computations (76.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
ival-div: 4.0ms (44.7% of total)
ival-mult: 2.0ms (22.4% of total)
ival-sub: 1.0ms (11.2% of total)
ival-add: 1.0ms (11.2% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

series8.0ms (0%)

Counts
5 → 120
Calls
Call 1
Inputs
#<alt (- x (/ y (+ 1 (/ (* x y) 2))))>
#<alt (/ y (+ 1 (/ (* x y) 2)))>
#<alt (+ 1 (/ (* x y) 2))>
#<alt (/ (* x y) 2)>
#<alt (* x y)>
Outputs
#<alt (* -1 y)>
#<alt (- (* x (+ 1 (* 1/2 (pow y 2)))) y)>
#<alt (- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)>
#<alt (- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)>
#<alt x>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))>
#<alt x>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))>
#<alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))>
#<alt x>
#<alt (+ x (* -1 y))>
#<alt (+ x (* y (- (* 1/2 (* x y)) 1)))>
#<alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))>
#<alt (- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt y>
#<alt (* y (+ 1 (* -1/2 (* x y))))>
#<alt (* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))>
#<alt (* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))>
#<alt (/ 2 x)>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))>
#<alt (- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))>
#<alt (/ 2 x)>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))>
#<alt y>
#<alt (+ y (* -1/2 (* x (pow y 2))))>
#<alt (+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))>
#<alt (+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))>
#<alt (/ 2 x)>
#<alt (/ (- 2 (* 4 (/ 1 (* x y)))) x)>
#<alt (/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)>
#<alt (/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)>
#<alt (/ 2 x)>
#<alt (* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))>
#<alt 1>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (* 1/2 (* x y))>
#<alt (* x (+ (* 1/2 y) (/ 1 x)))>
#<alt (* x (+ (* 1/2 y) (/ 1 x)))>
#<alt (* x (+ (* 1/2 y) (/ 1 x)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* x (- (* -1/2 y) (/ 1 x))))>
#<alt (* -1 (* x (- (* -1/2 y) (/ 1 x))))>
#<alt (* -1 (* x (- (* -1/2 y) (/ 1 x))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (* 1/2 (* x y))>
#<alt (* y (+ (* 1/2 x) (/ 1 y)))>
#<alt (* y (+ (* 1/2 x) (/ 1 y)))>
#<alt (* y (+ (* 1/2 x) (/ 1 y)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* y (- (* -1/2 x) (/ 1 y))))>
#<alt (* -1 (* y (- (* -1/2 x) (/ 1 y))))>
#<alt (* -1 (* y (- (* -1/2 x) (/ 1 y))))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
Calls

30 calls:

TimeVariablePointExpression
1.0ms
y
@inf
(- x (/ y (+ 1 (/ (* x y) 2))))
0.0ms
x
@inf
(- x (/ y (+ 1 (/ (* x y) 2))))
0.0ms
y
@-inf
(- x (/ y (+ 1 (/ (* x y) 2))))
0.0ms
x
@0
(- x (/ y (+ 1 (/ (* x y) 2))))
0.0ms
x
@-inf
(/ y (+ 1 (/ (* x y) 2)))

rewrite24.1s (81%)

Algorithm
1×batch-egg-rewrite
Rules
4140×*-lowering-*.f32
4140×*-lowering-*.f64
2970×/-lowering-/.f32
2970×/-lowering-/.f64
1742×sum5-define
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0935
15832
251832
3749732
0836832
Stop Event
1×iter limit
1×node limit
Counts
5 → 224
Calls
Call 1
Inputs
(- x (/ y (+ 1 (/ (* x y) 2))))
(/ y (+ 1 (/ (* x y) 2)))
(+ 1 (/ (* x y) 2))
(/ (* x y) 2)
(* x y)
Outputs
(+.f64 x (/.f64 y (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
(+.f64 (/.f64 y (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) x)
(+.f64 (/.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))))) (neg.f64 (/.f64 (/.f64 (/.f64 (*.f64 y y) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (/.f64 (*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) y)) (+.f64 (*.f64 x x) (*.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))))))))
(+.f64 (/.f64 (*.f64 x x) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (/.f64 y (/.f64 (*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) y)) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))))))
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
(-.f64 #s(literal 0 binary64) (-.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) x))
(-.f64 (/.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))))) (/.f64 (/.f64 (/.f64 (*.f64 y y) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (/.f64 (*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) y)) (+.f64 (*.f64 x x) (*.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))) (/.f64 (/.f64 y (/.f64 (*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) y)) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))))
(-.f64 (+.f64 x #s(literal 0 binary64)) (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
(fma.f64 y (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) x)
(fma.f64 (-.f64 #s(literal 0 binary64) y) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) x)
(fma.f64 #s(literal -1 binary64) (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) x)
(neg.f64 (/.f64 (-.f64 (*.f64 x (*.f64 x x)) (/.f64 (/.f64 (*.f64 y y) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (/.f64 (*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) y))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))))))))
(neg.f64 (/.f64 (+.f64 (*.f64 x x) (/.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) y))) (+.f64 (/.f64 y (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) x))))
(neg.f64 (/.f64 (+.f64 (neg.f64 (*.f64 x (*.f64 x x))) (/.f64 (/.f64 (*.f64 y y) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (/.f64 (*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) y))) (+.f64 (*.f64 x x) (*.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))))))
(neg.f64 (/.f64 (+.f64 (neg.f64 (*.f64 x x)) (/.f64 y (/.f64 (*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) y))) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 y (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))))
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(*.f64 (/.f64 x #s(literal 2 binary64)) y)
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(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x y)))
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(*.f64 x y)
(*.f64 y x)
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(*.f64 (*.f64 x y) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) y) (-.f64 #s(literal 0 binary64) x))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x y)))
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) y))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) y)

simplify328.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
3952×*-lowering-*.f32
3952×*-lowering-*.f64
1762×/-lowering-/.f32
1762×/-lowering-/.f64
1656×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02311040
1826982
22365947
37863947
08125947
Stop Event
1×iter limit
1×node limit
Counts
120 → 120
Calls
Call 1
Inputs
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
y
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
y
(+ y (* -1/2 (* x (pow y 2))))
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(/ 2 x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/ 2 x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
1
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(* 1/2 (* x y))
(* x (+ (* 1/2 y) (/ 1 x)))
(* x (+ (* 1/2 y) (/ 1 x)))
(* x (+ (* 1/2 y) (/ 1 x)))
(* 1/2 (* x y))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
1
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(* 1/2 (* x y))
(* y (+ (* 1/2 x) (/ 1 y)))
(* y (+ (* 1/2 x) (/ 1 y)))
(* y (+ (* 1/2 x) (/ 1 y)))
(* 1/2 (* x y))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
Outputs
(* -1 y)
(-.f64 #s(literal 0 binary64) y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 y y)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 y x)))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
(-.f64 (*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 y x))))) (*.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))) y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x))) (/.f64 (/.f64 #s(literal 4 binary64) (*.f64 y (*.f64 x x))) x)))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(*.f64 x (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 4 binary64) (*.f64 y (*.f64 x x))) x)) (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) (/.f64 #s(literal 8 binary64) (*.f64 y (*.f64 y (pow.f64 x #s(literal 4 binary64))))))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x))))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x))) (/.f64 (/.f64 #s(literal 4 binary64) (*.f64 y (*.f64 x x))) x)))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x)))) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal -8 binary64) (*.f64 x (*.f64 y y)))) (*.f64 x x)))
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 1/2 (* x y)) 1)))
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 y y)))) y)
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 y x)))))) y)
(- x (* 2 (/ 1 x)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(+.f64 x (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(+.f64 x (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal -8 binary64) (*.f64 x (*.f64 y y)))) x)) x))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(+.f64 x (+.f64 (/.f64 #s(literal 16 binary64) (*.f64 y (*.f64 y (*.f64 y (pow.f64 x #s(literal 4 binary64)))))) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal -8 binary64) (*.f64 x (*.f64 y y)))) x)) x)))
(- x (* 2 (/ 1 x)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(+.f64 x (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(+.f64 x (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal -8 binary64) (*.f64 x (*.f64 y y)))) x)) x))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(-.f64 (-.f64 x (/.f64 #s(literal 2 binary64) x)) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal -16 binary64) (*.f64 y (pow.f64 x #s(literal 4 binary64))))) y) (/.f64 #s(literal -4 binary64) (*.f64 x x))) y))
y
(* y (+ 1 (* -1/2 (* x y))))
(*.f64 y (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 y #s(literal -1/2 binary64)))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(+.f64 y (*.f64 x (*.f64 (*.f64 y y) (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 y x)) #s(literal -1/2 binary64)))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(*.f64 y (+.f64 #s(literal 1 binary64) (*.f64 y (+.f64 (*.f64 y (+.f64 (*.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 y (*.f64 x x))) x) (*.f64 (*.f64 x x) #s(literal 1/4 binary64)))) (*.f64 x #s(literal -1/2 binary64))))))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x)
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x)
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(+.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x) (/.f64 (/.f64 #s(literal -16 binary64) (*.f64 y (pow.f64 x #s(literal 4 binary64)))) (*.f64 y y)))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x)
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x)
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal -16 binary64) (*.f64 y (pow.f64 x #s(literal 4 binary64))))) y) (/.f64 #s(literal -4 binary64) (*.f64 x x))) y))
y
(+ y (* -1/2 (* x (pow y 2))))
(*.f64 y (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 y #s(literal -1/2 binary64)))))
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(+.f64 y (*.f64 x (*.f64 (*.f64 y y) (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 y x)) #s(literal -1/2 binary64)))))
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(+.f64 y (*.f64 x (+.f64 (*.f64 x (*.f64 (*.f64 x (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64))) (*.f64 (*.f64 y y) (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 y x)) #s(literal -1/2 binary64))))))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -16 binary64) (*.f64 (*.f64 x (*.f64 y (*.f64 y y))) (*.f64 x x))))) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x)
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 y y)) (/.f64 #s(literal -16 binary64) (*.f64 x (*.f64 y (*.f64 y y))))) x) (/.f64 #s(literal -4 binary64) y)) x)) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (* x y)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(+ 1 (* 1/2 (* x y)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(+ 1 (* 1/2 (* x y)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* x (+ (* 1/2 y) (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(* x (+ (* 1/2 y) (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(* x (+ (* 1/2 y) (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (*.f64 x (*.f64 y #s(literal -1/2 binary64)))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (*.f64 x (*.f64 y #s(literal -1/2 binary64)))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (*.f64 x (*.f64 y #s(literal -1/2 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (* x y)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(+ 1 (* 1/2 (* x y)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(+ 1 (* 1/2 (* x y)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* y (+ (* 1/2 x) (/ 1 y)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(* y (+ (* 1/2 x) (/ 1 y)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(* y (+ (* 1/2 x) (/ 1 y)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (*.f64 x (*.f64 y #s(literal -1/2 binary64)))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (*.f64 x (*.f64 y #s(literal -1/2 binary64)))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (*.f64 x (*.f64 y #s(literal -1/2 binary64)))))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)

eval57.0ms (0.2%)

Compiler

Compiled 10128 to 987 computations (90.3% saved)

prune38.0ms (0.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New3395344
Fresh000
Picked011
Done000
Total3396345
Accuracy
100.0%
Counts
345 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.9%
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
▶62.9%
(-.f64 x (/.f64 y (*.f64 y (*.f64 x #s(literal 1/2 binary64)))))
▶63.0%
(-.f64 x (/.f64 #s(literal 2 binary64) x))
▶99.9%
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) y)))
▶78.6%
(-.f64 x y)
▶64.7%
x
Compiler

Compiled 95 to 63 computations (33.7% saved)

simplify178.0ms (0.6%)

Algorithm
1×egg-herbie
Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 x #s(literal 1/2 binary64))
✓cost-diff0
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
✓cost-diff256
(/.f64 y (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
✓cost-diff256
(-.f64 x (/.f64 y (*.f64 y (*.f64 x #s(literal 1/2 binary64)))))
✓cost-diff0
(/.f64 #s(literal 2 binary64) x)
✓cost-diff0
(-.f64 x (/.f64 #s(literal 2 binary64) x))
✓cost-diff0
(-.f64 x y)
✓cost-diff0
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))
✓cost-diff0
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) y)
✓cost-diff128
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) y))
✓cost-diff128
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) y)))
Rules
2042×sum3-define
2018×fma-lowering-fma.f32
2018×fma-lowering-fma.f64
1820×fma-define
1718×fmm-def
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01885
14181
29679
323879
460279
5177079
6391479
7627179
0825279
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(- x (/ 1 (/ (+ 1 (/ (* x y) 2)) y)))
x
(/ 1 (/ (+ 1 (/ (* x y) 2)) y))
1
(/ (+ 1 (/ (* x y) 2)) y)
(+ 1 (/ (* x y) 2))
(/ (* x y) 2)
(* x y)
y
2
x
(- x y)
x
y
(- x (/ 2 x))
x
(/ 2 x)
2
(- x (/ y (* y (* x 1/2))))
x
(/ y (* y (* x 1/2)))
y
(* y (* x 1/2))
(* x 1/2)
1/2
Outputs
(- x (/ 1 (/ (+ 1 (/ (* x y) 2)) y)))
(+.f64 x (/.f64 y (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal -2 binary64)))))
x
(/ 1 (/ (+ 1 (/ (* x y) 2)) y))
(/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))
1
#s(literal 1 binary64)
(/ (+ 1 (/ (* x y) 2)) y)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) y)
(+ 1 (/ (* x y) 2))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))
(/ (* x y) 2)
(/.f64 (*.f64 x y) #s(literal 2 binary64))
(* x y)
(*.f64 x y)
y
2
#s(literal 2 binary64)
x
(- x y)
(-.f64 x y)
x
y
(- x (/ 2 x))
(+.f64 x (/.f64 #s(literal -2 binary64) x))
x
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
2
#s(literal 2 binary64)
(- x (/ y (* y (* x 1/2))))
(+.f64 x (/.f64 #s(literal -2 binary64) x))
x
(/ y (* y (* x 1/2)))
(/.f64 #s(literal 2 binary64) x)
y
(* y (* x 1/2))
(/.f64 (*.f64 x y) #s(literal 2 binary64))
(* x 1/2)
(/.f64 x #s(literal 2 binary64))
1/2
#s(literal 1/2 binary64)

localize76.0ms (0.3%)

Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(-.f64 x (/.f64 y (*.f64 y (*.f64 x #s(literal 1/2 binary64)))))
✓accuracy100.0%
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
✓accuracy100.0%
(*.f64 x #s(literal 1/2 binary64))
✓accuracy75.9%
(/.f64 y (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
✓accuracy100.0%
(/.f64 #s(literal 2 binary64) x)
✓accuracy100.0%
(-.f64 x (/.f64 #s(literal 2 binary64) x))
✓accuracy100.0%
(-.f64 x y)
✓accuracy100.0%
(*.f64 x y)
✓accuracy100.0%
(/.f64 (*.f64 x y) #s(literal 2 binary64))
✓accuracy99.9%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) y))
✓accuracy86.9%
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) y)
Results
47.0ms256×0valid
Compiler

Compiled 98 to 19 computations (80.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 24.0ms
ival-div: 9.0ms (37.2% of total)
ival-sub: 8.0ms (33.1% of total)
ival-mult: 6.0ms (24.8% of total)
ival-add: 1.0ms (4.1% of total)
const: 1.0ms (4.1% of total)
backward-pass: 0.0ms (0% of total)

series9.0ms (0%)

Counts
13 → 276
Calls
Call 1
Inputs
#<alt (- x (/ 1 (/ (+ 1 (/ (* x y) 2)) y)))>
#<alt (/ 1 (/ (+ 1 (/ (* x y) 2)) y))>
#<alt (/ (+ 1 (/ (* x y) 2)) y)>
#<alt (+ 1 (/ (* x y) 2))>
#<alt (- x y)>
#<alt (- x (/ 2 x))>
#<alt (/ 2 x)>
#<alt (- x (/ y (* y (* x 1/2))))>
#<alt (/ y (* y (* x 1/2)))>
#<alt (* y (* x 1/2))>
#<alt (* x 1/2)>
#<alt (/ (* x y) 2)>
#<alt (* x y)>
Outputs
#<alt (* -1 y)>
#<alt (- (* x (+ 1 (* 1/2 (pow y 2)))) y)>
#<alt (- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)>
#<alt (- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)>
#<alt x>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))>
#<alt x>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))>
#<alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))>
#<alt x>
#<alt (+ x (* -1 y))>
#<alt (+ x (* y (- (* 1/2 (* x y)) 1)))>
#<alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))>
#<alt (- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt y>
#<alt (+ y (* -1/2 (* x (pow y 2))))>
#<alt (+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))>
#<alt (+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))>
#<alt (/ 2 x)>
#<alt (/ (- 2 (* 4 (/ 1 (* x y)))) x)>
#<alt (/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)>
#<alt (/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)>
#<alt (/ 2 x)>
#<alt (* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))>
#<alt y>
#<alt (* y (+ 1 (* -1/2 (* x y))))>
#<alt (* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))>
#<alt (* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))>
#<alt (/ 2 x)>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))>
#<alt (- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))>
#<alt (/ 2 x)>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))>
#<alt (/ 1 y)>
#<alt (+ (* 1/2 x) (/ 1 y))>
#<alt (+ (* 1/2 x) (/ 1 y))>
#<alt (+ (* 1/2 x) (/ 1 y))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 (* x y))))>
#<alt (* x (+ 1/2 (/ 1 (* x y))))>
#<alt (* x (+ 1/2 (/ 1 (* x y))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 (* x y))))>
#<alt (* x (+ 1/2 (/ 1 (* x y))))>
#<alt (* x (+ 1/2 (/ 1 (* x y))))>
#<alt (/ 1 y)>
#<alt (/ (+ 1 (* 1/2 (* x y))) y)>
#<alt (/ (+ 1 (* 1/2 (* x y))) y)>
#<alt (/ (+ 1 (* 1/2 (* x y))) y)>
#<alt (* 1/2 x)>
#<alt (+ (* 1/2 x) (/ 1 y))>
#<alt (+ (* 1/2 x) (/ 1 y))>
#<alt (+ (* 1/2 x) (/ 1 y))>
#<alt (* 1/2 x)>
#<alt (+ (* 1/2 x) (/ 1 y))>
#<alt (+ (* 1/2 x) (/ 1 y))>
#<alt (+ (* 1/2 x) (/ 1 y))>
#<alt 1>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (* 1/2 (* x y))>
#<alt (* x (+ (* 1/2 y) (/ 1 x)))>
#<alt (* x (+ (* 1/2 y) (/ 1 x)))>
#<alt (* x (+ (* 1/2 y) (/ 1 x)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* x (- (* -1/2 y) (/ 1 x))))>
#<alt (* -1 (* x (- (* -1/2 y) (/ 1 x))))>
#<alt (* -1 (* x (- (* -1/2 y) (/ 1 x))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (* 1/2 (* x y))>
#<alt (* y (+ (* 1/2 x) (/ 1 y)))>
#<alt (* y (+ (* 1/2 x) (/ 1 y)))>
#<alt (* y (+ (* 1/2 x) (/ 1 y)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* y (- (* -1/2 x) (/ 1 y))))>
#<alt (* -1 (* y (- (* -1/2 x) (/ 1 y))))>
#<alt (* -1 (* y (- (* -1/2 x) (/ 1 y))))>
#<alt (* -1 y)>
#<alt (- x y)>
#<alt (- x y)>
#<alt (- x y)>
#<alt x>
#<alt (* x (+ 1 (* -1 (/ y x))))>
#<alt (* x (+ 1 (* -1 (/ y x))))>
#<alt (* x (+ 1 (* -1 (/ y x))))>
#<alt x>
#<alt (* -1 (* x (- (/ y x) 1)))>
#<alt (* -1 (* x (- (/ y x) 1)))>
#<alt (* -1 (* x (- (/ y x) 1)))>
#<alt x>
#<alt (+ x (* -1 y))>
#<alt (+ x (* -1 y))>
#<alt (+ x (* -1 y))>
#<alt (* -1 y)>
#<alt (* y (- (/ x y) 1))>
#<alt (* y (- (/ x y) 1))>
#<alt (* y (- (/ x y) 1))>
#<alt (* -1 y)>
#<alt (* -1 (* y (+ 1 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ x y)))))>
#<alt (/ -2 x)>
#<alt (/ (- (pow x 2) 2) x)>
#<alt (/ (- (pow x 2) 2) x)>
#<alt (/ (- (pow x 2) 2) x)>
#<alt x>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt x>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ -2 x)>
#<alt (/ (- (pow x 2) 2) x)>
#<alt (/ (- (pow x 2) 2) x)>
#<alt (/ (- (pow x 2) 2) x)>
#<alt x>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt x>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
Calls

69 calls:

TimeVariablePointExpression
1.0ms
y
@-inf
(/ (+ 1 (/ (* x y) 2)) y)
1.0ms
y
@0
(- x (/ y (* y (* x 1/2))))
0.0ms
x
@inf
(* x 1/2)
0.0ms
y
@0
(/ y (* y (* x 1/2)))
0.0ms
x
@0
(/ 2 x)

rewrite375.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
4228×*-lowering-*.f32
4228×*-lowering-*.f64
4140×/-lowering-/.f32
4140×/-lowering-/.f64
2080×+-lowering-+.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01873
113267
2129767
0843867
Stop Event
1×iter limit
1×node limit
Counts
13 → 473
Calls
Call 1
Inputs
(- x (/ 1 (/ (+ 1 (/ (* x y) 2)) y)))
(/ 1 (/ (+ 1 (/ (* x y) 2)) y))
(/ (+ 1 (/ (* x y) 2)) y)
(+ 1 (/ (* x y) 2))
(- x y)
(- x (/ 2 x))
(/ 2 x)
(- x (/ y (* y (* x 1/2))))
(/ y (* y (* x 1/2)))
(* y (* x 1/2))
(* x 1/2)
(/ (* x y) 2)
(* x y)
Outputs
(+.f64 x (-.f64 #s(literal 0 binary64) (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))))
(+.f64 (-.f64 #s(literal 0 binary64) (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))) x)
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
(-.f64 (/.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x x) (*.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))))) (/.f64 (*.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (/.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) y))) (+.f64 (*.f64 x x) (*.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))) (/.f64 (/.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) y)) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (-.f64 #s(literal 0 binary64) (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))))) (/.f64 (/.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))) y)) (-.f64 x (-.f64 #s(literal 0 binary64) (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))))))
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(*.f64 #s(literal 1/2 binary64) (*.f64 x y))
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(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 x y)) #s(literal -1/2 binary64))
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(*.f64 (*.f64 #s(literal 1 binary64) x) (/.f64 y #s(literal 2 binary64)))
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(-.f64 #s(literal 0 binary64) (/.f64 x #s(literal -2 binary64)))
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(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 y #s(literal -2 binary64))) (/.f64 (*.f64 x y) (*.f64 y #s(literal -2 binary64))))
(/.f64 x #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(/.f64 (*.f64 x y) (*.f64 y #s(literal 2 binary64)))
(/.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) y)
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(pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(pow.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 x (/.f64 (/.f64 y #s(literal 2 binary64)) y))
(*.f64 #s(literal 1 binary64) (/.f64 x #s(literal 2 binary64)))
(*.f64 y (/.f64 (/.f64 x #s(literal 2 binary64)) y))
(*.f64 (*.f64 x y) (/.f64 #s(literal 1/2 binary64) y))
(*.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) y))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (/.f64 x #s(literal 1 binary64)) (/.f64 (/.f64 y #s(literal 2 binary64)) y))
(*.f64 (/.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 (/.f64 y #s(literal 1 binary64)) (/.f64 (/.f64 x #s(literal 2 binary64)) y))
(*.f64 (/.f64 #s(literal -1 binary64) y) (/.f64 (*.f64 x y) #s(literal -2 binary64)))
(*.f64 (/.f64 x y) (/.f64 y #s(literal 2 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) y) y) (/.f64 x #s(literal -2 binary64)))
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(*.f64 (/.f64 (*.f64 x y) #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) y))
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(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x y)) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) y))
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(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 x y) #s(literal -2 binary64)))
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(*.f64 x y)
(*.f64 y x)

simplify946.0ms (3.2%)

Algorithm
1×egg-herbie
Rules
4646×*-lowering-*.f32
4646×*-lowering-*.f64
2154×/-lowering-/.f32
2154×/-lowering-/.f64
1838×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02531700
18861648
225421622
084961622
Stop Event
1×iter limit
1×node limit
Counts
276 → 276
Calls
Call 1
Inputs
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
y
(+ y (* -1/2 (* x (pow y 2))))
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(/ 2 x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/ 2 x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
y
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
(/ 1 y)
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(* 1/2 x)
(* x (+ 1/2 (/ 1 (* x y))))
(* x (+ 1/2 (/ 1 (* x y))))
(* x (+ 1/2 (/ 1 (* x y))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 (* x y))))
(* x (+ 1/2 (/ 1 (* x y))))
(* x (+ 1/2 (/ 1 (* x y))))
(/ 1 y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/ (+ 1 (* 1/2 (* x y))) y)
(* 1/2 x)
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(* 1/2 x)
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
1
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(* 1/2 (* x y))
(* x (+ (* 1/2 y) (/ 1 x)))
(* x (+ (* 1/2 y) (/ 1 x)))
(* x (+ (* 1/2 y) (/ 1 x)))
(* 1/2 (* x y))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
1
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(* 1/2 (* x y))
(* y (+ (* 1/2 x) (/ 1 y)))
(* y (+ (* 1/2 x) (/ 1 y)))
(* y (+ (* 1/2 x) (/ 1 y)))
(* 1/2 (* x y))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* -1 y)
(- x y)
(- x y)
(- x y)
x
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
(* -1 y)
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(/ -2 x)
(/ (- (pow x 2) 2) x)
(/ (- (pow x 2) 2) x)
(/ (- (pow x 2) 2) x)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ -2 x)
(/ (- (pow x 2) 2) x)
(/ (- (pow x 2) 2) x)
(/ (- (pow x 2) 2) x)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(- x (* 2 (/ 1 x)))
(- x (* 2 (/ 1 x)))
(- x (* 2 (/ 1 x)))
(- x (* 2 (/ 1 x)))
(- x (* 2 (/ 1 x)))
(- x (* 2 (/ 1 x)))
(- x (* 2 (/ 1 x)))
(- x (* 2 (/ 1 x)))
(- x (* 2 (/ 1 x)))
(- x (* 2 (/ 1 x)))
(- x (* 2 (/ 1 x)))
(- x (* 2 (/ 1 x)))
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
Outputs
(* -1 y)
(-.f64 #s(literal 0 binary64) y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 y y)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (+.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 #s(literal -1/4 binary64) y)))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 y y) (+.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 #s(literal -1/4 binary64) y)))) (*.f64 x (*.f64 #s(literal 1/8 binary64) (*.f64 x (pow.f64 y #s(literal 4 binary64)))))))) y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(*.f64 x (+.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))) (/.f64 (/.f64 (/.f64 (/.f64 #s(literal 4 binary64) y) x) x) x)))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(*.f64 x (+.f64 (+.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))) (/.f64 (/.f64 (/.f64 (/.f64 #s(literal 4 binary64) y) x) x) x)) (/.f64 (/.f64 #s(literal -8 binary64) (*.f64 y y)) (pow.f64 x #s(literal 4 binary64)))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(*.f64 x (+.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))) (/.f64 (/.f64 (/.f64 (/.f64 #s(literal 4 binary64) y) x) x) x)))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(+.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x)))) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal -8 binary64) (*.f64 x (*.f64 y y)))) (*.f64 x x)))
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 1/2 (* x y)) 1)))
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 y y)))) y)
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (+.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 #s(literal -1/4 binary64) y)))))) y)
(- x (* 2 (/ 1 x)))
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(+.f64 x (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 4 binary64) y) x) #s(literal -2 binary64)) x))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(-.f64 x (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(+.f64 (-.f64 x (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x)) (/.f64 (/.f64 (/.f64 #s(literal 16 binary64) y) (pow.f64 x #s(literal 4 binary64))) (*.f64 y y)))
(- x (* 2 (/ 1 x)))
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(+.f64 x (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 4 binary64) y) x) #s(literal -2 binary64)) x))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(-.f64 x (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(+.f64 x (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 16 binary64) y) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -8 binary64) (*.f64 x (*.f64 x x)))) y)) y) (/.f64 #s(literal -2 binary64) x)))
y
(+ y (* -1/2 (* x (pow y 2))))
(*.f64 y (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 y #s(literal -1/2 binary64)))))
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(+.f64 y (*.f64 x (*.f64 (*.f64 y y) (+.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) y)) #s(literal -1/2 binary64)))))
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(+.f64 y (*.f64 x (+.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 #s(literal -1/8 binary64) (*.f64 x x))) (*.f64 (*.f64 y y) (+.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) y)) #s(literal -1/2 binary64))))))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x) (/.f64 #s(literal -16 binary64) (*.f64 x (*.f64 y (*.f64 x (*.f64 x (*.f64 y y)))))))) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x)
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 y y)) (/.f64 #s(literal -16 binary64) (*.f64 y (*.f64 x (*.f64 y y))))) x) (/.f64 #s(literal -4 binary64) y)) x)) x)
y
(* y (+ 1 (* -1/2 (* x y))))
(*.f64 y (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 y #s(literal -1/2 binary64)))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(*.f64 y (+.f64 #s(literal 1 binary64) (*.f64 y (+.f64 (*.f64 (*.f64 y (*.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/2 binary64))))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(*.f64 y (+.f64 #s(literal 1 binary64) (*.f64 y (+.f64 (*.f64 y (+.f64 (*.f64 (*.f64 y (*.f64 x (*.f64 x x))) #s(literal -1/8 binary64)) (*.f64 x (*.f64 x #s(literal 1/4 binary64))))) (*.f64 x #s(literal -1/2 binary64))))))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x)
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x)
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(+.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x) (/.f64 (/.f64 (/.f64 #s(literal -16 binary64) y) (pow.f64 x #s(literal 4 binary64))) (*.f64 y y)))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x)
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x)
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x))) (/.f64 (/.f64 #s(literal -16 binary64) y) (pow.f64 x #s(literal 4 binary64)))) y) (/.f64 #s(literal -4 binary64) (*.f64 x x))) y))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(+ (* 1/2 x) (/ 1 y))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(+ (* 1/2 x) (/ 1 y))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(+ (* 1/2 x) (/ 1 y))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (/ 1 (* x y))))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 (* x y))))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 (* x y))))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (/ 1 (* x y))))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 (* x y))))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 (* x y))))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64)))) y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64)))) y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64)))) y)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(+ (* 1/2 x) (/ 1 y))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(+ (* 1/2 x) (/ 1 y))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(+ (* 1/2 x) (/ 1 y))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(+ (* 1/2 x) (/ 1 y))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(+ (* 1/2 x) (/ 1 y))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(+ (* 1/2 x) (/ 1 y))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (* x y)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(+ 1 (* 1/2 (* x y)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(+ 1 (* 1/2 (* x y)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* x (+ (* 1/2 y) (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(* x (+ (* 1/2 y) (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(* x (+ (* 1/2 y) (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 y x))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 y x))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 y x))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (* x y)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(+ 1 (* 1/2 (* x y)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(+ 1 (* 1/2 (* x y)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* y (+ (* 1/2 x) (/ 1 y)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(* y (+ (* 1/2 x) (/ 1 y)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(* y (+ (* 1/2 x) (/ 1 y)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal 1/2 binary64))))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 y x))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 y x))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 y x))))
(* -1 y)
(-.f64 #s(literal 0 binary64) y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
x
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
x
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(* -1 y)
(-.f64 #s(literal 0 binary64) y)
(* y (- (/ x y) 1))
(*.f64 y (+.f64 #s(literal -1 binary64) (/.f64 x y)))
(* y (- (/ x y) 1))
(*.f64 y (+.f64 #s(literal -1 binary64) (/.f64 x y)))
(* y (- (/ x y) 1))
(*.f64 y (+.f64 #s(literal -1 binary64) (/.f64 x y)))
(* -1 y)
(-.f64 #s(literal 0 binary64) y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(*.f64 y (+.f64 #s(literal -1 binary64) (/.f64 x y)))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(*.f64 y (+.f64 #s(literal -1 binary64) (/.f64 x y)))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(*.f64 y (+.f64 #s(literal -1 binary64) (/.f64 x y)))
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ (- (pow x 2) 2) x)
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(/ (- (pow x 2) 2) x)
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(/ (- (pow x 2) 2) x)
(+.f64 x (/.f64 #s(literal -2 binary64) x))
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ (- (pow x 2) 2) x)
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(/ (- (pow x 2) 2) x)
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(/ (- (pow x 2) 2) x)
(+.f64 x (/.f64 #s(literal -2 binary64) x))
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))
(- x (* 2 (/ 1 x)))
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(- x (* 2 (/ 1 x)))
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(- x (* 2 (/ 1 x)))
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(- x (* 2 (/ 1 x)))
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(- x (* 2 (/ 1 x)))
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(- x (* 2 (/ 1 x)))
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(- x (* 2 (/ 1 x)))
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(- x (* 2 (/ 1 x)))
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(- x (* 2 (/ 1 x)))
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(- x (* 2 (/ 1 x)))
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(- x (* 2 (/ 1 x)))
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(- x (* 2 (/ 1 x)))
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(*.f64 y (*.f64 x #s(literal 1/2 binary64)))
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)

eval90.0ms (0.3%)

Compiler

Compiled 11490 to 1480 computations (87.1% saved)

prune55.0ms (0.2%)

Pruning

6 alts after pruning (2 fresh and 4 done)

PrunedKeptTotal
New7472749
Fresh000
Picked145
Done101
Total7496755
Accuracy
100.0%
Counts
755 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶11.2%
(/.f64 #s(literal -2 binary64) x)
✓62.9%
(-.f64 x (/.f64 y (*.f64 y (*.f64 x #s(literal 1/2 binary64)))))
✓63.0%
(-.f64 x (/.f64 #s(literal 2 binary64) x))
▶99.9%
(-.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))))
✓78.6%
(-.f64 x y)
✓64.7%
x
Compiler

Compiled 44 to 30 computations (31.8% saved)

simplify36.0ms (0.1%)

Algorithm
1×egg-herbie
Localize:

Found 5 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 #s(literal -2 binary64) x)
✓cost-diff0
(/.f64 #s(literal 1 binary64) y)
✓cost-diff0
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64))))
✓cost-diff0
(-.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))))
Rules
268×fnmadd-define
238×fmsub-define
228×fnmsub-define
224×fma-lowering-fma.f32
224×fma-lowering-fma.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01136
11933
22933
34433
47933
515833
631333
751033
877333
997233
10109033
11111233
12113233
13114033
0114033
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(- x (/ 1 (+ (/ 1 y) (* x 1/2))))
x
(/ 1 (+ (/ 1 y) (* x 1/2)))
1
(+ (/ 1 y) (* x 1/2))
(/ 1 y)
y
(* x 1/2)
1/2
(/ -2 x)
-2
x
Outputs
(- x (/ 1 (+ (/ 1 y) (* x 1/2))))
(+.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1 binary64) y) (*.f64 x #s(literal -1/2 binary64)))))
x
(/ 1 (+ (/ 1 y) (* x 1/2)))
(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64))))
1
#s(literal 1 binary64)
(+ (/ 1 y) (* x 1/2))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
y
(* x 1/2)
(*.f64 x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
-2
#s(literal -2 binary64)
x

localize54.0ms (0.2%)

Localize:

Found 5 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(/.f64 #s(literal -2 binary64) x)
✓accuracy100.0%
(-.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))))
✓accuracy100.0%
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
✓accuracy100.0%
(*.f64 x #s(literal 1/2 binary64))
✓accuracy99.9%
(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64))))
Results
26.0ms256×0valid
Compiler

Compiled 45 to 12 computations (73.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.0ms
ival-div: 7.0ms (57.1% of total)
ival-mult: 2.0ms (16.3% of total)
ival-sub: 1.0ms (8.2% of total)
ival-add: 1.0ms (8.2% of total)
const: 1.0ms (8.2% of total)
backward-pass: 0.0ms (0% of total)

series5.0ms (0%)

Counts
6 → 108
Calls
Call 1
Inputs
#<alt (- x (/ 1 (+ (/ 1 y) (* x 1/2))))>
#<alt (/ 1 (+ (/ 1 y) (* x 1/2)))>
#<alt (+ (/ 1 y) (* x 1/2))>
#<alt (/ 1 y)>
#<alt (/ -2 x)>
#<alt (* x 1/2)>
Outputs
#<alt (* -1 y)>
#<alt (- (* x (+ 1 (* 1/2 (pow y 2)))) y)>
#<alt (- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)>
#<alt (- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)>
#<alt x>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))>
#<alt x>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))>
#<alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))>
#<alt x>
#<alt (+ x (* -1 y))>
#<alt (+ x (* y (- (* 1/2 (* x y)) 1)))>
#<alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))>
#<alt (- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt y>
#<alt (* y (+ 1 (* -1/2 (* x y))))>
#<alt (* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))>
#<alt (* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))>
#<alt (/ 2 x)>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))>
#<alt (- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))>
#<alt (/ 2 x)>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))>
#<alt y>
#<alt (+ y (* -1/2 (* x (pow y 2))))>
#<alt (+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))>
#<alt (+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))>
#<alt (/ 2 x)>
#<alt (/ (- 2 (* 4 (/ 1 (* x y)))) x)>
#<alt (/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)>
#<alt (/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)>
#<alt (/ 2 x)>
#<alt (* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))>
#<alt (/ 1 y)>
#<alt (/ (+ 1 (* 1/2 (* x y))) y)>
#<alt (/ (+ 1 (* 1/2 (* x y))) y)>
#<alt (/ (+ 1 (* 1/2 (* x y))) y)>
#<alt (* 1/2 x)>
#<alt (+ (* 1/2 x) (/ 1 y))>
#<alt (+ (* 1/2 x) (/ 1 y))>
#<alt (+ (* 1/2 x) (/ 1 y))>
#<alt (* 1/2 x)>
#<alt (+ (* 1/2 x) (/ 1 y))>
#<alt (+ (* 1/2 x) (/ 1 y))>
#<alt (+ (* 1/2 x) (/ 1 y))>
#<alt (/ 1 y)>
#<alt (+ (* 1/2 x) (/ 1 y))>
#<alt (+ (* 1/2 x) (/ 1 y))>
#<alt (+ (* 1/2 x) (/ 1 y))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 (* x y))))>
#<alt (* x (+ 1/2 (/ 1 (* x y))))>
#<alt (* x (+ 1/2 (/ 1 (* x y))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 (* x y))))>
#<alt (* x (+ 1/2 (/ 1 (* x y))))>
#<alt (* x (+ 1/2 (/ 1 (* x y))))>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ 1 y)>
#<alt (/ -2 x)>
#<alt (/ -2 x)>
#<alt (/ -2 x)>
#<alt (/ -2 x)>
#<alt (/ -2 x)>
#<alt (/ -2 x)>
#<alt (/ -2 x)>
#<alt (/ -2 x)>
#<alt (/ -2 x)>
#<alt (/ -2 x)>
#<alt (/ -2 x)>
#<alt (/ -2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
Calls

27 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(* x 1/2)
0.0ms
x
@-inf
(- x (/ 1 (+ (/ 1 y) (* x 1/2))))
0.0ms
x
@0
(/ -2 x)
0.0ms
x
@0
(- x (/ 1 (+ (/ 1 y) (* x 1/2))))
0.0ms
x
@inf
(- x (/ 1 (+ (/ 1 y) (* x 1/2))))

rewrite311.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
3444×*-lowering-*.f32
3444×*-lowering-*.f64
2540×/-lowering-/.f32
2540×/-lowering-/.f64
1502×sum3-define
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01130
16627
253527
3667227
0810127
Stop Event
1×iter limit
1×node limit
Counts
6 → 256
Calls
Call 1
Inputs
(- x (/ 1 (+ (/ 1 y) (* x 1/2))))
(/ 1 (+ (/ 1 y) (* x 1/2)))
(+ (/ 1 y) (* x 1/2))
(/ 1 y)
(/ -2 x)
(* x 1/2)
Outputs
(+.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))))
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))) x)
(+.f64 (/.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x x) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))) (-.f64 #s(literal 0 binary64) x)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))))) (neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64))) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))))) (+.f64 (*.f64 x x) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))) (-.f64 #s(literal 0 binary64) x)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)))))))
(+.f64 (/.f64 (*.f64 x x) (+.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64)))))) (neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)))) (+.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64))))))))
(-.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64)))))
(-.f64 #s(literal 0 binary64) (-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64)))) x))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))) (-.f64 #s(literal 0 binary64) x))
(-.f64 (/.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x x) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))) (-.f64 #s(literal 0 binary64) x)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))))) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64))) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))))) (+.f64 (*.f64 x x) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))) (-.f64 #s(literal 0 binary64) x)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64)))))) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)))) (+.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64)))))))
(-.f64 (+.f64 x #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64)))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))) x)
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64)))) x)
(neg.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)))))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))) (-.f64 #s(literal 0 binary64) x)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)))))))
(neg.f64 (/.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))) (-.f64 #s(literal 0 binary64) x))))
(neg.f64 (/.f64 (+.f64 (neg.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64))) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)))))) (+.f64 (*.f64 x x) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))) (-.f64 #s(literal 0 binary64) x)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))))))
(neg.f64 (/.f64 (+.f64 (neg.f64 (*.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))))) (+.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))))) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)))))))
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)))))) (+.f64 (*.f64 x x) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))) (-.f64 #s(literal 0 binary64) x)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)))))
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)))))) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)))) (-.f64 (*.f64 x x) (/.f64 x (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))))))
(/.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))))) (+.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64))))))
(/.f64 (+.f64 (neg.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64))) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)))))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))) (-.f64 #s(literal 0 binary64) x)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))))))
(/.f64 (+.f64 (neg.f64 (*.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64))) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64))) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)))) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64))) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)))))))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))) (-.f64 #s(literal 0 binary64) x)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64))) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))))) (+.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64))) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))))))))))
(/.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)))))) (*.f64 (+.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64))))) (+.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)))))))
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64))) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)))) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64))) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))))))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))) (-.f64 #s(literal 0 binary64) x)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)))) (+.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64))) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))))))))
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64))) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)))) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64))) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y))))))) (*.f64 (+.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 x #s(literal 2 binary64))))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)))) (+.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)) (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) y)))))))))
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(*.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y))) (*.f64 x (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))) (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 y (*.f64 y y))) (*.f64 (*.f64 x (-.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1/2 binary64) y))) (*.f64 x (-.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1/2 binary64) y)))))) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 y y)) (*.f64 x (-.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1/2 binary64) y)))))
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(exp.f64 (log.f64 (/.f64 #s(literal 1 binary64) y)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) y))
(neg.f64 (/.f64 #s(literal -1 binary64) y))
(/.f64 #s(literal 1 binary64) y)
(/.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64))
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(pow.f64 (pow.f64 y #s(literal -1/2 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) y))
(*.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64))
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(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 y #s(literal -1/2 binary64))) (pow.f64 y #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 x #s(literal -2 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) x))
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(/.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
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(*.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))
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(-.f64 #s(literal 0 binary64) (/.f64 x #s(literal -2 binary64)))
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(/.f64 x #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal -2 binary64) x)))
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(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 x #s(literal 2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 x #s(literal -2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64))

simplify268.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
3796×*-lowering-*.f32
3796×*-lowering-*.f64
1776×/-lowering-/.f32
1776×/-lowering-/.f64
1606×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0224908
1792859
22279830
37647830
08558830
Stop Event
1×iter limit
1×node limit
Counts
108 → 108
Calls
Call 1
Inputs
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
y
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
y
(+ y (* -1/2 (* x (pow y 2))))
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(/ 2 x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/ 2 x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
(/ 1 y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/ (+ 1 (* 1/2 (* x y))) y)
(* 1/2 x)
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(* 1/2 x)
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(/ 1 y)
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(+ (* 1/2 x) (/ 1 y))
(* 1/2 x)
(* x (+ 1/2 (/ 1 (* x y))))
(* x (+ 1/2 (/ 1 (* x y))))
(* x (+ 1/2 (/ 1 (* x y))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 (* x y))))
(* x (+ 1/2 (/ 1 (* x y))))
(* x (+ 1/2 (/ 1 (* x y))))
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ 1 y)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
Outputs
(* -1 y)
(-.f64 #s(literal 0 binary64) y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(+.f64 x (*.f64 y (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 y x)))))
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 y x)))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
(-.f64 (*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 y x))))) (*.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))) y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x))) (/.f64 (/.f64 #s(literal 4 binary64) y) (*.f64 x (*.f64 x x)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(*.f64 x (+.f64 (/.f64 (/.f64 #s(literal 4 binary64) y) (*.f64 x (*.f64 x x))) (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x))) (/.f64 (/.f64 #s(literal -8 binary64) (*.f64 y y)) (pow.f64 x #s(literal 4 binary64))))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x))))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x))) (/.f64 (/.f64 #s(literal 4 binary64) y) (*.f64 x (*.f64 x x)))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(*.f64 (+.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 y y))) (/.f64 #s(literal -4 binary64) y)) (*.f64 x (*.f64 x x))))) (-.f64 #s(literal 0 binary64) x))
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+.f64 x (*.f64 y (+.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 y x)))))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 y x)))))) y)
(- x (* 2 (/ 1 x)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(+.f64 x (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(+.f64 x (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 (/.f64 #s(literal -8 binary64) (*.f64 y y)) x)) x)) x))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(+.f64 (+.f64 x (/.f64 (/.f64 (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))) y) (*.f64 y y))) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 (/.f64 #s(literal -8 binary64) (*.f64 y y)) x)) x)) x))
(- x (* 2 (/ 1 x)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(+.f64 x (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(+.f64 x (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 (/.f64 #s(literal -8 binary64) (*.f64 y y)) x)) x)) x))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(+.f64 x (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))) y) (/.f64 #s(literal -8 binary64) (*.f64 x (*.f64 x x)))) y)) y) (/.f64 #s(literal -2 binary64) x)))
y
(* y (+ 1 (* -1/2 (* x y))))
(*.f64 y (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal -1/2 binary64)))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(+.f64 y (*.f64 x (*.f64 (*.f64 y y) (+.f64 (*.f64 x (*.f64 y #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(*.f64 y (+.f64 #s(literal 1 binary64) (*.f64 y (+.f64 (*.f64 y (+.f64 (*.f64 x (*.f64 (*.f64 y (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (*.f64 x x) #s(literal 1/4 binary64)))) (*.f64 x #s(literal -1/2 binary64))))))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x)
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x)
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(+.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x) (/.f64 (/.f64 #s(literal -16 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 y (*.f64 y y))))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x)
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x)
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
(-.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 x x)) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))) y) (/.f64 #s(literal -8 binary64) (*.f64 x (*.f64 x x)))) y)) y))
y
(+ y (* -1/2 (* x (pow y 2))))
(*.f64 y (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 x #s(literal -1/2 binary64)))))
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(+.f64 y (*.f64 x (*.f64 (*.f64 y y) (+.f64 (*.f64 x (*.f64 y #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))))
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(+.f64 y (*.f64 x (+.f64 (*.f64 x (*.f64 x (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -1/8 binary64)))) (*.f64 (*.f64 y y) (+.f64 (*.f64 x (*.f64 y #s(literal 1/4 binary64))) #s(literal -1/2 binary64))))))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x) (/.f64 (/.f64 #s(literal 16 binary64) (*.f64 x (*.f64 y (*.f64 y y)))) (*.f64 x x)))) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x)
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (*.f64 x (*.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 (+.f64 (/.f64 #s(literal 16 binary64) (*.f64 x (*.f64 y (*.f64 y y)))) (/.f64 #s(literal -8 binary64) (*.f64 y y))) x)) x)) x)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 y x))) y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 y x))) y)
(/ (+ 1 (* 1/2 (* x y))) y)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 y x))) y)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(+ (* 1/2 x) (/ 1 y))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(+ (* 1/2 x) (/ 1 y))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(+ (* 1/2 x) (/ 1 y))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(+ (* 1/2 x) (/ 1 y))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(+ (* 1/2 x) (/ 1 y))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(+ (* 1/2 x) (/ 1 y))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(+ (* 1/2 x) (/ 1 y))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(+ (* 1/2 x) (/ 1 y))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(+ (* 1/2 x) (/ 1 y))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (/ 1 (* x y))))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 (* x y))))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 (* x y))))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (/ 1 (* x y))))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 (* x y))))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 (* x y))))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))

eval44.0ms (0.1%)

Compiler

Compiled 11591 to 1031 computations (91.1% saved)

prune38.0ms (0.1%)

Pruning

6 alts after pruning (0 fresh and 6 done)

PrunedKeptTotal
New3640364
Fresh000
Picked022
Done044
Total3646370
Accuracy
100.0%
Counts
370 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓11.2%
(/.f64 #s(literal -2 binary64) x)
✓62.9%
(-.f64 x (/.f64 y (*.f64 y (*.f64 x #s(literal 1/2 binary64)))))
✓63.0%
(-.f64 x (/.f64 #s(literal 2 binary64) x))
✓99.9%
(-.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))))
✓78.6%
(-.f64 x y)
✓64.7%
x
Compiler

Compiled 102 to 56 computations (45.1% saved)

regimes11.0ms (0%)

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

3 calls:

4.0ms
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
3.0ms
y
3.0ms
x
Results
AccuracySegmentsBranch
99.9%1x
99.9%1y
99.9%1(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes5.0ms (0%)

Counts
5 → 3
Calls
Call 1
Inputs
x
(-.f64 x y)
(/.f64 #s(literal -2 binary64) x)
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(-.f64 x (/.f64 y (*.f64 y (*.f64 x #s(literal 1/2 binary64)))))
Outputs
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(-.f64 x y)
(-.f64 x (/.f64 #s(literal 2 binary64) x))
Calls

2 calls:

2.0ms
y
2.0ms
x
Results
AccuracySegmentsBranch
91.0%3x
93.4%3y
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0%)

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

2 calls:

3.0ms
x
2.0ms
y
Results
AccuracySegmentsBranch
90.3%3x
85.5%3y
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
x
Outputs
x
Calls

2 calls:

1.0ms
y
1.0ms
x
Results
AccuracySegmentsBranch
64.7%1y
64.7%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch13.0ms (0%)

Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
6.0ms
3.111006042253189e+131
4.77228680466399e+131
6.0ms
-2.0714099212189659e+124
-1.4706272121459122e+124
Results
8.0ms128×0valid
Compiler

Compiled 130 to 93 computations (28.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-div: 2.0ms (45.1% of total)
ival-sub: 1.0ms (22.5% of total)
ival-add: 1.0ms (22.5% of total)
ival-mult: 1.0ms (22.5% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

bsearch27.0ms (0.1%)

Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
10.0ms
9.637726178354864e-17
4.013073467215199e-15
14.0ms
-2366252506146097000.0
-448155953296.73505
Results
17.0ms256×0valid
Compiler

Compiled 178 to 125 computations (29.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-div: 3.0ms (30.9% of total)
ival-sub: 2.0ms (20.6% of total)
ival-mult: 2.0ms (20.6% of total)
ival-add: 1.0ms (10.3% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

simplify14.0ms (0%)

Algorithm
1×egg-herbie
Rules
52×unsub-neg_binary64
52×neg-mul-1_binary64
30×*-commutative_binary64
28×+-commutative_binary64
26×sub-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02542
14242
26042
37842
410442
514442
620642
721842
821942
Stop Event
1×saturated
Calls
Call 1
Inputs
(-.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))))
(if (<=.f64 y #s(literal -20500000000000000056798069475560676837012558648363367074968265688276043180461617687266988700071503457221685099122656473513984 binary64)) (-.f64 x (/.f64 #s(literal 2 binary64) x)) (if (<=.f64 y #s(literal 360000000000000031372409717677201269732734474120074716784443759555953962394114064768610615152700303377611115442024557690828837879808 binary64)) (-.f64 x y) (-.f64 x (/.f64 #s(literal 2 binary64) x))))
(if (<=.f64 x #s(literal -450000000000 binary64)) x (if (<=.f64 x #s(literal 2535301200456459/633825300114114700748351602688 binary64)) (-.f64 x y) x))
x
Outputs
(-.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))))
(+.f64 x (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal -1 binary64) y) (*.f64 x #s(literal 1/2 binary64)))))
(if (<=.f64 y #s(literal -20500000000000000056798069475560676837012558648363367074968265688276043180461617687266988700071503457221685099122656473513984 binary64)) (-.f64 x (/.f64 #s(literal 2 binary64) x)) (if (<=.f64 y #s(literal 360000000000000031372409717677201269732734474120074716784443759555953962394114064768610615152700303377611115442024557690828837879808 binary64)) (-.f64 x y) (-.f64 x (/.f64 #s(literal 2 binary64) x))))
(if (<=.f64 x #s(literal -450000000000 binary64)) x (if (<=.f64 x #s(literal 2535301200456459/633825300114114700748351602688 binary64)) (-.f64 x y) x))
x

soundness1.1s (3.7%)

Rules
4646×*-lowering-*.f32
4646×*-lowering-*.f64
4140×*-lowering-*.f32
4140×*-lowering-*.f64
3952×*-lowering-*.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02311040
1826982
22365947
37863947
08125947
02531700
18861648
225421622
084961622
0935
15832
251832
3749732
0836832
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 99 to 60 computations (39.4% saved)

preprocess30.0ms (0.1%)

Compiler

Compiled 122 to 70 computations (42.6% saved)

end0.0ms (0%)

Profiling

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