Octave 3.8, jcobi/4, as called

Time bar (total: 5.8s)

analyze4.0ms (0.1%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%50%50%0%0%0%0
0%0%50%50%0%0%0%1
50%25%25%50%0%0%0%2
50%25%25%50%0%0%0%3
75%37.5%12.5%50%0%0%0%4
87.5%43.7%6.2%50%0%0%0%5
93.8%46.9%3.1%50%0%0%0%6
96.9%48.4%1.6%50%0%0%0%7
98.4%49.2%0.8%50%0%0%0%8
99.2%49.6%0.4%50%0%0%0%9
99.6%49.8%0.2%50%0%0%0%10
99.8%49.9%0.1%50%0%0%0%11
99.9%49.9%0%50%0%0%0%12
Compiler

Compiled 29 to 12 computations (58.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.0ms
ival-mult: 1.0ms (50.9% of total)
ival-sub: 0.0ms (0% of total)
ival-div: 0.0ms (0% of total)
const: 0.0ms (0% of total)
ival->: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample1.0s (18.2%)

Results
825.0ms8256×0valid
Precisions
Click to see histograms. Total time spent on operations: 583.0ms
ival-mult: 296.0ms (50.8% of total)
ival-div: 128.0ms (22% of total)
ival->: 74.0ms (12.7% of total)
ival-sub: 66.0ms (11.3% of total)
const: 16.0ms (2.7% of total)
backward-pass: 3.0ms (0.5% of total)
Bogosity

preprocess421.0ms (7.3%)

Algorithm
2×egg-herbie
Rules
4808×*-lowering-*.f32
4808×*-lowering-*.f64
3132×/-lowering-/.f32
3132×/-lowering-/.f64
1672×associate-/r/
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01964
18855
258836
3441236
01021
14018
219312
3108612
4376011
5581211
0825211
Stop Event
1×iter limit
1×node limit
1×node limit
Calls
Call 1
Inputs
(/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1))
Outputs
(/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1))
(*.f64 i (/.f64 i (+.f64 (*.f64 (*.f64 i i) #s(literal 16 binary64)) #s(literal -4 binary64))))
Call 2
Inputs
(/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1))
(/ (/ (* (* (neg i) (neg i)) (* (neg i) (neg i))) (* (* 2 (neg i)) (* 2 (neg i)))) (- (* (* 2 (neg i)) (* 2 (neg i))) 1))
(neg (/ (/ (* (* (neg i) (neg i)) (* (neg i) (neg i))) (* (* 2 (neg i)) (* 2 (neg i)))) (- (* (* 2 (neg i)) (* 2 (neg i))) 1)))
Outputs
(/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1))
(* i (* i (/ 1/4 (fnmsub i (* i -4) 1))))
(/ (/ (* (* (neg i) (neg i)) (* (neg i) (neg i))) (* (* 2 (neg i)) (* 2 (neg i)))) (- (* (* 2 (neg i)) (* 2 (neg i))) 1))
(* i (* i (/ 1/4 (fnmsub i (* i -4) 1))))
(neg (/ (/ (* (* (neg i) (neg i)) (* (neg i) (neg i))) (* (* 2 (neg i)) (* 2 (neg i)))) (- (* (* 2 (neg i)) (* 2 (neg i))) 1)))
(* i (* i (/ 1/4 (fnmsub i (* i 4) -1))))
Symmetry

(abs i)

explain130.0ms (2.3%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1990-0-(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i)))
700-0-(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i))) (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i)) #s(literal 1 binary64)))
00-0-(*.f64 #s(literal 2 binary64) i)
00-0-#s(literal 2 binary64)
00-0-i
00-0-(-.f64 (*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i)) #s(literal 1 binary64))
00-0-(*.f64 (*.f64 i i) (*.f64 i i))
00-0-(*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i))
00-0-(*.f64 i i)
00-0-#s(literal 1 binary64)
Results
56.0ms512×0valid
Compiler

Compiled 174 to 32 computations (81.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 25.0ms
ival-mult: 14.0ms (56.4% of total)
ival-div: 7.0ms (28.2% of total)
ival-sub: 3.0ms (12.1% of total)
const: 1.0ms (4% of total)
backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 12 to 8 computations (33.3% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶23.8%
(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i))) (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i)) #s(literal 1 binary64)))
▶73.4%
(*.f64 i (/.f64 i (+.f64 (*.f64 (*.f64 i i) #s(literal 16 binary64)) #s(literal -4 binary64))))
Compiler

Compiled 38 to 18 computations (52.6% saved)

simplify232.0ms (4%)

Algorithm
1×egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓cost-diff128
(-.f64 (*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i)) #s(literal 1 binary64))
✓cost-diff128
(*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i))
✓cost-diff640
(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i)))
✓cost-diff896
(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i))) (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i)) #s(literal 1 binary64)))
✓cost-diff0
(*.f64 (*.f64 i i) #s(literal 16 binary64))
✓cost-diff0
(+.f64 (*.f64 (*.f64 i i) #s(literal 16 binary64)) #s(literal -4 binary64))
✓cost-diff0
(/.f64 i (+.f64 (*.f64 (*.f64 i i) #s(literal 16 binary64)) #s(literal -4 binary64)))
✓cost-diff0
(*.f64 i (/.f64 i (+.f64 (*.f64 (*.f64 i i) #s(literal 16 binary64)) #s(literal -4 binary64))))
Rules
4816×*-lowering-*.f32
4816×*-lowering-*.f64
3132×/-lowering-/.f32
3132×/-lowering-/.f64
1670×associate-/r/
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01686
15381
221273
3110573
4373773
5580073
0823473
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* i (/ i (+ (* (* i i) 16) -4)))
i
(/ i (+ (* (* i i) 16) -4))
(+ (* (* i i) 16) -4)
(* (* i i) 16)
(* i i)
16
-4
(/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1))
(/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i)))
(* (* i i) (* i i))
(* i i)
i
(* (* 2 i) (* 2 i))
(* 2 i)
2
(- (* (* 2 i) (* 2 i)) 1)
1
Outputs
(* i (/ i (+ (* (* i i) 16) -4)))
(/.f64 (*.f64 i i) (+.f64 #s(literal -4 binary64) (*.f64 (*.f64 i i) #s(literal 16 binary64))))
i
(/ i (+ (* (* i i) 16) -4))
(/.f64 i (+.f64 #s(literal -4 binary64) (*.f64 (*.f64 i i) #s(literal 16 binary64))))
(+ (* (* i i) 16) -4)
(+.f64 #s(literal -4 binary64) (*.f64 (*.f64 i i) #s(literal 16 binary64)))
(* (* i i) 16)
(*.f64 (*.f64 i i) #s(literal 16 binary64))
(* i i)
(*.f64 i i)
16
#s(literal 16 binary64)
-4
#s(literal -4 binary64)
(/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1))
(/.f64 (*.f64 i i) (+.f64 #s(literal -4 binary64) (*.f64 (*.f64 i i) #s(literal 16 binary64))))
(/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i)))
(/.f64 (*.f64 i i) #s(literal 4 binary64))
(* (* i i) (* i i))
(*.f64 i (*.f64 i (*.f64 i i)))
(* i i)
(*.f64 i i)
i
(* (* 2 i) (* 2 i))
(*.f64 (*.f64 i i) #s(literal 4 binary64))
(* 2 i)
(*.f64 i #s(literal 2 binary64))
2
#s(literal 2 binary64)
(- (* (* 2 i) (* 2 i)) 1)
(+.f64 (*.f64 (*.f64 i i) #s(literal 4 binary64)) #s(literal -1 binary64))
1
#s(literal 1 binary64)

localize62.0ms (1.1%)

Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 #s(literal 2 binary64) i)
✓accuracy99.8%
(*.f64 (*.f64 i i) (*.f64 i i))
✓accuracy73.5%
(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i))) (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i)) #s(literal 1 binary64)))
✓accuracy30.0%
(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i)))
✓accuracy100.0%
(*.f64 i i)
✓accuracy100.0%
(*.f64 (*.f64 i i) #s(literal 16 binary64))
✓accuracy99.8%
(*.f64 i (/.f64 i (+.f64 (*.f64 (*.f64 i i) #s(literal 16 binary64)) #s(literal -4 binary64))))
✓accuracy74.8%
(/.f64 i (+.f64 (*.f64 (*.f64 i i) #s(literal 16 binary64)) #s(literal -4 binary64)))
Results
41.0ms256×0valid
Compiler

Compiled 112 to 17 computations (84.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 22.0ms
ival-mult: 13.0ms (60.3% of total)
ival-div: 5.0ms (23.2% of total)
ival-sub: 1.0ms (4.6% of total)
ival-add: 1.0ms (4.6% of total)
const: 1.0ms (4.6% of total)
backward-pass: 0.0ms (0% of total)

series14.0ms (0.2%)

Counts
11 → 132
Calls
Call 1
Inputs
#<alt (* i (/ i (+ (* (* i i) 16) -4)))>
#<alt (/ i (+ (* (* i i) 16) -4))>
#<alt (+ (* (* i i) 16) -4)>
#<alt (* (* i i) 16)>
#<alt (/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1))>
#<alt (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i)))>
#<alt (* (* 2 i) (* 2 i))>
#<alt (- (* (* 2 i) (* 2 i)) 1)>
#<alt (* i i)>
#<alt (* (* i i) (* i i))>
#<alt (* 2 i)>
Outputs
#<alt (* -1/4 (pow i 2))>
#<alt (* (pow i 2) (- (* -1 (pow i 2)) 1/4))>
#<alt (* (pow i 2) (- (* (pow i 2) (- (* -4 (pow i 2)) 1)) 1/4))>
#<alt (* (pow i 2) (- (* (pow i 2) (- (* (pow i 2) (- (* -16 (pow i 2)) 4)) 1)) 1/4))>
#<alt 1/16>
#<alt (+ 1/16 (* 1/64 (/ 1 (pow i 2))))>
#<alt (+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))>
#<alt (+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))>
#<alt 1/16>
#<alt (+ 1/16 (* 1/64 (/ 1 (pow i 2))))>
#<alt (+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))>
#<alt (+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))>
#<alt (* -1/4 i)>
#<alt (* i (- (* -1 (pow i 2)) 1/4))>
#<alt (* i (- (* (pow i 2) (- (* -4 (pow i 2)) 1)) 1/4))>
#<alt (* i (- (* (pow i 2) (- (* (pow i 2) (- (* -16 (pow i 2)) 4)) 1)) 1/4))>
#<alt (/ 1/16 i)>
#<alt (/ (+ 1/16 (* 1/64 (/ 1 (pow i 2)))) i)>
#<alt (/ (+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2))))) i)>
#<alt (/ (+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6)))))) i)>
#<alt (/ 1/16 i)>
#<alt (/ (+ 1/16 (* 1/64 (/ 1 (pow i 2)))) i)>
#<alt (* -1 (/ (- (* -1 (/ (+ 1/64 (* 1/256 (/ 1 (pow i 2)))) (pow i 2))) 1/16) i))>
#<alt (* -1 (/ (- (* -1 (/ (+ 1/256 (* 1/1024 (/ 1 (pow i 2)))) (pow i 4))) (+ 1/16 (* 1/64 (/ 1 (pow i 2))))) i))>
#<alt -4>
#<alt (- (* 16 (pow i 2)) 4)>
#<alt (- (* 16 (pow i 2)) 4)>
#<alt (- (* 16 (pow i 2)) 4)>
#<alt (* 16 (pow i 2))>
#<alt (* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))>
#<alt (* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))>
#<alt (* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))>
#<alt (* 16 (pow i 2))>
#<alt (* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))>
#<alt (* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))>
#<alt (* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 (pow i 2))>
#<alt (* -1/4 (pow i 2))>
#<alt (* (pow i 2) (- (* -1 (pow i 2)) 1/4))>
#<alt (* (pow i 2) (- (* (pow i 2) (- (* -4 (pow i 2)) 1)) 1/4))>
#<alt (* (pow i 2) (- (* (pow i 2) (- (* (pow i 2) (- (* -16 (pow i 2)) 4)) 1)) 1/4))>
#<alt 1/16>
#<alt (+ 1/16 (* 1/64 (/ 1 (pow i 2))))>
#<alt (+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))>
#<alt (+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))>
#<alt 1/16>
#<alt (+ 1/16 (* 1/64 (/ 1 (pow i 2))))>
#<alt (+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))>
#<alt (+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))>
#<alt (* 1/4 (pow i 2))>
#<alt (* 1/4 (pow i 2))>
#<alt (* 1/4 (pow i 2))>
#<alt (* 1/4 (pow i 2))>
#<alt (* 1/4 (pow i 2))>
#<alt (* 1/4 (pow i 2))>
#<alt (* 1/4 (pow i 2))>
#<alt (* 1/4 (pow i 2))>
#<alt (* 1/4 (pow i 2))>
#<alt (* 1/4 (pow i 2))>
#<alt (* 1/4 (pow i 2))>
#<alt (* 1/4 (pow i 2))>
#<alt (* 4 (pow i 2))>
#<alt (* 4 (pow i 2))>
#<alt (* 4 (pow i 2))>
#<alt (* 4 (pow i 2))>
#<alt (* 4 (pow i 2))>
#<alt (* 4 (pow i 2))>
#<alt (* 4 (pow i 2))>
#<alt (* 4 (pow i 2))>
#<alt (* 4 (pow i 2))>
#<alt (* 4 (pow i 2))>
#<alt (* 4 (pow i 2))>
#<alt (* 4 (pow i 2))>
#<alt -1>
#<alt (- (* 4 (pow i 2)) 1)>
#<alt (- (* 4 (pow i 2)) 1)>
#<alt (- (* 4 (pow i 2)) 1)>
#<alt (* 4 (pow i 2))>
#<alt (* (pow i 2) (- 4 (/ 1 (pow i 2))))>
#<alt (* (pow i 2) (- 4 (/ 1 (pow i 2))))>
#<alt (* (pow i 2) (- 4 (/ 1 (pow i 2))))>
#<alt (* 4 (pow i 2))>
#<alt (* (pow i 2) (- 4 (/ 1 (pow i 2))))>
#<alt (* (pow i 2) (- 4 (/ 1 (pow i 2))))>
#<alt (* (pow i 2) (- 4 (/ 1 (pow i 2))))>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 4)>
#<alt (pow i 4)>
#<alt (pow i 4)>
#<alt (pow i 4)>
#<alt (pow i 4)>
#<alt (pow i 4)>
#<alt (pow i 4)>
#<alt (pow i 4)>
#<alt (pow i 4)>
#<alt (pow i 4)>
#<alt (pow i 4)>
#<alt (pow i 4)>
#<alt (* 2 i)>
#<alt (* 2 i)>
#<alt (* 2 i)>
#<alt (* 2 i)>
#<alt (* 2 i)>
#<alt (* 2 i)>
#<alt (* 2 i)>
#<alt (* 2 i)>
#<alt (* 2 i)>
#<alt (* 2 i)>
#<alt (* 2 i)>
#<alt (* 2 i)>
Calls

33 calls:

TimeVariablePointExpression
7.0ms
i
@-inf
(* 2 i)
1.0ms
i
@inf
(/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i)))
0.0ms
i
@inf
(* i (/ i (+ (* (* i i) 16) -4)))
0.0ms
i
@0
(* i (/ i (+ (* (* i i) 16) -4)))
0.0ms
i
@inf
(* (* i i) 16)

rewrite314.0ms (5.4%)

Algorithm
1×batch-egg-rewrite
Rules
5958×*-lowering-*.f32
5958×*-lowering-*.f64
3702×/-lowering-/.f32
3702×/-lowering-/.f64
1090×frac-times
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01682
110374
291266
0882166
Stop Event
1×iter limit
1×node limit
Counts
11 → 751
Calls
Call 1
Inputs
(* i (/ i (+ (* (* i i) 16) -4)))
(/ i (+ (* (* i i) 16) -4))
(+ (* (* i i) 16) -4)
(* (* i i) 16)
(/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1))
(/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i)))
(* (* 2 i) (* 2 i))
(- (* (* 2 i) (* 2 i)) 1)
(* i i)
(* (* i i) (* i i))
(* 2 i)
Outputs
(+.f64 (*.f64 (/.f64 (*.f64 i i) (+.f64 (*.f64 i (*.f64 (*.f64 i i) (*.f64 (*.f64 i (*.f64 i i)) #s(literal 4096 binary64)))) #s(literal -64 binary64))) (*.f64 i (*.f64 i (*.f64 (*.f64 i i) #s(literal 256 binary64))))) (*.f64 (/.f64 (*.f64 i i) (+.f64 (*.f64 i (*.f64 (*.f64 i i) (*.f64 (*.f64 i (*.f64 i i)) #s(literal 4096 binary64)))) #s(literal -64 binary64))) (+.f64 #s(literal 16 binary64) (*.f64 (*.f64 i i) #s(literal 64 binary64)))))
(+.f64 (*.f64 (/.f64 (*.f64 i i) (+.f64 (*.f64 i (*.f64 (*.f64 i i) (*.f64 (*.f64 i (*.f64 i i)) #s(literal 4096 binary64)))) #s(literal -64 binary64))) (+.f64 #s(literal 16 binary64) (*.f64 (*.f64 i i) #s(literal 64 binary64)))) (*.f64 (/.f64 (*.f64 i i) (+.f64 (*.f64 i (*.f64 (*.f64 i i) (*.f64 (*.f64 i (*.f64 i i)) #s(literal 4096 binary64)))) #s(literal -64 binary64))) (*.f64 i (*.f64 i (*.f64 (*.f64 i i) #s(literal 256 binary64))))))
(+.f64 (*.f64 (/.f64 (*.f64 i i) (+.f64 (*.f64 i (*.f64 i (*.f64 (*.f64 i i) #s(literal 256 binary64)))) #s(literal -16 binary64))) (*.f64 i (*.f64 i #s(literal 16 binary64)))) (*.f64 (/.f64 (*.f64 i i) (+.f64 (*.f64 i (*.f64 i (*.f64 (*.f64 i i) #s(literal 256 binary64)))) #s(literal -16 binary64))) #s(literal 4 binary64)))
(+.f64 (*.f64 (*.f64 i (*.f64 i (*.f64 (*.f64 i i) #s(literal 256 binary64)))) (/.f64 (*.f64 i i) (+.f64 (*.f64 i (*.f64 (*.f64 i i) (*.f64 (*.f64 i (*.f64 i i)) #s(literal 4096 binary64)))) #s(literal -64 binary64)))) (*.f64 (+.f64 #s(literal 16 binary64) (*.f64 (*.f64 i i) #s(literal 64 binary64))) (/.f64 (*.f64 i i) (+.f64 (*.f64 i (*.f64 (*.f64 i i) (*.f64 (*.f64 i (*.f64 i i)) #s(literal 4096 binary64)))) #s(literal -64 binary64)))))
(+.f64 (*.f64 (+.f64 #s(literal 16 binary64) (*.f64 (*.f64 i i) #s(literal 64 binary64))) (/.f64 (*.f64 i i) (+.f64 (*.f64 i (*.f64 (*.f64 i i) (*.f64 (*.f64 i (*.f64 i i)) #s(literal 4096 binary64)))) #s(literal -64 binary64)))) (*.f64 (*.f64 i (*.f64 i (*.f64 (*.f64 i i) #s(literal 256 binary64)))) (/.f64 (*.f64 i i) (+.f64 (*.f64 i (*.f64 (*.f64 i i) (*.f64 (*.f64 i (*.f64 i i)) #s(literal 4096 binary64)))) #s(literal -64 binary64)))))
(+.f64 (*.f64 (*.f64 i (*.f64 i #s(literal 16 binary64))) (/.f64 (*.f64 i i) (+.f64 (*.f64 i (*.f64 i (*.f64 (*.f64 i i) #s(literal 256 binary64)))) #s(literal -16 binary64)))) (*.f64 #s(literal 4 binary64) (/.f64 (*.f64 i i) (+.f64 (*.f64 i (*.f64 i (*.f64 (*.f64 i i) #s(literal 256 binary64)))) #s(literal -16 binary64)))))
(neg.f64 (*.f64 (/.f64 i (-.f64 #s(literal 4 binary64) (*.f64 i (*.f64 i #s(literal 16 binary64))))) i))
(neg.f64 (*.f64 i (/.f64 i (-.f64 #s(literal 4 binary64) (*.f64 i (*.f64 i #s(literal 16 binary64)))))))
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(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 i)) #s(literal 1 binary64)))
(pow.f64 i #s(literal 2 binary64))
(pow.f64 (*.f64 i i) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 i)) #s(literal 2 binary64))
(*.f64 i i)
(*.f64 (*.f64 i i) #s(literal 1 binary64))
(*.f64 (exp.f64 (log.f64 i)) (exp.f64 (log.f64 i)))
(*.f64 (pow.f64 (*.f64 i i) #s(literal 1/2 binary64)) (pow.f64 (*.f64 i i) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 i)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 i) #s(literal 4 binary64)))
(exp.f64 (+.f64 (*.f64 #s(literal 2 binary64) (log.f64 i)) (*.f64 #s(literal 2 binary64) (log.f64 i))))
(-.f64 #s(literal 0 binary64) (*.f64 i (-.f64 #s(literal 0 binary64) (*.f64 i (*.f64 i i)))))
(neg.f64 (*.f64 i (-.f64 #s(literal 0 binary64) (*.f64 i (*.f64 i i)))))
(pow.f64 i #s(literal 4 binary64))
(pow.f64 (*.f64 i i) #s(literal 2 binary64))
(pow.f64 (*.f64 i (*.f64 i (*.f64 i i))) #s(literal 1 binary64))
(*.f64 i (*.f64 i (*.f64 i i)))
(*.f64 i (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 i (*.f64 i i)))))
(*.f64 i (*.f64 (*.f64 i (*.f64 i i)) #s(literal 1 binary64)))
(*.f64 (*.f64 i i) (*.f64 i i))
(*.f64 (*.f64 i i) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 i i))))
(*.f64 (*.f64 i (*.f64 i (*.f64 i i))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 i (*.f64 i (*.f64 i i))))
(*.f64 #s(literal -1 binary64) (*.f64 i (-.f64 #s(literal 0 binary64) (*.f64 i (*.f64 i i)))))
(*.f64 (-.f64 #s(literal 0 binary64) i) (-.f64 #s(literal 0 binary64) (*.f64 i (*.f64 i i))))
(*.f64 (*.f64 i (*.f64 i i)) i)
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 i i)) (-.f64 #s(literal 0 binary64) (*.f64 i i)))
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 i (*.f64 i i))) (-.f64 #s(literal 0 binary64) i))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 i i))) (*.f64 i i))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 i (*.f64 i i)))) i)
(exp.f64 (*.f64 (log.f64 (*.f64 i #s(literal 2 binary64))) #s(literal 1 binary64)))
(pow.f64 (*.f64 i #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 i #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) i)
(*.f64 (*.f64 i #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (pow.f64 (*.f64 i #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 i #s(literal 2 binary64)) #s(literal 1/2 binary64)))

simplify266.0ms (4.6%)

Algorithm
1×egg-herbie
Rules
2334×*-lowering-*.f32
2334×*-lowering-*.f64
2038×fma-lowering-fma.f32
2038×fma-lowering-fma.f64
1492×+-lowering-+.f64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
078820
1195799
2498796
31330782
43542782
08278782
Stop Event
1×iter limit
1×node limit
Counts
132 → 132
Calls
Call 1
Inputs
(* -1/4 (pow i 2))
(* (pow i 2) (- (* -1 (pow i 2)) 1/4))
(* (pow i 2) (- (* (pow i 2) (- (* -4 (pow i 2)) 1)) 1/4))
(* (pow i 2) (- (* (pow i 2) (- (* (pow i 2) (- (* -16 (pow i 2)) 4)) 1)) 1/4))
1/16
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))
1/16
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))
(* -1/4 i)
(* i (- (* -1 (pow i 2)) 1/4))
(* i (- (* (pow i 2) (- (* -4 (pow i 2)) 1)) 1/4))
(* i (- (* (pow i 2) (- (* (pow i 2) (- (* -16 (pow i 2)) 4)) 1)) 1/4))
(/ 1/16 i)
(/ (+ 1/16 (* 1/64 (/ 1 (pow i 2)))) i)
(/ (+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2))))) i)
(/ (+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6)))))) i)
(/ 1/16 i)
(/ (+ 1/16 (* 1/64 (/ 1 (pow i 2)))) i)
(* -1 (/ (- (* -1 (/ (+ 1/64 (* 1/256 (/ 1 (pow i 2)))) (pow i 2))) 1/16) i))
(* -1 (/ (- (* -1 (/ (+ 1/256 (* 1/1024 (/ 1 (pow i 2)))) (pow i 4))) (+ 1/16 (* 1/64 (/ 1 (pow i 2))))) i))
-4
(- (* 16 (pow i 2)) 4)
(- (* 16 (pow i 2)) 4)
(- (* 16 (pow i 2)) 4)
(* 16 (pow i 2))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(* 16 (pow i 2))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(* 16 (pow i 2))
(* 16 (pow i 2))
(* 16 (pow i 2))
(* 16 (pow i 2))
(* 16 (pow i 2))
(* 16 (pow i 2))
(* 16 (pow i 2))
(* 16 (pow i 2))
(* 16 (pow i 2))
(* 16 (pow i 2))
(* 16 (pow i 2))
(* 16 (pow i 2))
(* -1/4 (pow i 2))
(* (pow i 2) (- (* -1 (pow i 2)) 1/4))
(* (pow i 2) (- (* (pow i 2) (- (* -4 (pow i 2)) 1)) 1/4))
(* (pow i 2) (- (* (pow i 2) (- (* (pow i 2) (- (* -16 (pow i 2)) 4)) 1)) 1/4))
1/16
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))
1/16
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))
(* 1/4 (pow i 2))
(* 1/4 (pow i 2))
(* 1/4 (pow i 2))
(* 1/4 (pow i 2))
(* 1/4 (pow i 2))
(* 1/4 (pow i 2))
(* 1/4 (pow i 2))
(* 1/4 (pow i 2))
(* 1/4 (pow i 2))
(* 1/4 (pow i 2))
(* 1/4 (pow i 2))
(* 1/4 (pow i 2))
(* 4 (pow i 2))
(* 4 (pow i 2))
(* 4 (pow i 2))
(* 4 (pow i 2))
(* 4 (pow i 2))
(* 4 (pow i 2))
(* 4 (pow i 2))
(* 4 (pow i 2))
(* 4 (pow i 2))
(* 4 (pow i 2))
(* 4 (pow i 2))
(* 4 (pow i 2))
-1
(- (* 4 (pow i 2)) 1)
(- (* 4 (pow i 2)) 1)
(- (* 4 (pow i 2)) 1)
(* 4 (pow i 2))
(* (pow i 2) (- 4 (/ 1 (pow i 2))))
(* (pow i 2) (- 4 (/ 1 (pow i 2))))
(* (pow i 2) (- 4 (/ 1 (pow i 2))))
(* 4 (pow i 2))
(* (pow i 2) (- 4 (/ 1 (pow i 2))))
(* (pow i 2) (- 4 (/ 1 (pow i 2))))
(* (pow i 2) (- 4 (/ 1 (pow i 2))))
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 4)
(pow i 4)
(pow i 4)
(pow i 4)
(pow i 4)
(pow i 4)
(pow i 4)
(pow i 4)
(pow i 4)
(pow i 4)
(pow i 4)
(pow i 4)
(* 2 i)
(* 2 i)
(* 2 i)
(* 2 i)
(* 2 i)
(* 2 i)
(* 2 i)
(* 2 i)
(* 2 i)
(* 2 i)
(* 2 i)
(* 2 i)
Outputs
(* -1/4 (pow i 2))
(*.f64 #s(literal -1/4 binary64) (*.f64 i i))
(* (pow i 2) (- (* -1 (pow i 2)) 1/4))
(*.f64 (*.f64 i i) (-.f64 #s(literal -1/4 binary64) (*.f64 i i)))
(* (pow i 2) (- (* (pow i 2) (- (* -4 (pow i 2)) 1)) 1/4))
(*.f64 (*.f64 i i) (+.f64 #s(literal -1/4 binary64) (*.f64 i (*.f64 i (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 i i) #s(literal -4 binary64)))))))
(* (pow i 2) (- (* (pow i 2) (- (* (pow i 2) (- (* -16 (pow i 2)) 4)) 1)) 1/4))
(*.f64 (*.f64 i i) (+.f64 #s(literal -1/4 binary64) (*.f64 i (*.f64 i (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 i i) (+.f64 #s(literal -4 binary64) (*.f64 (*.f64 i i) #s(literal -16 binary64)))))))))
1/16
#s(literal 1/16 binary64)
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))
(+.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))) (/.f64 #s(literal 1/256 binary64) (*.f64 i (*.f64 i (*.f64 i i)))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))
(+.f64 (/.f64 #s(literal 1/256 binary64) (*.f64 i (*.f64 i (*.f64 i i)))) (+.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))) (/.f64 #s(literal 1/1024 binary64) (pow.f64 i #s(literal 6 binary64)))))
1/16
#s(literal 1/16 binary64)
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))
(+.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))) (/.f64 #s(literal 1/256 binary64) (*.f64 i (*.f64 i (*.f64 i i)))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))
(+.f64 (/.f64 #s(literal 1/256 binary64) (*.f64 i (*.f64 i (*.f64 i i)))) (+.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))) (/.f64 #s(literal 1/1024 binary64) (pow.f64 i #s(literal 6 binary64)))))
(* -1/4 i)
(*.f64 #s(literal -1/4 binary64) i)
(* i (- (* -1 (pow i 2)) 1/4))
(*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i)))
(* i (- (* (pow i 2) (- (* -4 (pow i 2)) 1)) 1/4))
(*.f64 i (+.f64 #s(literal -1/4 binary64) (*.f64 i (*.f64 i (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 i i) #s(literal -4 binary64)))))))
(* i (- (* (pow i 2) (- (* (pow i 2) (- (* -16 (pow i 2)) 4)) 1)) 1/4))
(*.f64 i (+.f64 #s(literal -1/4 binary64) (*.f64 i (*.f64 i (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 i i) (+.f64 #s(literal -4 binary64) (*.f64 (*.f64 i i) #s(literal -16 binary64)))))))))
(/ 1/16 i)
(/.f64 #s(literal 1/16 binary64) i)
(/ (+ 1/16 (* 1/64 (/ 1 (pow i 2)))) i)
(/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))) i)
(/ (+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2))))) i)
(/.f64 (+.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))) (/.f64 #s(literal 1/256 binary64) (*.f64 i (*.f64 i (*.f64 i i))))) i)
(/ (+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6)))))) i)
(/.f64 (+.f64 (/.f64 #s(literal 1/256 binary64) (*.f64 i (*.f64 i (*.f64 i i)))) (+.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))) (/.f64 #s(literal 1/1024 binary64) (pow.f64 i #s(literal 6 binary64))))) i)
(/ 1/16 i)
(/.f64 #s(literal 1/16 binary64) i)
(/ (+ 1/16 (* 1/64 (/ 1 (pow i 2)))) i)
(/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))) i)
(* -1 (/ (- (* -1 (/ (+ 1/64 (* 1/256 (/ 1 (pow i 2)))) (pow i 2))) 1/16) i))
(/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal -1/256 binary64) (*.f64 i i))) (*.f64 i i))) i)
(* -1 (/ (- (* -1 (/ (+ 1/256 (* 1/1024 (/ 1 (pow i 2)))) (pow i 4))) (+ 1/16 (* 1/64 (/ 1 (pow i 2))))) i))
(/.f64 (+.f64 #s(literal 1/16 binary64) (+.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 i i)) (/.f64 (+.f64 #s(literal 1/256 binary64) (/.f64 #s(literal 1/1024 binary64) (*.f64 i i))) (*.f64 i (*.f64 i (*.f64 i i)))))) i)
-4
#s(literal -4 binary64)
(- (* 16 (pow i 2)) 4)
(+.f64 #s(literal -4 binary64) (*.f64 i (*.f64 i #s(literal 16 binary64))))
(- (* 16 (pow i 2)) 4)
(+.f64 #s(literal -4 binary64) (*.f64 i (*.f64 i #s(literal 16 binary64))))
(- (* 16 (pow i 2)) 4)
(+.f64 #s(literal -4 binary64) (*.f64 i (*.f64 i #s(literal 16 binary64))))
(* 16 (pow i 2))
(*.f64 i (*.f64 i #s(literal 16 binary64)))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(+.f64 #s(literal -4 binary64) (*.f64 i (*.f64 i #s(literal 16 binary64))))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(+.f64 #s(literal -4 binary64) (*.f64 i (*.f64 i #s(literal 16 binary64))))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(+.f64 #s(literal -4 binary64) (*.f64 i (*.f64 i #s(literal 16 binary64))))
(* 16 (pow i 2))
(*.f64 i (*.f64 i #s(literal 16 binary64)))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(+.f64 #s(literal -4 binary64) (*.f64 i (*.f64 i #s(literal 16 binary64))))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(+.f64 #s(literal -4 binary64) (*.f64 i (*.f64 i #s(literal 16 binary64))))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(+.f64 #s(literal -4 binary64) (*.f64 i (*.f64 i #s(literal 16 binary64))))
(* 16 (pow i 2))
(*.f64 i (*.f64 i #s(literal 16 binary64)))
(* 16 (pow i 2))
(*.f64 i (*.f64 i #s(literal 16 binary64)))
(* 16 (pow i 2))
(*.f64 i (*.f64 i #s(literal 16 binary64)))
(* 16 (pow i 2))
(*.f64 i (*.f64 i #s(literal 16 binary64)))
(* 16 (pow i 2))
(*.f64 i (*.f64 i #s(literal 16 binary64)))
(* 16 (pow i 2))
(*.f64 i (*.f64 i #s(literal 16 binary64)))
(* 16 (pow i 2))
(*.f64 i (*.f64 i #s(literal 16 binary64)))
(* 16 (pow i 2))
(*.f64 i (*.f64 i #s(literal 16 binary64)))
(* 16 (pow i 2))
(*.f64 i (*.f64 i #s(literal 16 binary64)))
(* 16 (pow i 2))
(*.f64 i (*.f64 i #s(literal 16 binary64)))
(* 16 (pow i 2))
(*.f64 i (*.f64 i #s(literal 16 binary64)))
(* 16 (pow i 2))
(*.f64 i (*.f64 i #s(literal 16 binary64)))
(* -1/4 (pow i 2))
(*.f64 #s(literal -1/4 binary64) (*.f64 i i))
(* (pow i 2) (- (* -1 (pow i 2)) 1/4))
(*.f64 (*.f64 i i) (-.f64 #s(literal -1/4 binary64) (*.f64 i i)))
(* (pow i 2) (- (* (pow i 2) (- (* -4 (pow i 2)) 1)) 1/4))
(*.f64 (*.f64 i i) (+.f64 #s(literal -1/4 binary64) (*.f64 i (*.f64 i (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 i i) #s(literal -4 binary64)))))))
(* (pow i 2) (- (* (pow i 2) (- (* (pow i 2) (- (* -16 (pow i 2)) 4)) 1)) 1/4))
(*.f64 (*.f64 i i) (+.f64 #s(literal -1/4 binary64) (*.f64 i (*.f64 i (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 i i) (+.f64 #s(literal -4 binary64) (*.f64 (*.f64 i i) #s(literal -16 binary64)))))))))
1/16
#s(literal 1/16 binary64)
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))
(+.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))) (/.f64 #s(literal 1/256 binary64) (*.f64 i (*.f64 i (*.f64 i i)))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))
(+.f64 (/.f64 #s(literal 1/256 binary64) (*.f64 i (*.f64 i (*.f64 i i)))) (+.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))) (/.f64 #s(literal 1/1024 binary64) (pow.f64 i #s(literal 6 binary64)))))
1/16
#s(literal 1/16 binary64)
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))
(+.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))) (/.f64 #s(literal 1/256 binary64) (*.f64 i (*.f64 i (*.f64 i i)))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))
(+.f64 (/.f64 #s(literal 1/256 binary64) (*.f64 i (*.f64 i (*.f64 i i)))) (+.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))) (/.f64 #s(literal 1/1024 binary64) (pow.f64 i #s(literal 6 binary64)))))
(* 1/4 (pow i 2))
(*.f64 i (*.f64 i #s(literal 1/4 binary64)))
(* 1/4 (pow i 2))
(*.f64 i (*.f64 i #s(literal 1/4 binary64)))
(* 1/4 (pow i 2))
(*.f64 i (*.f64 i #s(literal 1/4 binary64)))
(* 1/4 (pow i 2))
(*.f64 i (*.f64 i #s(literal 1/4 binary64)))
(* 1/4 (pow i 2))
(*.f64 i (*.f64 i #s(literal 1/4 binary64)))
(* 1/4 (pow i 2))
(*.f64 i (*.f64 i #s(literal 1/4 binary64)))
(* 1/4 (pow i 2))
(*.f64 i (*.f64 i #s(literal 1/4 binary64)))
(* 1/4 (pow i 2))
(*.f64 i (*.f64 i #s(literal 1/4 binary64)))
(* 1/4 (pow i 2))
(*.f64 i (*.f64 i #s(literal 1/4 binary64)))
(* 1/4 (pow i 2))
(*.f64 i (*.f64 i #s(literal 1/4 binary64)))
(* 1/4 (pow i 2))
(*.f64 i (*.f64 i #s(literal 1/4 binary64)))
(* 1/4 (pow i 2))
(*.f64 i (*.f64 i #s(literal 1/4 binary64)))
(* 4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 4 binary64))
(* 4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 4 binary64))
(* 4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 4 binary64))
(* 4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 4 binary64))
(* 4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 4 binary64))
(* 4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 4 binary64))
(* 4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 4 binary64))
(* 4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 4 binary64))
(* 4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 4 binary64))
(* 4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 4 binary64))
(* 4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 4 binary64))
(* 4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 4 binary64))
-1
#s(literal -1 binary64)
(- (* 4 (pow i 2)) 1)
(+.f64 #s(literal -1 binary64) (*.f64 (*.f64 i i) #s(literal 4 binary64)))
(- (* 4 (pow i 2)) 1)
(+.f64 #s(literal -1 binary64) (*.f64 (*.f64 i i) #s(literal 4 binary64)))
(- (* 4 (pow i 2)) 1)
(+.f64 #s(literal -1 binary64) (*.f64 (*.f64 i i) #s(literal 4 binary64)))
(* 4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 4 binary64))
(* (pow i 2) (- 4 (/ 1 (pow i 2))))
(+.f64 #s(literal -1 binary64) (*.f64 (*.f64 i i) #s(literal 4 binary64)))
(* (pow i 2) (- 4 (/ 1 (pow i 2))))
(+.f64 #s(literal -1 binary64) (*.f64 (*.f64 i i) #s(literal 4 binary64)))
(* (pow i 2) (- 4 (/ 1 (pow i 2))))
(+.f64 #s(literal -1 binary64) (*.f64 (*.f64 i i) #s(literal 4 binary64)))
(* 4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 4 binary64))
(* (pow i 2) (- 4 (/ 1 (pow i 2))))
(+.f64 #s(literal -1 binary64) (*.f64 (*.f64 i i) #s(literal 4 binary64)))
(* (pow i 2) (- 4 (/ 1 (pow i 2))))
(+.f64 #s(literal -1 binary64) (*.f64 (*.f64 i i) #s(literal 4 binary64)))
(* (pow i 2) (- 4 (/ 1 (pow i 2))))
(+.f64 #s(literal -1 binary64) (*.f64 (*.f64 i i) #s(literal 4 binary64)))
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 4)
(*.f64 i (*.f64 i (*.f64 i i)))
(pow i 4)
(*.f64 i (*.f64 i (*.f64 i i)))
(pow i 4)
(*.f64 i (*.f64 i (*.f64 i i)))
(pow i 4)
(*.f64 i (*.f64 i (*.f64 i i)))
(pow i 4)
(*.f64 i (*.f64 i (*.f64 i i)))
(pow i 4)
(*.f64 i (*.f64 i (*.f64 i i)))
(pow i 4)
(*.f64 i (*.f64 i (*.f64 i i)))
(pow i 4)
(*.f64 i (*.f64 i (*.f64 i i)))
(pow i 4)
(*.f64 i (*.f64 i (*.f64 i i)))
(pow i 4)
(*.f64 i (*.f64 i (*.f64 i i)))
(pow i 4)
(*.f64 i (*.f64 i (*.f64 i i)))
(pow i 4)
(*.f64 i (*.f64 i (*.f64 i i)))
(* 2 i)
(*.f64 i #s(literal 2 binary64))
(* 2 i)
(*.f64 i #s(literal 2 binary64))
(* 2 i)
(*.f64 i #s(literal 2 binary64))
(* 2 i)
(*.f64 i #s(literal 2 binary64))
(* 2 i)
(*.f64 i #s(literal 2 binary64))
(* 2 i)
(*.f64 i #s(literal 2 binary64))
(* 2 i)
(*.f64 i #s(literal 2 binary64))
(* 2 i)
(*.f64 i #s(literal 2 binary64))
(* 2 i)
(*.f64 i #s(literal 2 binary64))
(* 2 i)
(*.f64 i #s(literal 2 binary64))
(* 2 i)
(*.f64 i #s(literal 2 binary64))
(* 2 i)
(*.f64 i #s(literal 2 binary64))

eval110.0ms (1.9%)

Compiler

Compiled 26610 to 2439 computations (90.8% saved)

prune119.0ms (2.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New101961025
Fresh000
Picked202
Done000
Total102161027
Accuracy
100.0%
Counts
1027 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
72.7%
(/.f64 (*.f64 i i) (+.f64 (*.f64 i (*.f64 i #s(literal 16 binary64))) #s(literal -4 binary64)))
▶73.1%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 (*.f64 i (*.f64 i #s(literal 16 binary64))) #s(literal -4 binary64)) i) i))
▶53.6%
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
▶46.0%
(*.f64 i (/.f64 i #s(literal -4 binary64)))
▶46.4%
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i))))
▶54.0%
#s(literal 1/16 binary64)
Compiler

Compiled 104 to 72 computations (30.8% saved)

simplify139.0ms (2.4%)

Algorithm
1×egg-herbie
Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 i i)
✓cost-diff0
(-.f64 #s(literal -1/4 binary64) (*.f64 i i))
✓cost-diff0
(*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i)))
✓cost-diff0
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i))))
✓cost-diff0
(*.f64 i i)
✓cost-diff0
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
✓cost-diff0
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
✓cost-diff0
(/.f64 i #s(literal -4 binary64))
✓cost-diff0
(*.f64 i (/.f64 i #s(literal -4 binary64)))
✓cost-diff0
(+.f64 (*.f64 i (*.f64 i #s(literal 16 binary64))) #s(literal -4 binary64))
✓cost-diff128
(/.f64 (+.f64 (*.f64 i (*.f64 i #s(literal 16 binary64))) #s(literal -4 binary64)) i)
✓cost-diff256
(/.f64 (/.f64 (+.f64 (*.f64 i (*.f64 i #s(literal 16 binary64))) #s(literal -4 binary64)) i) i)
✓cost-diff256
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 (*.f64 i (*.f64 i #s(literal 16 binary64))) #s(literal -4 binary64)) i) i))
Rules
1676×fma-define
1470×sum3-define
1448×fnmadd-define
1144×sum5-define
1126×fmsub-define
Iterations

Useful iterations: 13 (0.0ms)

IterNodesCost
021102
145102
27598
314298
428298
541698
661998
795398
8301098
9349198
10392698
11449998
12536998
13653392
0822792
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ 1 (/ (/ (+ (* i (* i 16)) -4) i) i))
1
(/ (/ (+ (* i (* i 16)) -4) i) i)
(/ (+ (* i (* i 16)) -4) i)
(+ (* i (* i 16)) -4)
(* i (* i 16))
i
(* i 16)
16
-4
1/16
(* i (/ i -4))
i
(/ i -4)
-4
(+ 1/16 (/ 1/64 (* i i)))
1/16
(/ 1/64 (* i i))
1/64
(* i i)
i
(* i (* i (- -1/4 (* i i))))
i
(* i (- -1/4 (* i i)))
(- -1/4 (* i i))
-1/4
(* i i)
Outputs
(/ 1 (/ (/ (+ (* i (* i 16)) -4) i) i))
(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 #s(literal -4 binary64) i) i) #s(literal 16 binary64)))
1
#s(literal 1 binary64)
(/ (/ (+ (* i (* i 16)) -4) i) i)
(+.f64 (/.f64 (/.f64 #s(literal -4 binary64) i) i) #s(literal 16 binary64))
(/ (+ (* i (* i 16)) -4) i)
(+.f64 (/.f64 #s(literal -4 binary64) i) (*.f64 i #s(literal 16 binary64)))
(+ (* i (* i 16)) -4)
(+.f64 (*.f64 i (*.f64 i #s(literal 16 binary64))) #s(literal -4 binary64))
(* i (* i 16))
(*.f64 i (*.f64 i #s(literal 16 binary64)))
i
(* i 16)
(*.f64 i #s(literal 16 binary64))
16
#s(literal 16 binary64)
-4
#s(literal -4 binary64)
1/16
#s(literal 1/16 binary64)
(* i (/ i -4))
(/.f64 (*.f64 i i) #s(literal -4 binary64))
i
(/ i -4)
(/.f64 i #s(literal -4 binary64))
-4
#s(literal -4 binary64)
(+ 1/16 (/ 1/64 (* i i)))
(-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/64 binary64) (*.f64 i i)))
1/16
#s(literal 1/16 binary64)
(/ 1/64 (* i i))
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
1/64
#s(literal 1/64 binary64)
(* i i)
(*.f64 i i)
i
(* i (* i (- -1/4 (* i i))))
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i))))
i
(* i (- -1/4 (* i i)))
(*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i)))
(- -1/4 (* i i))
(-.f64 #s(literal -1/4 binary64) (*.f64 i i))
-1/4
#s(literal -1/4 binary64)
(* i i)
(*.f64 i i)

localize100.0ms (1.7%)

Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 i i)
✓accuracy100.0%
(-.f64 #s(literal -1/4 binary64) (*.f64 i i))
✓accuracy99.9%
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i))))
✓accuracy99.9%
(*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i)))
✓accuracy100.0%
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
✓accuracy100.0%
(*.f64 i i)
✓accuracy99.5%
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
✓accuracy100.0%
(/.f64 i #s(literal -4 binary64))
✓accuracy100.0%
(*.f64 i (/.f64 i #s(literal -4 binary64)))
✓accuracy100.0%
(*.f64 i #s(literal 16 binary64))
✓accuracy99.7%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 (*.f64 i (*.f64 i #s(literal 16 binary64))) #s(literal -4 binary64)) i) i))
✓accuracy98.4%
(/.f64 (/.f64 (+.f64 (*.f64 i (*.f64 i #s(literal 16 binary64))) #s(literal -4 binary64)) i) i)
✓accuracy76.0%
(/.f64 (+.f64 (*.f64 i (*.f64 i #s(literal 16 binary64))) #s(literal -4 binary64)) i)
Results
55.0ms256×0valid
Compiler

Compiled 109 to 22 computations (79.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 29.0ms
ival-mult: 15.0ms (51.4% of total)
ival-div: 9.0ms (30.8% of total)
ival-add: 3.0ms (10.3% of total)
ival-sub: 1.0ms (3.4% of total)
const: 1.0ms (3.4% of total)
backward-pass: 0.0ms (0% of total)

series15.0ms (0.3%)

Counts
13 → 156
Calls
Call 1
Inputs
#<alt (/ 1 (/ (/ (+ (* i (* i 16)) -4) i) i))>
#<alt (/ (/ (+ (* i (* i 16)) -4) i) i)>
#<alt (/ (+ (* i (* i 16)) -4) i)>
#<alt (+ (* i (* i 16)) -4)>
#<alt (* i (/ i -4))>
#<alt (/ i -4)>
#<alt (+ 1/16 (/ 1/64 (* i i)))>
#<alt (/ 1/64 (* i i))>
#<alt (* i i)>
#<alt (* i (* i (- -1/4 (* i i))))>
#<alt (* i (- -1/4 (* i i)))>
#<alt (- -1/4 (* i i))>
#<alt (* i 16)>
Outputs
#<alt (* -1/4 (pow i 2))>
#<alt (* (pow i 2) (- (* -1 (pow i 2)) 1/4))>
#<alt (* (pow i 2) (- (* (pow i 2) (- (* -4 (pow i 2)) 1)) 1/4))>
#<alt (* (pow i 2) (- (* (pow i 2) (- (* (pow i 2) (- (* -16 (pow i 2)) 4)) 1)) 1/4))>
#<alt 1/16>
#<alt (+ 1/16 (* 1/64 (/ 1 (pow i 2))))>
#<alt (+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))>
#<alt (+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))>
#<alt 1/16>
#<alt (+ 1/16 (* 1/64 (/ 1 (pow i 2))))>
#<alt (+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))>
#<alt (+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))>
#<alt (/ -4 (pow i 2))>
#<alt (/ (- (* 16 (pow i 2)) 4) (pow i 2))>
#<alt (/ (- (* 16 (pow i 2)) 4) (pow i 2))>
#<alt (/ (- (* 16 (pow i 2)) 4) (pow i 2))>
#<alt 16>
#<alt (- 16 (* 4 (/ 1 (pow i 2))))>
#<alt (- 16 (* 4 (/ 1 (pow i 2))))>
#<alt (- 16 (* 4 (/ 1 (pow i 2))))>
#<alt 16>
#<alt (- 16 (* 4 (/ 1 (pow i 2))))>
#<alt (- 16 (* 4 (/ 1 (pow i 2))))>
#<alt (- 16 (* 4 (/ 1 (pow i 2))))>
#<alt (/ -4 i)>
#<alt (/ (- (* 16 (pow i 2)) 4) i)>
#<alt (/ (- (* 16 (pow i 2)) 4) i)>
#<alt (/ (- (* 16 (pow i 2)) 4) i)>
#<alt (* 16 i)>
#<alt (* i (- 16 (* 4 (/ 1 (pow i 2)))))>
#<alt (* i (- 16 (* 4 (/ 1 (pow i 2)))))>
#<alt (* i (- 16 (* 4 (/ 1 (pow i 2)))))>
#<alt (* 16 i)>
#<alt (* -1 (* i (- (* 4 (/ 1 (pow i 2))) 16)))>
#<alt (* -1 (* i (- (* 4 (/ 1 (pow i 2))) 16)))>
#<alt (* -1 (* i (- (* 4 (/ 1 (pow i 2))) 16)))>
#<alt -4>
#<alt (- (* 16 (pow i 2)) 4)>
#<alt (- (* 16 (pow i 2)) 4)>
#<alt (- (* 16 (pow i 2)) 4)>
#<alt (* 16 (pow i 2))>
#<alt (* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))>
#<alt (* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))>
#<alt (* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))>
#<alt (* 16 (pow i 2))>
#<alt (* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))>
#<alt (* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))>
#<alt (* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))>
#<alt (* -1/4 (pow i 2))>
#<alt (* -1/4 (pow i 2))>
#<alt (* -1/4 (pow i 2))>
#<alt (* -1/4 (pow i 2))>
#<alt (* -1/4 (pow i 2))>
#<alt (* -1/4 (pow i 2))>
#<alt (* -1/4 (pow i 2))>
#<alt (* -1/4 (pow i 2))>
#<alt (* -1/4 (pow i 2))>
#<alt (* -1/4 (pow i 2))>
#<alt (* -1/4 (pow i 2))>
#<alt (* -1/4 (pow i 2))>
#<alt (* -1/4 i)>
#<alt (* -1/4 i)>
#<alt (* -1/4 i)>
#<alt (* -1/4 i)>
#<alt (* -1/4 i)>
#<alt (* -1/4 i)>
#<alt (* -1/4 i)>
#<alt (* -1/4 i)>
#<alt (* -1/4 i)>
#<alt (* -1/4 i)>
#<alt (* -1/4 i)>
#<alt (* -1/4 i)>
#<alt (/ 1/64 (pow i 2))>
#<alt (/ (+ 1/64 (* 1/16 (pow i 2))) (pow i 2))>
#<alt (/ (+ 1/64 (* 1/16 (pow i 2))) (pow i 2))>
#<alt (/ (+ 1/64 (* 1/16 (pow i 2))) (pow i 2))>
#<alt 1/16>
#<alt (+ 1/16 (* 1/64 (/ 1 (pow i 2))))>
#<alt (+ 1/16 (* 1/64 (/ 1 (pow i 2))))>
#<alt (+ 1/16 (* 1/64 (/ 1 (pow i 2))))>
#<alt 1/16>
#<alt (+ 1/16 (* 1/64 (/ 1 (pow i 2))))>
#<alt (+ 1/16 (* 1/64 (/ 1 (pow i 2))))>
#<alt (+ 1/16 (* 1/64 (/ 1 (pow i 2))))>
#<alt (/ 1/64 (pow i 2))>
#<alt (/ 1/64 (pow i 2))>
#<alt (/ 1/64 (pow i 2))>
#<alt (/ 1/64 (pow i 2))>
#<alt (/ 1/64 (pow i 2))>
#<alt (/ 1/64 (pow i 2))>
#<alt (/ 1/64 (pow i 2))>
#<alt (/ 1/64 (pow i 2))>
#<alt (/ 1/64 (pow i 2))>
#<alt (/ 1/64 (pow i 2))>
#<alt (/ 1/64 (pow i 2))>
#<alt (/ 1/64 (pow i 2))>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (* -1/4 (pow i 2))>
#<alt (* (pow i 2) (- (* -1 (pow i 2)) 1/4))>
#<alt (* (pow i 2) (- (* -1 (pow i 2)) 1/4))>
#<alt (* (pow i 2) (- (* -1 (pow i 2)) 1/4))>
#<alt (* -1 (pow i 4))>
#<alt (* -1 (* (pow i 4) (+ 1 (* 1/4 (/ 1 (pow i 2))))))>
#<alt (* -1 (* (pow i 4) (+ 1 (* 1/4 (/ 1 (pow i 2))))))>
#<alt (* -1 (* (pow i 4) (+ 1 (* 1/4 (/ 1 (pow i 2))))))>
#<alt (* -1 (pow i 4))>
#<alt (* -1 (* (pow i 4) (+ 1 (* 1/4 (/ 1 (pow i 2))))))>
#<alt (* -1 (* (pow i 4) (+ 1 (* 1/4 (/ 1 (pow i 2))))))>
#<alt (* -1 (* (pow i 4) (+ 1 (* 1/4 (/ 1 (pow i 2))))))>
#<alt (* -1/4 i)>
#<alt (* i (- (* -1 (pow i 2)) 1/4))>
#<alt (* i (- (* -1 (pow i 2)) 1/4))>
#<alt (* i (- (* -1 (pow i 2)) 1/4))>
#<alt (* -1 (pow i 3))>
#<alt (* -1 (* (pow i 3) (+ 1 (* 1/4 (/ 1 (pow i 2))))))>
#<alt (* -1 (* (pow i 3) (+ 1 (* 1/4 (/ 1 (pow i 2))))))>
#<alt (* -1 (* (pow i 3) (+ 1 (* 1/4 (/ 1 (pow i 2))))))>
#<alt (* -1 (pow i 3))>
#<alt (* -1 (* (pow i 3) (+ 1 (* 1/4 (/ 1 (pow i 2))))))>
#<alt (* -1 (* (pow i 3) (+ 1 (* 1/4 (/ 1 (pow i 2))))))>
#<alt (* -1 (* (pow i 3) (+ 1 (* 1/4 (/ 1 (pow i 2))))))>
#<alt -1/4>
#<alt (- (* -1 (pow i 2)) 1/4)>
#<alt (- (* -1 (pow i 2)) 1/4)>
#<alt (- (* -1 (pow i 2)) 1/4)>
#<alt (* -1 (pow i 2))>
#<alt (* -1 (* (pow i 2) (+ 1 (* 1/4 (/ 1 (pow i 2))))))>
#<alt (* -1 (* (pow i 2) (+ 1 (* 1/4 (/ 1 (pow i 2))))))>
#<alt (* -1 (* (pow i 2) (+ 1 (* 1/4 (/ 1 (pow i 2))))))>
#<alt (* -1 (pow i 2))>
#<alt (* -1 (* (pow i 2) (+ 1 (* 1/4 (/ 1 (pow i 2))))))>
#<alt (* -1 (* (pow i 2) (+ 1 (* 1/4 (/ 1 (pow i 2))))))>
#<alt (* -1 (* (pow i 2) (+ 1 (* 1/4 (/ 1 (pow i 2))))))>
#<alt (* 16 i)>
#<alt (* 16 i)>
#<alt (* 16 i)>
#<alt (* 16 i)>
#<alt (* 16 i)>
#<alt (* 16 i)>
#<alt (* 16 i)>
#<alt (* 16 i)>
#<alt (* 16 i)>
#<alt (* 16 i)>
#<alt (* 16 i)>
#<alt (* 16 i)>
Calls

39 calls:

TimeVariablePointExpression
7.0ms
i
@inf
(+ 1/16 (/ 1/64 (* i i)))
1.0ms
i
@0
(* i (* i (- -1/4 (* i i))))
0.0ms
i
@inf
(* i (* i (- -1/4 (* i i))))
0.0ms
i
@inf
(* i (/ i -4))
0.0ms
i
@0
(/ 1/64 (* i i))

rewrite297.0ms (5.2%)

Algorithm
1×batch-egg-rewrite
Rules
4284×*-lowering-*.f32
4284×*-lowering-*.f64
3584×/-lowering-/.f32
3584×/-lowering-/.f64
1178×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02182
112080
283677
0810977
Stop Event
1×iter limit
1×node limit
Counts
13 → 588
Calls
Call 1
Inputs
(/ 1 (/ (/ (+ (* i (* i 16)) -4) i) i))
(/ (/ (+ (* i (* i 16)) -4) i) i)
(/ (+ (* i (* i 16)) -4) i)
(+ (* i (* i 16)) -4)
(* i (/ i -4))
(/ i -4)
(+ 1/16 (/ 1/64 (* i i)))
(/ 1/64 (* i i))
(* i i)
(* i (* i (- -1/4 (* i i))))
(* i (- -1/4 (* i i)))
(- -1/4 (* i i))
(* i 16)
Outputs
(exp.f64 (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 i i)) #s(literal -4 binary64)) (*.f64 i i)))))
(-.f64 #s(literal 0 binary64) (*.f64 i (/.f64 i (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 i i) #s(literal -16 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 i i) #s(literal -16 binary64))) i)) (*.f64 i (/.f64 i (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 i i) #s(literal -16 binary64))))))
(neg.f64 (*.f64 i (/.f64 i (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 i i) #s(literal -16 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 i i)) #s(literal -4 binary64)) (*.f64 i i)))
(/.f64 i (/.f64 (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 i i)) #s(literal -4 binary64)) i))
(/.f64 (*.f64 i i) (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 i i)) #s(literal -4 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 i i) #s(literal -16 binary64))) (*.f64 i i)))
(/.f64 (-.f64 #s(literal 0 binary64) i) (/.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 i i) #s(literal -16 binary64))) i))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 i i)) (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 i i) #s(literal -16 binary64))))
(/.f64 (/.f64 (*.f64 i i) (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 i i)) #s(literal -4 binary64))) #s(literal 1 binary64))
(/.f64 (/.f64 i (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 i i)) #s(literal -4 binary64))) (/.f64 #s(literal 1 binary64) i))
(/.f64 (*.f64 i (/.f64 i (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 i i) #s(literal -16 binary64))))) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 i i)) #s(literal -4 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 i i)))
(/.f64 (/.f64 i (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 i i) #s(literal -16 binary64)))) (/.f64 #s(literal -1 binary64) i))
(/.f64 (/.f64 i (/.f64 #s(literal 1 binary64) i)) (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 i i)) #s(literal -4 binary64)))
(/.f64 (/.f64 (*.f64 i i) (+.f64 (*.f64 (*.f64 i (*.f64 i (*.f64 i i))) (*.f64 (*.f64 i i) #s(literal 4096 binary64))) #s(literal -64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 16 binary64) (*.f64 (*.f64 i i) (-.f64 (*.f64 (*.f64 i i) #s(literal 256 binary64)) #s(literal -64 binary64))))))
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(/.f64 (*.f64 (-.f64 #s(literal 1/4096 binary64) (*.f64 (*.f64 i (*.f64 i (*.f64 i i))) (*.f64 (*.f64 i (*.f64 i (*.f64 i i))) (*.f64 i (*.f64 i (*.f64 i i)))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 i i) #s(literal -1/4 binary64)))) (+.f64 #s(literal 1/256 binary64) (*.f64 (*.f64 i (*.f64 i (*.f64 i i))) (+.f64 #s(literal 1/16 binary64) (*.f64 i (*.f64 i (*.f64 i i)))))))
(/.f64 (*.f64 (-.f64 #s(literal 1/256 binary64) (*.f64 (*.f64 i (*.f64 i (*.f64 i i))) (*.f64 i (*.f64 i (*.f64 i i))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 i i) #s(literal -1/4 binary64)))) (+.f64 #s(literal 1/16 binary64) (*.f64 i (*.f64 i (*.f64 i i)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1/4 binary64) (*.f64 i i))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal -1/4 binary64) (*.f64 i i)))
(*.f64 (-.f64 #s(literal -1/64 binary64) (*.f64 i (*.f64 (*.f64 i (*.f64 i i)) (*.f64 i i)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/16 binary64) (*.f64 i (*.f64 i (+.f64 (*.f64 i i) #s(literal -1/4 binary64)))))))
(*.f64 (-.f64 #s(literal -1/64 binary64) (*.f64 i (*.f64 (*.f64 i (*.f64 i i)) (*.f64 i i)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/16 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 i i)) (-.f64 (-.f64 #s(literal 0 binary64) (*.f64 i i)) #s(literal -1/4 binary64))))))
(*.f64 (-.f64 #s(literal 1/16 binary64) (*.f64 i (*.f64 i (*.f64 i i)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 i i) #s(literal -1/4 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1/64 binary64) (*.f64 i (*.f64 (*.f64 i (*.f64 i i)) (*.f64 i i))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/16 binary64) (neg.f64 (*.f64 i (*.f64 i (+.f64 (*.f64 i i) #s(literal -1/4 binary64))))))))
(*.f64 (+.f64 #s(literal -1/16 binary64) (*.f64 i (*.f64 i (*.f64 i i)))) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 i i)) #s(literal 1/4 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/16 binary64) (*.f64 i (*.f64 i (+.f64 (*.f64 i i) #s(literal -1/4 binary64)))))) (-.f64 #s(literal -1/64 binary64) (*.f64 i (*.f64 (*.f64 i (*.f64 i i)) (*.f64 i i)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 i i) #s(literal -1/4 binary64))) (-.f64 #s(literal 1/16 binary64) (*.f64 i (*.f64 i (*.f64 i i)))))
(*.f64 (/.f64 (-.f64 #s(literal 1/16 binary64) (*.f64 i (*.f64 i (*.f64 i i)))) (-.f64 #s(literal 1/16 binary64) (*.f64 i (*.f64 i (*.f64 i i))))) (-.f64 #s(literal -1/4 binary64) (*.f64 i i)))
(*.f64 (/.f64 (-.f64 #s(literal -1/64 binary64) (*.f64 i (*.f64 (*.f64 i (*.f64 i i)) (*.f64 i i)))) (+.f64 #s(literal 1/4096 binary64) (*.f64 (*.f64 i (*.f64 i (+.f64 (*.f64 i i) #s(literal -1/4 binary64)))) (*.f64 (*.f64 i i) (*.f64 (+.f64 (*.f64 i i) #s(literal -1/4 binary64)) (*.f64 i (*.f64 i (+.f64 (*.f64 i i) #s(literal -1/4 binary64))))))))) (+.f64 #s(literal 1/256 binary64) (*.f64 (*.f64 i (*.f64 i (+.f64 (*.f64 i i) #s(literal -1/4 binary64)))) (-.f64 (*.f64 i (*.f64 i (+.f64 (*.f64 i i) #s(literal -1/4 binary64)))) #s(literal 1/16 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal -1/64 binary64) (*.f64 i (*.f64 (*.f64 i (*.f64 i i)) (*.f64 i i)))) (-.f64 #s(literal 1/256 binary64) (*.f64 (*.f64 i i) (*.f64 (+.f64 (*.f64 i i) #s(literal -1/4 binary64)) (*.f64 i (*.f64 i (+.f64 (*.f64 i i) #s(literal -1/4 binary64)))))))) (-.f64 #s(literal 1/16 binary64) (*.f64 i (*.f64 i (+.f64 (*.f64 i i) #s(literal -1/4 binary64))))))
(*.f64 (/.f64 (-.f64 #s(literal 1/16 binary64) (*.f64 i (*.f64 i (*.f64 i i)))) (+.f64 #s(literal -1/64 binary64) (*.f64 i (*.f64 (*.f64 i (*.f64 i i)) (*.f64 i i))))) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 i i) (-.f64 (*.f64 i i) #s(literal -1/4 binary64)))))
(*.f64 i #s(literal 16 binary64))
(*.f64 #s(literal 16 binary64) i)

simplify178.0ms (3.1%)

Algorithm
1×egg-herbie
Rules
1926×*-lowering-*.f32
1926×*-lowering-*.f64
1378×fnmadd-define
1374×fma-lowering-fma.f32
1374×fma-lowering-fma.f64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
077932
1203867
2593840
32056818
46029818
08163818
Stop Event
1×iter limit
1×node limit
Counts
156 → 156
Calls
Call 1
Inputs
(* -1/4 (pow i 2))
(* (pow i 2) (- (* -1 (pow i 2)) 1/4))
(* (pow i 2) (- (* (pow i 2) (- (* -4 (pow i 2)) 1)) 1/4))
(* (pow i 2) (- (* (pow i 2) (- (* (pow i 2) (- (* -16 (pow i 2)) 4)) 1)) 1/4))
1/16
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))
1/16
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))
(/ -4 (pow i 2))
(/ (- (* 16 (pow i 2)) 4) (pow i 2))
(/ (- (* 16 (pow i 2)) 4) (pow i 2))
(/ (- (* 16 (pow i 2)) 4) (pow i 2))
16
(- 16 (* 4 (/ 1 (pow i 2))))
(- 16 (* 4 (/ 1 (pow i 2))))
(- 16 (* 4 (/ 1 (pow i 2))))
16
(- 16 (* 4 (/ 1 (pow i 2))))
(- 16 (* 4 (/ 1 (pow i 2))))
(- 16 (* 4 (/ 1 (pow i 2))))
(/ -4 i)
(/ (- (* 16 (pow i 2)) 4) i)
(/ (- (* 16 (pow i 2)) 4) i)
(/ (- (* 16 (pow i 2)) 4) i)
(* 16 i)
(* i (- 16 (* 4 (/ 1 (pow i 2)))))
(* i (- 16 (* 4 (/ 1 (pow i 2)))))
(* i (- 16 (* 4 (/ 1 (pow i 2)))))
(* 16 i)
(* -1 (* i (- (* 4 (/ 1 (pow i 2))) 16)))
(* -1 (* i (- (* 4 (/ 1 (pow i 2))) 16)))
(* -1 (* i (- (* 4 (/ 1 (pow i 2))) 16)))
-4
(- (* 16 (pow i 2)) 4)
(- (* 16 (pow i 2)) 4)
(- (* 16 (pow i 2)) 4)
(* 16 (pow i 2))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(* 16 (pow i 2))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(* -1/4 (pow i 2))
(* -1/4 (pow i 2))
(* -1/4 (pow i 2))
(* -1/4 (pow i 2))
(* -1/4 (pow i 2))
(* -1/4 (pow i 2))
(* -1/4 (pow i 2))
(* -1/4 (pow i 2))
(* -1/4 (pow i 2))
(* -1/4 (pow i 2))
(* -1/4 (pow i 2))
(* -1/4 (pow i 2))
(* -1/4 i)
(* -1/4 i)
(* -1/4 i)
(* -1/4 i)
(* -1/4 i)
(* -1/4 i)
(* -1/4 i)
(* -1/4 i)
(* -1/4 i)
(* -1/4 i)
(* -1/4 i)
(* -1/4 i)
(/ 1/64 (pow i 2))
(/ (+ 1/64 (* 1/16 (pow i 2))) (pow i 2))
(/ (+ 1/64 (* 1/16 (pow i 2))) (pow i 2))
(/ (+ 1/64 (* 1/16 (pow i 2))) (pow i 2))
1/16
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
1/16
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(/ 1/64 (pow i 2))
(/ 1/64 (pow i 2))
(/ 1/64 (pow i 2))
(/ 1/64 (pow i 2))
(/ 1/64 (pow i 2))
(/ 1/64 (pow i 2))
(/ 1/64 (pow i 2))
(/ 1/64 (pow i 2))
(/ 1/64 (pow i 2))
(/ 1/64 (pow i 2))
(/ 1/64 (pow i 2))
(/ 1/64 (pow i 2))
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(* -1/4 (pow i 2))
(* (pow i 2) (- (* -1 (pow i 2)) 1/4))
(* (pow i 2) (- (* -1 (pow i 2)) 1/4))
(* (pow i 2) (- (* -1 (pow i 2)) 1/4))
(* -1 (pow i 4))
(* -1 (* (pow i 4) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(* -1 (* (pow i 4) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(* -1 (* (pow i 4) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(* -1 (pow i 4))
(* -1 (* (pow i 4) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(* -1 (* (pow i 4) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(* -1 (* (pow i 4) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(* -1/4 i)
(* i (- (* -1 (pow i 2)) 1/4))
(* i (- (* -1 (pow i 2)) 1/4))
(* i (- (* -1 (pow i 2)) 1/4))
(* -1 (pow i 3))
(* -1 (* (pow i 3) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(* -1 (* (pow i 3) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(* -1 (* (pow i 3) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(* -1 (pow i 3))
(* -1 (* (pow i 3) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(* -1 (* (pow i 3) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(* -1 (* (pow i 3) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
-1/4
(- (* -1 (pow i 2)) 1/4)
(- (* -1 (pow i 2)) 1/4)
(- (* -1 (pow i 2)) 1/4)
(* -1 (pow i 2))
(* -1 (* (pow i 2) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(* -1 (* (pow i 2) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(* -1 (* (pow i 2) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(* -1 (pow i 2))
(* -1 (* (pow i 2) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(* -1 (* (pow i 2) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(* -1 (* (pow i 2) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(* 16 i)
(* 16 i)
(* 16 i)
(* 16 i)
(* 16 i)
(* 16 i)
(* 16 i)
(* 16 i)
(* 16 i)
(* 16 i)
(* 16 i)
(* 16 i)
Outputs
(* -1/4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal -1/4 binary64))
(* (pow i 2) (- (* -1 (pow i 2)) 1/4))
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i))))
(* (pow i 2) (- (* (pow i 2) (- (* -4 (pow i 2)) 1)) 1/4))
(*.f64 i (*.f64 i (+.f64 (*.f64 i (*.f64 i (+.f64 #s(literal -1 binary64) (*.f64 i (*.f64 i #s(literal -4 binary64)))))) #s(literal -1/4 binary64))))
(* (pow i 2) (- (* (pow i 2) (- (* (pow i 2) (- (* -16 (pow i 2)) 4)) 1)) 1/4))
(*.f64 (*.f64 i i) (+.f64 (*.f64 i (*.f64 i (+.f64 #s(literal -1 binary64) (*.f64 i (*.f64 i (+.f64 #s(literal -4 binary64) (*.f64 (*.f64 i i) #s(literal -16 binary64)))))))) #s(literal -1/4 binary64)))
1/16
#s(literal 1/16 binary64)
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))
(+.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))) (/.f64 #s(literal 1/256 binary64) (*.f64 (*.f64 i i) (*.f64 i i))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))
(+.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))) (+.f64 (/.f64 #s(literal 1/256 binary64) (*.f64 (*.f64 i i) (*.f64 i i))) (/.f64 #s(literal 1/1024 binary64) (pow.f64 i #s(literal 6 binary64)))))
1/16
#s(literal 1/16 binary64)
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))
(+.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))) (/.f64 #s(literal 1/256 binary64) (*.f64 (*.f64 i i) (*.f64 i i))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))
(+.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))) (+.f64 (/.f64 #s(literal 1/256 binary64) (*.f64 (*.f64 i i) (*.f64 i i))) (/.f64 #s(literal 1/1024 binary64) (pow.f64 i #s(literal 6 binary64)))))
(/ -4 (pow i 2))
(/.f64 #s(literal -4 binary64) (*.f64 i i))
(/ (- (* 16 (pow i 2)) 4) (pow i 2))
(-.f64 #s(literal 16 binary64) (/.f64 #s(literal 4 binary64) (*.f64 i i)))
(/ (- (* 16 (pow i 2)) 4) (pow i 2))
(-.f64 #s(literal 16 binary64) (/.f64 #s(literal 4 binary64) (*.f64 i i)))
(/ (- (* 16 (pow i 2)) 4) (pow i 2))
(-.f64 #s(literal 16 binary64) (/.f64 #s(literal 4 binary64) (*.f64 i i)))
16
#s(literal 16 binary64)
(- 16 (* 4 (/ 1 (pow i 2))))
(-.f64 #s(literal 16 binary64) (/.f64 #s(literal 4 binary64) (*.f64 i i)))
(- 16 (* 4 (/ 1 (pow i 2))))
(-.f64 #s(literal 16 binary64) (/.f64 #s(literal 4 binary64) (*.f64 i i)))
(- 16 (* 4 (/ 1 (pow i 2))))
(-.f64 #s(literal 16 binary64) (/.f64 #s(literal 4 binary64) (*.f64 i i)))
16
#s(literal 16 binary64)
(- 16 (* 4 (/ 1 (pow i 2))))
(-.f64 #s(literal 16 binary64) (/.f64 #s(literal 4 binary64) (*.f64 i i)))
(- 16 (* 4 (/ 1 (pow i 2))))
(-.f64 #s(literal 16 binary64) (/.f64 #s(literal 4 binary64) (*.f64 i i)))
(- 16 (* 4 (/ 1 (pow i 2))))
(-.f64 #s(literal 16 binary64) (/.f64 #s(literal 4 binary64) (*.f64 i i)))
(/ -4 i)
(/.f64 #s(literal -4 binary64) i)
(/ (- (* 16 (pow i 2)) 4) i)
(+.f64 (*.f64 i #s(literal 16 binary64)) (/.f64 #s(literal -4 binary64) i))
(/ (- (* 16 (pow i 2)) 4) i)
(+.f64 (*.f64 i #s(literal 16 binary64)) (/.f64 #s(literal -4 binary64) i))
(/ (- (* 16 (pow i 2)) 4) i)
(+.f64 (*.f64 i #s(literal 16 binary64)) (/.f64 #s(literal -4 binary64) i))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* i (- 16 (* 4 (/ 1 (pow i 2)))))
(+.f64 (*.f64 i #s(literal 16 binary64)) (/.f64 #s(literal -4 binary64) i))
(* i (- 16 (* 4 (/ 1 (pow i 2)))))
(+.f64 (*.f64 i #s(literal 16 binary64)) (/.f64 #s(literal -4 binary64) i))
(* i (- 16 (* 4 (/ 1 (pow i 2)))))
(+.f64 (*.f64 i #s(literal 16 binary64)) (/.f64 #s(literal -4 binary64) i))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* -1 (* i (- (* 4 (/ 1 (pow i 2))) 16)))
(+.f64 (*.f64 i #s(literal 16 binary64)) (/.f64 #s(literal -4 binary64) i))
(* -1 (* i (- (* 4 (/ 1 (pow i 2))) 16)))
(+.f64 (*.f64 i #s(literal 16 binary64)) (/.f64 #s(literal -4 binary64) i))
(* -1 (* i (- (* 4 (/ 1 (pow i 2))) 16)))
(+.f64 (*.f64 i #s(literal 16 binary64)) (/.f64 #s(literal -4 binary64) i))
-4
#s(literal -4 binary64)
(- (* 16 (pow i 2)) 4)
(+.f64 #s(literal -4 binary64) (*.f64 i (*.f64 i #s(literal 16 binary64))))
(- (* 16 (pow i 2)) 4)
(+.f64 #s(literal -4 binary64) (*.f64 i (*.f64 i #s(literal 16 binary64))))
(- (* 16 (pow i 2)) 4)
(+.f64 #s(literal -4 binary64) (*.f64 i (*.f64 i #s(literal 16 binary64))))
(* 16 (pow i 2))
(*.f64 i (*.f64 i #s(literal 16 binary64)))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(+.f64 #s(literal -4 binary64) (*.f64 i (*.f64 i #s(literal 16 binary64))))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(+.f64 #s(literal -4 binary64) (*.f64 i (*.f64 i #s(literal 16 binary64))))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(+.f64 #s(literal -4 binary64) (*.f64 i (*.f64 i #s(literal 16 binary64))))
(* 16 (pow i 2))
(*.f64 i (*.f64 i #s(literal 16 binary64)))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(+.f64 #s(literal -4 binary64) (*.f64 i (*.f64 i #s(literal 16 binary64))))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(+.f64 #s(literal -4 binary64) (*.f64 i (*.f64 i #s(literal 16 binary64))))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(+.f64 #s(literal -4 binary64) (*.f64 i (*.f64 i #s(literal 16 binary64))))
(* -1/4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal -1/4 binary64))
(* -1/4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal -1/4 binary64))
(* -1/4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal -1/4 binary64))
(* -1/4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal -1/4 binary64))
(* -1/4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal -1/4 binary64))
(* -1/4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal -1/4 binary64))
(* -1/4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal -1/4 binary64))
(* -1/4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal -1/4 binary64))
(* -1/4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal -1/4 binary64))
(* -1/4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal -1/4 binary64))
(* -1/4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal -1/4 binary64))
(* -1/4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal -1/4 binary64))
(* -1/4 i)
(*.f64 i #s(literal -1/4 binary64))
(* -1/4 i)
(*.f64 i #s(literal -1/4 binary64))
(* -1/4 i)
(*.f64 i #s(literal -1/4 binary64))
(* -1/4 i)
(*.f64 i #s(literal -1/4 binary64))
(* -1/4 i)
(*.f64 i #s(literal -1/4 binary64))
(* -1/4 i)
(*.f64 i #s(literal -1/4 binary64))
(* -1/4 i)
(*.f64 i #s(literal -1/4 binary64))
(* -1/4 i)
(*.f64 i #s(literal -1/4 binary64))
(* -1/4 i)
(*.f64 i #s(literal -1/4 binary64))
(* -1/4 i)
(*.f64 i #s(literal -1/4 binary64))
(* -1/4 i)
(*.f64 i #s(literal -1/4 binary64))
(* -1/4 i)
(*.f64 i #s(literal -1/4 binary64))
(/ 1/64 (pow i 2))
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
(/ (+ 1/64 (* 1/16 (pow i 2))) (pow i 2))
(/.f64 (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 i i) #s(literal 1/16 binary64))) (*.f64 i i))
(/ (+ 1/64 (* 1/16 (pow i 2))) (pow i 2))
(/.f64 (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 i i) #s(literal 1/16 binary64))) (*.f64 i i))
(/ (+ 1/64 (* 1/16 (pow i 2))) (pow i 2))
(/.f64 (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 i i) #s(literal 1/16 binary64))) (*.f64 i i))
1/16
#s(literal 1/16 binary64)
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
1/16
#s(literal 1/16 binary64)
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(/ 1/64 (pow i 2))
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
(/ 1/64 (pow i 2))
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
(/ 1/64 (pow i 2))
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
(/ 1/64 (pow i 2))
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
(/ 1/64 (pow i 2))
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
(/ 1/64 (pow i 2))
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
(/ 1/64 (pow i 2))
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
(/ 1/64 (pow i 2))
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
(/ 1/64 (pow i 2))
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
(/ 1/64 (pow i 2))
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
(/ 1/64 (pow i 2))
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
(/ 1/64 (pow i 2))
(/.f64 #s(literal 1/64 binary64) (*.f64 i i))
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(* -1/4 (pow i 2))
(*.f64 (*.f64 i i) #s(literal -1/4 binary64))
(* (pow i 2) (- (* -1 (pow i 2)) 1/4))
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i))))
(* (pow i 2) (- (* -1 (pow i 2)) 1/4))
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i))))
(* (pow i 2) (- (* -1 (pow i 2)) 1/4))
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i))))
(* -1 (pow i 4))
(*.f64 (*.f64 i i) (-.f64 #s(literal 0 binary64) (*.f64 i i)))
(* -1 (* (pow i 4) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i))))
(* -1 (* (pow i 4) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i))))
(* -1 (* (pow i 4) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i))))
(* -1 (pow i 4))
(*.f64 (*.f64 i i) (-.f64 #s(literal 0 binary64) (*.f64 i i)))
(* -1 (* (pow i 4) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i))))
(* -1 (* (pow i 4) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i))))
(* -1 (* (pow i 4) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i))))
(* -1/4 i)
(*.f64 i #s(literal -1/4 binary64))
(* i (- (* -1 (pow i 2)) 1/4))
(*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i)))
(* i (- (* -1 (pow i 2)) 1/4))
(*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i)))
(* i (- (* -1 (pow i 2)) 1/4))
(*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i)))
(* -1 (pow i 3))
(-.f64 #s(literal 0 binary64) (*.f64 i (*.f64 i i)))
(* -1 (* (pow i 3) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i)))
(* -1 (* (pow i 3) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i)))
(* -1 (* (pow i 3) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i)))
(* -1 (pow i 3))
(-.f64 #s(literal 0 binary64) (*.f64 i (*.f64 i i)))
(* -1 (* (pow i 3) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i)))
(* -1 (* (pow i 3) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i)))
(* -1 (* (pow i 3) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i)))
-1/4
#s(literal -1/4 binary64)
(- (* -1 (pow i 2)) 1/4)
(-.f64 #s(literal -1/4 binary64) (*.f64 i i))
(- (* -1 (pow i 2)) 1/4)
(-.f64 #s(literal -1/4 binary64) (*.f64 i i))
(- (* -1 (pow i 2)) 1/4)
(-.f64 #s(literal -1/4 binary64) (*.f64 i i))
(* -1 (pow i 2))
(-.f64 #s(literal 0 binary64) (*.f64 i i))
(* -1 (* (pow i 2) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(-.f64 #s(literal -1/4 binary64) (*.f64 i i))
(* -1 (* (pow i 2) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(-.f64 #s(literal -1/4 binary64) (*.f64 i i))
(* -1 (* (pow i 2) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(-.f64 #s(literal -1/4 binary64) (*.f64 i i))
(* -1 (pow i 2))
(-.f64 #s(literal 0 binary64) (*.f64 i i))
(* -1 (* (pow i 2) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(-.f64 #s(literal -1/4 binary64) (*.f64 i i))
(* -1 (* (pow i 2) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(-.f64 #s(literal -1/4 binary64) (*.f64 i i))
(* -1 (* (pow i 2) (+ 1 (* 1/4 (/ 1 (pow i 2))))))
(-.f64 #s(literal -1/4 binary64) (*.f64 i i))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))

eval88.0ms (1.5%)

Compiler

Compiled 16811 to 1981 computations (88.2% saved)

prune95.0ms (1.7%)

Pruning

6 alts after pruning (2 fresh and 4 done)

PrunedKeptTotal
New7701771
Fresh011
Picked145
Done000
Total7716777
Accuracy
100.0%
Counts
777 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶72.7%
(/.f64 (*.f64 i i) (+.f64 (*.f64 i (*.f64 i #s(literal 16 binary64))) #s(literal -4 binary64)))
▶99.7%
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 16 binary64) (/.f64 #s(literal 4 binary64) (*.f64 i i))))
✓53.6%
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
✓46.0%
(*.f64 i (/.f64 i #s(literal -4 binary64)))
✓46.4%
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i))))
✓54.0%
#s(literal 1/16 binary64)
Compiler

Compiled 48 to 34 computations (29.2% saved)

simplify26.0ms (0.5%)

Algorithm
1×egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 i (*.f64 i #s(literal 16 binary64)))
✓cost-diff0
(+.f64 (*.f64 i (*.f64 i #s(literal 16 binary64))) #s(literal -4 binary64))
✓cost-diff0
(*.f64 i i)
✓cost-diff0
(/.f64 (*.f64 i i) (+.f64 (*.f64 i (*.f64 i #s(literal 16 binary64))) #s(literal -4 binary64)))
✓cost-diff0
(*.f64 i i)
✓cost-diff0
(/.f64 #s(literal 4 binary64) (*.f64 i i))
✓cost-diff0
(-.f64 #s(literal 16 binary64) (/.f64 #s(literal 4 binary64) (*.f64 i i)))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 16 binary64) (/.f64 #s(literal 4 binary64) (*.f64 i i))))
Rules
166×sum3-define
128×fma-define
82×fma-lowering-fma.f32
82×fma-lowering-fma.f64
80×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01357
12757
24357
36157
48557
511157
616857
720757
826557
940757
1042157
1142657
1242957
042957
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(/ 1 (- 16 (/ 4 (* i i))))
1
(- 16 (/ 4 (* i i)))
16
(/ 4 (* i i))
4
(* i i)
i
(/ (* i i) (+ (* i (* i 16)) -4))
(* i i)
i
(+ (* i (* i 16)) -4)
(* i (* i 16))
(* i 16)
16
-4
Outputs
(/ 1 (- 16 (/ 4 (* i i))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 16 binary64) (/.f64 #s(literal -4 binary64) (*.f64 i i))))
1
#s(literal 1 binary64)
(- 16 (/ 4 (* i i)))
(+.f64 #s(literal 16 binary64) (/.f64 #s(literal -4 binary64) (*.f64 i i)))
16
#s(literal 16 binary64)
(/ 4 (* i i))
(/.f64 #s(literal 4 binary64) (*.f64 i i))
4
#s(literal 4 binary64)
(* i i)
(*.f64 i i)
i
(/ (* i i) (+ (* i (* i 16)) -4))
(/.f64 (*.f64 i i) (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 i i)) #s(literal -4 binary64)))
(* i i)
(*.f64 i i)
i
(+ (* i (* i 16)) -4)
(+.f64 (*.f64 #s(literal 16 binary64) (*.f64 i i)) #s(literal -4 binary64))
(* i (* i 16))
(*.f64 #s(literal 16 binary64) (*.f64 i i))
(* i 16)
(*.f64 #s(literal 16 binary64) i)
16
#s(literal 16 binary64)
-4
#s(literal -4 binary64)

localize94.0ms (1.6%)

Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 i (*.f64 i #s(literal 16 binary64)))
✓accuracy100.0%
(*.f64 i i)
✓accuracy100.0%
(*.f64 i #s(literal 16 binary64))
✓accuracy73.5%
(/.f64 (*.f64 i i) (+.f64 (*.f64 i (*.f64 i #s(literal 16 binary64))) #s(literal -4 binary64)))
✓accuracy100.0%
(*.f64 i i)
✓accuracy100.0%
(-.f64 #s(literal 16 binary64) (/.f64 #s(literal 4 binary64) (*.f64 i i)))
✓accuracy99.7%
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 16 binary64) (/.f64 #s(literal 4 binary64) (*.f64 i i))))
✓accuracy99.4%
(/.f64 #s(literal 4 binary64) (*.f64 i i))
Results
53.0ms256×0valid
Compiler

Compiled 62 to 14 computations (77.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 15.0ms
ival-mult: 6.0ms (40.4% of total)
ival-div: 5.0ms (33.7% of total)
ival-sub: 1.0ms (6.7% of total)
ival-add: 1.0ms (6.7% of total)
const: 1.0ms (6.7% of total)
backward-pass: 0.0ms (0% of total)

series2.0ms (0%)

Counts
8 → 96
Calls
Call 1
Inputs
#<alt (/ 1 (- 16 (/ 4 (* i i))))>
#<alt (- 16 (/ 4 (* i i)))>
#<alt (/ 4 (* i i))>
#<alt (* i i)>
#<alt (/ (* i i) (+ (* i (* i 16)) -4))>
#<alt (+ (* i (* i 16)) -4)>
#<alt (* i (* i 16))>
#<alt (* i 16)>
Outputs
#<alt (* -1/4 (pow i 2))>
#<alt (* (pow i 2) (- (* -1 (pow i 2)) 1/4))>
#<alt (* (pow i 2) (- (* (pow i 2) (- (* -4 (pow i 2)) 1)) 1/4))>
#<alt (* (pow i 2) (- (* (pow i 2) (- (* (pow i 2) (- (* -16 (pow i 2)) 4)) 1)) 1/4))>
#<alt 1/16>
#<alt (+ 1/16 (* 1/64 (/ 1 (pow i 2))))>
#<alt (+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))>
#<alt (+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))>
#<alt 1/16>
#<alt (+ 1/16 (* 1/64 (/ 1 (pow i 2))))>
#<alt (+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))>
#<alt (+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))>
#<alt (/ -4 (pow i 2))>
#<alt (/ (- (* 16 (pow i 2)) 4) (pow i 2))>
#<alt (/ (- (* 16 (pow i 2)) 4) (pow i 2))>
#<alt (/ (- (* 16 (pow i 2)) 4) (pow i 2))>
#<alt 16>
#<alt (- 16 (* 4 (/ 1 (pow i 2))))>
#<alt (- 16 (* 4 (/ 1 (pow i 2))))>
#<alt (- 16 (* 4 (/ 1 (pow i 2))))>
#<alt 16>
#<alt (- 16 (* 4 (/ 1 (pow i 2))))>
#<alt (- 16 (* 4 (/ 1 (pow i 2))))>
#<alt (- 16 (* 4 (/ 1 (pow i 2))))>
#<alt (/ 4 (pow i 2))>
#<alt (/ 4 (pow i 2))>
#<alt (/ 4 (pow i 2))>
#<alt (/ 4 (pow i 2))>
#<alt (/ 4 (pow i 2))>
#<alt (/ 4 (pow i 2))>
#<alt (/ 4 (pow i 2))>
#<alt (/ 4 (pow i 2))>
#<alt (/ 4 (pow i 2))>
#<alt (/ 4 (pow i 2))>
#<alt (/ 4 (pow i 2))>
#<alt (/ 4 (pow i 2))>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (pow i 2)>
#<alt (* -1/4 (pow i 2))>
#<alt (* (pow i 2) (- (* -1 (pow i 2)) 1/4))>
#<alt (* (pow i 2) (- (* (pow i 2) (- (* -4 (pow i 2)) 1)) 1/4))>
#<alt (* (pow i 2) (- (* (pow i 2) (- (* (pow i 2) (- (* -16 (pow i 2)) 4)) 1)) 1/4))>
#<alt 1/16>
#<alt (+ 1/16 (* 1/64 (/ 1 (pow i 2))))>
#<alt (+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))>
#<alt (+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))>
#<alt 1/16>
#<alt (+ 1/16 (* 1/64 (/ 1 (pow i 2))))>
#<alt (+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))>
#<alt (+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))>
#<alt -4>
#<alt (- (* 16 (pow i 2)) 4)>
#<alt (- (* 16 (pow i 2)) 4)>
#<alt (- (* 16 (pow i 2)) 4)>
#<alt (* 16 (pow i 2))>
#<alt (* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))>
#<alt (* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))>
#<alt (* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))>
#<alt (* 16 (pow i 2))>
#<alt (* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))>
#<alt (* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))>
#<alt (* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 (pow i 2))>
#<alt (* 16 i)>
#<alt (* 16 i)>
#<alt (* 16 i)>
#<alt (* 16 i)>
#<alt (* 16 i)>
#<alt (* 16 i)>
#<alt (* 16 i)>
#<alt (* 16 i)>
#<alt (* 16 i)>
#<alt (* 16 i)>
#<alt (* 16 i)>
#<alt (* 16 i)>
Calls

24 calls:

TimeVariablePointExpression
0.0ms
i
@0
(/ 1 (- 16 (/ 4 (* i i))))
0.0ms
i
@inf
(/ 1 (- 16 (/ 4 (* i i))))
0.0ms
i
@-inf
(/ 1 (- 16 (/ 4 (* i i))))
0.0ms
i
@inf
(/ (* i i) (+ (* i (* i 16)) -4))
0.0ms
i
@0
(/ (* i i) (+ (* i (* i 16)) -4))

rewrite308.0ms (5.3%)

Algorithm
1×batch-egg-rewrite
Rules
3618×*-lowering-*.f32
3618×*-lowering-*.f64
2862×/-lowering-/.f32
2862×/-lowering-/.f64
2074×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01347
17847
256845
3650545
0836045
Stop Event
1×iter limit
1×node limit
Counts
8 → 350
Calls
Call 1
Inputs
(/ 1 (- 16 (/ 4 (* i i))))
(- 16 (/ 4 (* i i)))
(/ 4 (* i i))
(* i i)
(/ (* i i) (+ (* i (* i 16)) -4))
(+ (* i (* i 16)) -4)
(* i (* i 16))
(* i 16)
Outputs
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -4096 binary64) (/.f64 (/.f64 #s(literal 64 binary64) (*.f64 i i)) (*.f64 i (*.f64 i (*.f64 i i)))))) #s(literal 256 binary64)) (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -4096 binary64) (/.f64 (/.f64 #s(literal 64 binary64) (*.f64 i i)) (*.f64 i (*.f64 i (*.f64 i i)))))) (/.f64 (+.f64 #s(literal 16 binary64) (/.f64 (/.f64 #s(literal 4 binary64) i) i)) (/.f64 i (/.f64 #s(literal 4 binary64) i)))))
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -4096 binary64) (/.f64 (/.f64 #s(literal 64 binary64) (*.f64 i i)) (*.f64 i (*.f64 i (*.f64 i i)))))) (/.f64 (+.f64 #s(literal 16 binary64) (/.f64 (/.f64 #s(literal 4 binary64) i) i)) (/.f64 i (/.f64 #s(literal 4 binary64) i)))) (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -4096 binary64) (/.f64 (/.f64 #s(literal 64 binary64) (*.f64 i i)) (*.f64 i (*.f64 i (*.f64 i i)))))) #s(literal 256 binary64)))
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -4096 binary64) (/.f64 (/.f64 #s(literal 64 binary64) (*.f64 i i)) (*.f64 i (*.f64 i (*.f64 i i)))))) (+.f64 #s(literal 256 binary64) (/.f64 #s(literal 16 binary64) (*.f64 i (*.f64 i (*.f64 i i)))))) (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -4096 binary64) (/.f64 (/.f64 #s(literal 64 binary64) (*.f64 i i)) (*.f64 i (*.f64 i (*.f64 i i)))))) (/.f64 #s(literal 64 binary64) (*.f64 i i))))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 256 binary64) (/.f64 #s(literal 16 binary64) (*.f64 i (*.f64 i (*.f64 i i)))))) #s(literal 16 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 256 binary64) (/.f64 #s(literal 16 binary64) (*.f64 i (*.f64 i (*.f64 i i)))))) (/.f64 (/.f64 #s(literal 4 binary64) i) i)))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 256 binary64) (/.f64 #s(literal 16 binary64) (*.f64 i (*.f64 i (*.f64 i i)))))) (/.f64 (/.f64 #s(literal 4 binary64) i) i)) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 256 binary64) (/.f64 #s(literal 16 binary64) (*.f64 i (*.f64 i (*.f64 i i)))))) #s(literal 16 binary64)))
(+.f64 (*.f64 #s(literal 256 binary64) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -4096 binary64) (/.f64 (/.f64 #s(literal 64 binary64) (*.f64 i i)) (*.f64 i (*.f64 i (*.f64 i i))))))) (*.f64 (/.f64 (+.f64 #s(literal 16 binary64) (/.f64 (/.f64 #s(literal 4 binary64) i) i)) (/.f64 i (/.f64 #s(literal 4 binary64) i))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -4096 binary64) (/.f64 (/.f64 #s(literal 64 binary64) (*.f64 i i)) (*.f64 i (*.f64 i (*.f64 i i))))))))
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(*.f64 (/.f64 (+.f64 (*.f64 (*.f64 i i) (*.f64 (*.f64 i (*.f64 i (*.f64 i i))) #s(literal 4096 binary64))) #s(literal -64 binary64)) (*.f64 (+.f64 #s(literal 16 binary64) (*.f64 (*.f64 i i) (-.f64 (*.f64 (*.f64 i i) #s(literal 256 binary64)) #s(literal -64 binary64)))) (+.f64 (+.f64 (*.f64 i (*.f64 i (*.f64 (*.f64 i i) #s(literal 256 binary64)))) #s(literal -16 binary64)) (*.f64 (*.f64 i i) #s(literal -64 binary64))))) (+.f64 (+.f64 (*.f64 i (*.f64 i (*.f64 (*.f64 i i) #s(literal 256 binary64)))) #s(literal -16 binary64)) (*.f64 (*.f64 i i) #s(literal -64 binary64))))
(*.f64 (/.f64 (+.f64 (*.f64 i (*.f64 i (*.f64 (*.f64 i i) #s(literal 256 binary64)))) #s(literal -16 binary64)) (+.f64 (*.f64 (*.f64 i i) (*.f64 (*.f64 i (*.f64 i (*.f64 i i))) #s(literal 4096 binary64))) #s(literal 64 binary64))) (+.f64 (*.f64 i (*.f64 i (*.f64 (*.f64 i i) #s(literal 256 binary64)))) (+.f64 #s(literal 16 binary64) (*.f64 (*.f64 i i) #s(literal -64 binary64)))))
(*.f64 #s(literal 16 binary64) (*.f64 i i))
(*.f64 i (*.f64 #s(literal 16 binary64) i))
(*.f64 (*.f64 i i) #s(literal 16 binary64))
(*.f64 (*.f64 #s(literal 16 binary64) i) i)
(*.f64 #s(literal 16 binary64) i)
(*.f64 i #s(literal 16 binary64))

simplify216.0ms (3.7%)

Algorithm
1×egg-herbie
Rules
2194×*-lowering-*.f32
2194×*-lowering-*.f64
1756×+-lowering-+.f64
1756×+-lowering-+.f32
1422×sum4-define
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
054614
1123598
2302571
3779563
41840563
53840563
08207563
Stop Event
1×iter limit
1×node limit
Counts
96 → 96
Calls
Call 1
Inputs
(* -1/4 (pow i 2))
(* (pow i 2) (- (* -1 (pow i 2)) 1/4))
(* (pow i 2) (- (* (pow i 2) (- (* -4 (pow i 2)) 1)) 1/4))
(* (pow i 2) (- (* (pow i 2) (- (* (pow i 2) (- (* -16 (pow i 2)) 4)) 1)) 1/4))
1/16
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))
1/16
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))
(/ -4 (pow i 2))
(/ (- (* 16 (pow i 2)) 4) (pow i 2))
(/ (- (* 16 (pow i 2)) 4) (pow i 2))
(/ (- (* 16 (pow i 2)) 4) (pow i 2))
16
(- 16 (* 4 (/ 1 (pow i 2))))
(- 16 (* 4 (/ 1 (pow i 2))))
(- 16 (* 4 (/ 1 (pow i 2))))
16
(- 16 (* 4 (/ 1 (pow i 2))))
(- 16 (* 4 (/ 1 (pow i 2))))
(- 16 (* 4 (/ 1 (pow i 2))))
(/ 4 (pow i 2))
(/ 4 (pow i 2))
(/ 4 (pow i 2))
(/ 4 (pow i 2))
(/ 4 (pow i 2))
(/ 4 (pow i 2))
(/ 4 (pow i 2))
(/ 4 (pow i 2))
(/ 4 (pow i 2))
(/ 4 (pow i 2))
(/ 4 (pow i 2))
(/ 4 (pow i 2))
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(pow i 2)
(* -1/4 (pow i 2))
(* (pow i 2) (- (* -1 (pow i 2)) 1/4))
(* (pow i 2) (- (* (pow i 2) (- (* -4 (pow i 2)) 1)) 1/4))
(* (pow i 2) (- (* (pow i 2) (- (* (pow i 2) (- (* -16 (pow i 2)) 4)) 1)) 1/4))
1/16
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))
1/16
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))
-4
(- (* 16 (pow i 2)) 4)
(- (* 16 (pow i 2)) 4)
(- (* 16 (pow i 2)) 4)
(* 16 (pow i 2))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(* 16 (pow i 2))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(* 16 (pow i 2))
(* 16 (pow i 2))
(* 16 (pow i 2))
(* 16 (pow i 2))
(* 16 (pow i 2))
(* 16 (pow i 2))
(* 16 (pow i 2))
(* 16 (pow i 2))
(* 16 (pow i 2))
(* 16 (pow i 2))
(* 16 (pow i 2))
(* 16 (pow i 2))
(* 16 i)
(* 16 i)
(* 16 i)
(* 16 i)
(* 16 i)
(* 16 i)
(* 16 i)
(* 16 i)
(* 16 i)
(* 16 i)
(* 16 i)
(* 16 i)
Outputs
(* -1/4 (pow i 2))
(*.f64 #s(literal -1/4 binary64) (*.f64 i i))
(* (pow i 2) (- (* -1 (pow i 2)) 1/4))
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i))))
(* (pow i 2) (- (* (pow i 2) (- (* -4 (pow i 2)) 1)) 1/4))
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 i i) (-.f64 #s(literal 1 binary64) (*.f64 i (*.f64 i #s(literal -4 binary64))))))))
(* (pow i 2) (- (* (pow i 2) (- (* (pow i 2) (- (* -16 (pow i 2)) 4)) 1)) 1/4))
(*.f64 (*.f64 i i) (+.f64 #s(literal -1/4 binary64) (*.f64 i (*.f64 i (+.f64 #s(literal -1 binary64) (*.f64 i (*.f64 i (+.f64 #s(literal -4 binary64) (*.f64 (*.f64 i i) #s(literal -16 binary64))))))))))
1/16
#s(literal 1/16 binary64)
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))
(+.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))) (/.f64 #s(literal 1/256 binary64) (*.f64 i (*.f64 i (*.f64 i i)))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))
(+.f64 #s(literal 1/16 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 i i)) (/.f64 #s(literal 1/256 binary64) (*.f64 i (*.f64 i (*.f64 i i))))) (/.f64 #s(literal 1/1024 binary64) (*.f64 i (*.f64 i (*.f64 i (*.f64 i (*.f64 i i))))))))
1/16
#s(literal 1/16 binary64)
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))
(+.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))) (/.f64 #s(literal 1/256 binary64) (*.f64 i (*.f64 i (*.f64 i i)))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))
(+.f64 #s(literal 1/16 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 i i)) (/.f64 #s(literal 1/256 binary64) (*.f64 i (*.f64 i (*.f64 i i))))) (/.f64 #s(literal 1/1024 binary64) (*.f64 i (*.f64 i (*.f64 i (*.f64 i (*.f64 i i))))))))
(/ -4 (pow i 2))
(/.f64 #s(literal -4 binary64) (*.f64 i i))
(/ (- (* 16 (pow i 2)) 4) (pow i 2))
(+.f64 #s(literal 16 binary64) (/.f64 #s(literal -4 binary64) (*.f64 i i)))
(/ (- (* 16 (pow i 2)) 4) (pow i 2))
(+.f64 #s(literal 16 binary64) (/.f64 #s(literal -4 binary64) (*.f64 i i)))
(/ (- (* 16 (pow i 2)) 4) (pow i 2))
(+.f64 #s(literal 16 binary64) (/.f64 #s(literal -4 binary64) (*.f64 i i)))
16
#s(literal 16 binary64)
(- 16 (* 4 (/ 1 (pow i 2))))
(+.f64 #s(literal 16 binary64) (/.f64 #s(literal -4 binary64) (*.f64 i i)))
(- 16 (* 4 (/ 1 (pow i 2))))
(+.f64 #s(literal 16 binary64) (/.f64 #s(literal -4 binary64) (*.f64 i i)))
(- 16 (* 4 (/ 1 (pow i 2))))
(+.f64 #s(literal 16 binary64) (/.f64 #s(literal -4 binary64) (*.f64 i i)))
16
#s(literal 16 binary64)
(- 16 (* 4 (/ 1 (pow i 2))))
(+.f64 #s(literal 16 binary64) (/.f64 #s(literal -4 binary64) (*.f64 i i)))
(- 16 (* 4 (/ 1 (pow i 2))))
(+.f64 #s(literal 16 binary64) (/.f64 #s(literal -4 binary64) (*.f64 i i)))
(- 16 (* 4 (/ 1 (pow i 2))))
(+.f64 #s(literal 16 binary64) (/.f64 #s(literal -4 binary64) (*.f64 i i)))
(/ 4 (pow i 2))
(/.f64 #s(literal 4 binary64) (*.f64 i i))
(/ 4 (pow i 2))
(/.f64 #s(literal 4 binary64) (*.f64 i i))
(/ 4 (pow i 2))
(/.f64 #s(literal 4 binary64) (*.f64 i i))
(/ 4 (pow i 2))
(/.f64 #s(literal 4 binary64) (*.f64 i i))
(/ 4 (pow i 2))
(/.f64 #s(literal 4 binary64) (*.f64 i i))
(/ 4 (pow i 2))
(/.f64 #s(literal 4 binary64) (*.f64 i i))
(/ 4 (pow i 2))
(/.f64 #s(literal 4 binary64) (*.f64 i i))
(/ 4 (pow i 2))
(/.f64 #s(literal 4 binary64) (*.f64 i i))
(/ 4 (pow i 2))
(/.f64 #s(literal 4 binary64) (*.f64 i i))
(/ 4 (pow i 2))
(/.f64 #s(literal 4 binary64) (*.f64 i i))
(/ 4 (pow i 2))
(/.f64 #s(literal 4 binary64) (*.f64 i i))
(/ 4 (pow i 2))
(/.f64 #s(literal 4 binary64) (*.f64 i i))
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(pow i 2)
(*.f64 i i)
(* -1/4 (pow i 2))
(*.f64 #s(literal -1/4 binary64) (*.f64 i i))
(* (pow i 2) (- (* -1 (pow i 2)) 1/4))
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i))))
(* (pow i 2) (- (* (pow i 2) (- (* -4 (pow i 2)) 1)) 1/4))
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 i i) (-.f64 #s(literal 1 binary64) (*.f64 i (*.f64 i #s(literal -4 binary64))))))))
(* (pow i 2) (- (* (pow i 2) (- (* (pow i 2) (- (* -16 (pow i 2)) 4)) 1)) 1/4))
(*.f64 (*.f64 i i) (+.f64 #s(literal -1/4 binary64) (*.f64 i (*.f64 i (+.f64 #s(literal -1 binary64) (*.f64 i (*.f64 i (+.f64 #s(literal -4 binary64) (*.f64 (*.f64 i i) #s(literal -16 binary64))))))))))
1/16
#s(literal 1/16 binary64)
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))
(+.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))) (/.f64 #s(literal 1/256 binary64) (*.f64 i (*.f64 i (*.f64 i i)))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))
(+.f64 #s(literal 1/16 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 i i)) (/.f64 #s(literal 1/256 binary64) (*.f64 i (*.f64 i (*.f64 i i))))) (/.f64 #s(literal 1/1024 binary64) (*.f64 i (*.f64 i (*.f64 i (*.f64 i (*.f64 i i))))))))
1/16
#s(literal 1/16 binary64)
(+ 1/16 (* 1/64 (/ 1 (pow i 2))))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (* 1/64 (/ 1 (pow i 2)))))
(+.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))) (/.f64 #s(literal 1/256 binary64) (*.f64 i (*.f64 i (*.f64 i i)))))
(+ 1/16 (+ (/ 1/256 (pow i 4)) (+ (* 1/64 (/ 1 (pow i 2))) (* 1/1024 (/ 1 (pow i 6))))))
(+.f64 #s(literal 1/16 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 i i)) (/.f64 #s(literal 1/256 binary64) (*.f64 i (*.f64 i (*.f64 i i))))) (/.f64 #s(literal 1/1024 binary64) (*.f64 i (*.f64 i (*.f64 i (*.f64 i (*.f64 i i))))))))
-4
#s(literal -4 binary64)
(- (* 16 (pow i 2)) 4)
(+.f64 #s(literal -4 binary64) (*.f64 (*.f64 i i) #s(literal 16 binary64)))
(- (* 16 (pow i 2)) 4)
(+.f64 #s(literal -4 binary64) (*.f64 (*.f64 i i) #s(literal 16 binary64)))
(- (* 16 (pow i 2)) 4)
(+.f64 #s(literal -4 binary64) (*.f64 (*.f64 i i) #s(literal 16 binary64)))
(* 16 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 16 binary64))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(+.f64 #s(literal -4 binary64) (*.f64 (*.f64 i i) #s(literal 16 binary64)))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(+.f64 #s(literal -4 binary64) (*.f64 (*.f64 i i) #s(literal 16 binary64)))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(+.f64 #s(literal -4 binary64) (*.f64 (*.f64 i i) #s(literal 16 binary64)))
(* 16 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 16 binary64))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(+.f64 #s(literal -4 binary64) (*.f64 (*.f64 i i) #s(literal 16 binary64)))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(+.f64 #s(literal -4 binary64) (*.f64 (*.f64 i i) #s(literal 16 binary64)))
(* (pow i 2) (- 16 (* 4 (/ 1 (pow i 2)))))
(+.f64 #s(literal -4 binary64) (*.f64 (*.f64 i i) #s(literal 16 binary64)))
(* 16 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 16 binary64))
(* 16 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 16 binary64))
(* 16 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 16 binary64))
(* 16 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 16 binary64))
(* 16 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 16 binary64))
(* 16 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 16 binary64))
(* 16 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 16 binary64))
(* 16 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 16 binary64))
(* 16 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 16 binary64))
(* 16 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 16 binary64))
(* 16 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 16 binary64))
(* 16 (pow i 2))
(*.f64 (*.f64 i i) #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))
(* 16 i)
(*.f64 i #s(literal 16 binary64))

eval53.0ms (0.9%)

Compiler

Compiled 11691 to 1103 computations (90.6% saved)

prune69.0ms (1.2%)

Pruning

6 alts after pruning (0 fresh and 6 done)

PrunedKeptTotal
New4770477
Fresh000
Picked022
Done044
Total4776483
Accuracy
100.0%
Counts
483 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓72.7%
(/.f64 (*.f64 i i) (+.f64 (*.f64 i (*.f64 i #s(literal 16 binary64))) #s(literal -4 binary64)))
✓99.7%
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 16 binary64) (/.f64 #s(literal 4 binary64) (*.f64 i i))))
✓53.6%
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
✓46.0%
(*.f64 i (/.f64 i #s(literal -4 binary64)))
✓46.4%
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i))))
✓54.0%
#s(literal 1/16 binary64)
Compiler

Compiled 140 to 71 computations (49.3% saved)

regimes8.0ms (0.1%)

Counts
9 → 1
Calls
Call 1
Inputs
#s(literal 1/16 binary64)
(*.f64 i (/.f64 i #s(literal -4 binary64)))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i))))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 16 binary64) (/.f64 #s(literal 4 binary64) (*.f64 i i))))
(*.f64 i (/.f64 i (+.f64 (*.f64 (*.f64 i i) #s(literal 16 binary64)) #s(literal -4 binary64))))
(/.f64 (*.f64 i i) (+.f64 (*.f64 i (*.f64 i #s(literal 16 binary64))) #s(literal -4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 (*.f64 i (*.f64 i #s(literal 16 binary64))) #s(literal -4 binary64)) i) i))
(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i))) (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i)) #s(literal 1 binary64)))
Outputs
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 16 binary64) (/.f64 #s(literal 4 binary64) (*.f64 i i))))
Calls

2 calls:

5.0ms
i
3.0ms
(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i))) (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i)) #s(literal 1 binary64)))
Results
AccuracySegmentsBranch
99.7%1i
99.7%1(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i))) (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) i) (*.f64 #s(literal 2 binary64) i)) #s(literal 1 binary64)))
Compiler

Compiled 28 to 11 computations (60.7% saved)

regimes2.0ms (0%)

Counts
4 → 2
Calls
Call 1
Inputs
#s(literal 1/16 binary64)
(*.f64 i (/.f64 i #s(literal -4 binary64)))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i))))
Outputs
(*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i))))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
Calls

1 calls:

2.0ms
i
Results
AccuracySegmentsBranch
98.8%2i
Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts
3 → 2
Calls
Call 1
Inputs
#s(literal 1/16 binary64)
(*.f64 i (/.f64 i #s(literal -4 binary64)))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
Outputs
(*.f64 i (/.f64 i #s(literal -4 binary64)))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i)))
Calls

1 calls:

2.0ms
i
Results
AccuracySegmentsBranch
98.4%2i
Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts
2 → 2
Calls
Call 1
Inputs
#s(literal 1/16 binary64)
(*.f64 i (/.f64 i #s(literal -4 binary64)))
Outputs
(*.f64 i (/.f64 i #s(literal -4 binary64)))
#s(literal 1/16 binary64)
Calls

1 calls:

1.0ms
i
Results
AccuracySegmentsBranch
98.3%2i
Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(literal 1/16 binary64)
Outputs
#s(literal 1/16 binary64)
Calls

1 calls:

1.0ms
i
Results
AccuracySegmentsBranch
54.0%1i
Compiler

Compiled 2 to 1 computations (50% saved)

bsearch14.0ms (0.2%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
13.0ms
0.21423460446584752
0.9543489862800312
Results
9.0ms96×0valid
Compiler

Compiled 150 to 97 computations (35.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-sub: 3.0ms (44.2% of total)
ival-mult: 3.0ms (44.2% of total)
ival-div: 1.0ms (14.7% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

bsearch18.0ms (0.3%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
16.0ms
0.21423460446584752
0.9543489862800312
Results
13.0ms96×0valid
Compiler

Compiled 126 to 85 computations (32.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-mult: 9.0ms (83.4% of total)
ival-sub: 1.0ms (9.3% of total)
ival-div: 1.0ms (9.3% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

bsearch11.0ms (0.2%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
10.0ms
0.21423460446584752
0.9543489862800312
Results
7.0ms96×0valid
Compiler

Compiled 90 to 61 computations (32.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-mult: 3.0ms (67.2% of total)
ival-div: 1.0ms (22.4% of total)
ival-sub: 0.0ms (0% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

simplify12.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
14×*-commutative_binary64
14×+-commutative_binary64
12×sub-neg_binary64
8×neg-sub0_binary64
8×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02456
13856
25156
35956
46456
56556
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 16 binary64) (/.f64 #s(literal 4 binary64) (*.f64 i i))))
(if (<=.f64 i #s(literal 1/2 binary64)) (*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i)))) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))))
(if (<=.f64 i #s(literal 1/2 binary64)) (*.f64 i (/.f64 i #s(literal -4 binary64))) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))))
(if (<=.f64 i #s(literal 1/2 binary64)) (*.f64 i (/.f64 i #s(literal -4 binary64))) #s(literal 1/16 binary64))
#s(literal 1/16 binary64)
Outputs
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 16 binary64) (/.f64 #s(literal 4 binary64) (*.f64 i i))))
(if (<=.f64 i #s(literal 1/2 binary64)) (*.f64 i (*.f64 i (-.f64 #s(literal -1/4 binary64) (*.f64 i i)))) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))))
(if (<=.f64 i #s(literal 1/2 binary64)) (*.f64 i (/.f64 i #s(literal -4 binary64))) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 i i))))
(if (<=.f64 i #s(literal 1/2 binary64)) (*.f64 i (/.f64 i #s(literal -4 binary64))) #s(literal 1/16 binary64))
#s(literal 1/16 binary64)

soundness1.3s (21.9%)

Rules
5958×*-lowering-*.f32
5958×*-lowering-*.f64
4808×*-lowering-*.f32
4808×*-lowering-*.f64
3702×/-lowering-/.f32
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
078820
1195799
2498796
31330782
43542782
08278782
01682
110374
291266
0882166
01021
14018
219312
3108612
4376011
5581211
0825211
077932
1203867
2593840
32056818
46029818
08163818
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 131 to 80 computations (38.9% saved)

preprocess31.0ms (0.5%)

Remove

(abs i)

Compiler

Compiled 186 to 84 computations (54.8% saved)

end0.0ms (0%)

Profiling

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