Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H

Time bar (total: 4.0s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
100%100%0%0%0%0%0%1
Compiler

Compiled 9 to 8 computations (11.1% saved)

sample534.0ms (13.4%)

Memory
-6.5MiB live, 809.6MiB allocated
Samples
342.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 197.0ms
ival-mult: 68.0ms (34.6% of total)
ival-div: 57.0ms (29% of total)
ival-sub: 54.0ms (27.5% of total)
exact: 8.0ms (4.1% of total)
ival-true: 6.0ms (3.1% of total)
ival-assert: 3.0ms (1.5% of total)
Bogosity

explain61.0ms (1.5%)

Memory
36.6MiB live, 113.0MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-#s(literal 6 binary64)
00-0-#s(literal 3 binary64)
00-0-(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
00-0-(*.f64 x x)
00-0-(-.f64 (*.f64 x x) #s(literal 3 binary64))
00-0-x
Confusion
Predicted +Predicted -
+00
-0256
Precision
0/0
Recall
0/0
Confusion?
Predicted +Predicted MaybePredicted -
+000
-00256
Precision?
0/0
Recall?
0/0
Freqs
test
numberfreq
0256
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-001
Precision?
0/0
Recall?
0/0
Samples
22.0ms512×0valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-mult: 4.0ms (36.6% of total)
ival-div: 3.0ms (27.4% of total)
ival-sub: 2.0ms (18.3% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess21.0ms (0.5%)

Memory
-16.7MiB live, 20.9MiB allocated
Algorithm
1×egg-herbie
Rules
40×associate-/l*
36×distribute-lft-neg-in
36×associate-*r*
32×sub-neg
30×div-sub
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0814
13114
26914
316614
429214
537114
639714
740514
067
097
1167
2227
3247
0246
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
Outputs
(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
(/.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 6 binary64))
Symmetry

(abs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.9%
(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0.1%)

Memory
2.9MiB live, 2.9MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x x)
cost-diff0
(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
cost-diff128
(-.f64 (*.f64 x x) #s(literal 3 binary64))
Rules
8×lower-+.f64
8×lower-+.f32
6×lower-fma.f64
6×lower-/.f32
6×lower-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
0918
11618
22218
32418
02416
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
(-.f64 (*.f64 x x) #s(literal 3 binary64))
(*.f64 x x)
x
#s(literal 3 binary64)
#s(literal 6 binary64)
Outputs
(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
(/.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 6 binary64))
(-.f64 (*.f64 x x) #s(literal 3 binary64))
(fma.f64 x x #s(literal -3 binary64))
(*.f64 x x)
x
#s(literal 3 binary64)
#s(literal 6 binary64)

localize15.0ms (0.4%)

Memory
16.2MiB live, 16.2MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0
(-.f64 (*.f64 x x) #s(literal 3 binary64))
accuracy0
(*.f64 x x)
accuracy0.0703125
(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
Samples
10.0ms256×0valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-div: 2.0ms (40.5% of total)
ival-mult: 2.0ms (40.5% of total)
ival-sub: 1.0ms (20.2% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory
2.9MiB live, 2.9MiB allocated
Counts
3 → 36
Calls
Call 1
Inputs
#s(alt (-.f64 (*.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (*.f64 x x) #s(literal 3 binary64)) #<representation:binary64>) () ())
#s(alt (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation:binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())
Outputs
#s(alt -3 (taylor 0 x) (#s(alt (-.f64 (*.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (*.f64 x x) #s(literal 3 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (pow x 2) 3) (taylor 0 x) (#s(alt (-.f64 (*.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (*.f64 x x) #s(literal 3 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (pow x 2) 3) (taylor 0 x) (#s(alt (-.f64 (*.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (*.f64 x x) #s(literal 3 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (pow x 2) 3) (taylor 0 x) (#s(alt (-.f64 (*.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (*.f64 x x) #s(literal 3 binary64)) #<representation:binary64>) () ())) ())
#s(alt -1/2 (taylor 0 x) (#s(alt (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (-.f64 (*.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (*.f64 x x) #s(literal 3 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (-.f64 (*.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (*.f64 x x) #s(literal 3 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (-.f64 (*.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (*.f64 x x) #s(literal 3 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (-.f64 (*.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (*.f64 x x) #s(literal 3 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor inf x) (#s(alt (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (-.f64 (*.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (*.f64 x x) #s(literal 3 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (*.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (*.f64 x x) #s(literal 3 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (*.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (*.f64 x x) #s(literal 3 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (*.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (*.f64 x x) #s(literal 3 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@inf
((- (* x x) 3) (/ (- (* x x) 3) 6) (* x x))
1.0ms
x
@0
((- (* x x) 3) (/ (- (* x x) 3) 6) (* x x))
0.0ms
x
@-inf
((- (* x x) 3) (/ (- (* x x) 3) 6) (* x x))

simplify129.0ms (3.3%)

Memory
-42.4MiB live, 82.5MiB allocated
Algorithm
1×egg-herbie
Rules
4 388×lower-*.f64
4 388×lower-*.f32
2 828×lower-fma.f64
2 828×lower-fma.f32
1 846×cube-prod
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
019162
143162
298162
3236162
4759162
51590162
62334162
73514162
84236162
95345162
106402162
117126162
08039144
Stop Event
1×iter limit
1×node limit
Counts
36 → 36
Calls
Call 1
Inputs
-3
(- (pow x 2) 3)
(- (pow x 2) 3)
(- (pow x 2) 3)
-1/2
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
Outputs
-3
#s(literal -3 binary64)
(- (pow x 2) 3)
(fma.f64 x x #s(literal -3 binary64))
(- (pow x 2) 3)
(fma.f64 x x #s(literal -3 binary64))
(- (pow x 2) 3)
(fma.f64 x x #s(literal -3 binary64))
-1/2
#s(literal -1/2 binary64)
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* 1/6 (pow x 2))
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* 1/6 (pow x 2))
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite496.0ms (12.5%)

Memory
-172.0MiB live, 316.4MiB allocated
Rules
5 168×lower-/.f32
5 166×lower-/.f64
4 318×lower-*.f32
4 316×lower-*.f64
4 062×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0615
0915
14215
223015
3183115
0868513
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
3 → 516
Calls
Call 1
Inputs
(-.f64 (*.f64 x x) #s(literal 3 binary64))
(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
(*.f64 x x)
Outputs
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64)) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64)) (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64))))) (pow.f64 (neg.f64 (fma.f64 x x #s(literal 3 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64)) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64)) (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 27 binary64)))) (pow.f64 (neg.f64 (fma.f64 (*.f64 #s(literal 3 binary64) x) x (+.f64 #s(literal 9 binary64) (pow.f64 x #s(literal 4 binary64))))) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64)) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64)) #s(literal 1 binary64))) (fma.f64 x x #s(literal -3 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64)) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64)))) (pow.f64 (fma.f64 x x #s(literal 3 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64)) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 27 binary64)))) (pow.f64 (-.f64 (+.f64 #s(literal 9 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal -3 binary64) (*.f64 x x))) #s(literal -1 binary64)))
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(+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(+.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval75.0ms (1.9%)

Memory
-24.6MiB live, 163.9MiB allocated
Compiler

Compiled 14 583 to 1 650 computations (88.7% saved)

prune14.0ms (0.3%)

Memory
10.5MiB live, 49.9MiB allocated
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New5448552
Fresh000
Picked101
Done000
Total5458553
Accuracy
100.0%
Counts
553 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.9%
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
▶99.9%
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
▶50.9%
(pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
63.1%
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64)) (*.f64 (fma.f64 x x #s(literal 3 binary64)) #s(literal 6 binary64)))
51.9%
(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
▶99.9%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))))
51.9%
#s(approx (/ (- (* x x) 3) 6) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
▶48.5%
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
Compiler

Compiled 112 to 98 computations (12.5% saved)

simplify5.0ms (0.1%)

Memory
10.5MiB live, 10.5MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 x x #s(literal -3 binary64))
cost-diff0
(/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))
cost-diff0
(pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64))
cost-diff13312
(pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
cost-diff0
(fma.f64 x x #s(literal -3 binary64))
cost-diff0
(/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))
cost-diff1088
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))))
cost-diff0
(*.f64 x x)
cost-diff0
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
cost-diff0
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
cost-diff0
(*.f64 x #s(literal 1/6 binary64))
cost-diff0
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
Rules
24×lower-*.f32
20×lower-*.f64
14×lower-fma.f32
12×lower-+.f64
12×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02189
03282
15082
26082
36282
06282
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(*.f64 x #s(literal 1/6 binary64))
x
#s(literal 1/6 binary64)
#s(literal -1/2 binary64)
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(*.f64 x x)
x
#s(literal 1/6 binary64)
#s(literal -1/2 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))))
#s(literal 1 binary64)
(/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))
#s(literal 6 binary64)
(fma.f64 x x #s(literal -3 binary64))
x
#s(literal -3 binary64)
(pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64))
(/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))
#s(literal 6 binary64)
(fma.f64 x x #s(literal -3 binary64))
x
#s(literal -3 binary64)
#s(literal -1/2 binary64)
#s(literal 2 binary64)
Outputs
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))
(*.f64 x #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) x)
x
#s(literal 1/6 binary64)
#s(literal -1/2 binary64)
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))
(*.f64 x x)
x
#s(literal 1/6 binary64)
#s(literal -1/2 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))))
(*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))
#s(literal 1 binary64)
(/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))
#s(literal 6 binary64)
(fma.f64 x x #s(literal -3 binary64))
x
#s(literal -3 binary64)
(pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))
(pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64))
(/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))
#s(literal 6 binary64)
(fma.f64 x x #s(literal -3 binary64))
x
#s(literal -3 binary64)
#s(literal -1/2 binary64)
#s(literal 2 binary64)

localize57.0ms (1.4%)

Memory
-13.6MiB live, 80.4MiB allocated
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
accuracy0
(fma.f64 x x #s(literal -3 binary64))
accuracy0.12109375
(pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
accuracy0.567642068672055
(/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))
accuracy15.523542232524486
(pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64))
accuracy0
(fma.f64 x x #s(literal -3 binary64))
accuracy0.0546875
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))))
accuracy0.567642068672055
(/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))
accuracy0
(*.f64 x x)
accuracy0.0859375
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
accuracy32.470017635328574
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
accuracy0.046875
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
accuracy0.15625
(*.f64 x #s(literal 1/6 binary64))
Samples
23.0ms125×0invalid
21.0ms131×0valid
Compiler

Compiled 98 to 23 computations (76.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 31.0ms
const: 8.0ms (25.6% of total)
ival-mult: 6.0ms (19.2% of total)
ival-div: 5.0ms (16% of total)
ival-add: 4.0ms (12.8% of total)
ival-pow2: 3.0ms (9.6% of total)
ival-pow: 3.0ms (9.6% of total)
ival-sub: 1.0ms (3.2% of total)
exact: 1.0ms (3.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series9.0ms (0.2%)

Memory
11.2MiB live, 11.2MiB allocated
Counts
10 → 120
Calls
Call 1
Inputs
#s(alt (fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64)) #<representation:binary64>) () ())
#s(alt (*.f64 x #s(literal 1/6 binary64)) (patch (*.f64 x #s(literal 1/6 binary64)) #<representation:binary64>) () ())
#s(alt #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) (patch #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) #<representation:binary64>) () ())
#s(alt (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) #<representation:binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) #<representation:binary64>) () ())
#s(alt (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) (patch (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #<representation:binary64>) () ())
#s(alt (fma.f64 x x #s(literal -3 binary64)) (patch (fma.f64 x x #s(literal -3 binary64)) #<representation:binary64>) () ())
#s(alt (pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())
#s(alt (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #<representation:binary64>) () ())
Outputs
#s(alt -1/2 (taylor 0 x) (#s(alt (fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 1/6 binary64)) (patch (*.f64 x #s(literal 1/6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 1/6 binary64)) (patch (*.f64 x #s(literal 1/6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 1/6 binary64)) (patch (*.f64 x #s(literal 1/6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor 0 x) (#s(alt (*.f64 x #s(literal 1/6 binary64)) (patch (*.f64 x #s(literal 1/6 binary64)) #<representation:binary64>) () ())) ())
#s(alt -1/2 (taylor 0 x) (#s(alt #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) (patch #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) (patch #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) (patch #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) (patch #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt -1/2 (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt -1/2 (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) #<representation:binary64>) () ())) ())
#s(alt -2 (taylor 0 x) (#s(alt (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) (patch (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #<representation:binary64>) () ())) ())
#s(alt (- (* -2/3 (pow x 2)) 2) (taylor 0 x) (#s(alt (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) (patch (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #<representation:binary64>) () ())) ())
#s(alt (- (* (pow x 2) (- (* -2/9 (pow x 2)) 2/3)) 2) (taylor 0 x) (#s(alt (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) (patch (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #<representation:binary64>) () ())) ())
#s(alt (- (* (pow x 2) (- (* (pow x 2) (- (* -2/27 (pow x 2)) 2/9)) 2/3)) 2) (taylor 0 x) (#s(alt (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) (patch (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #<representation:binary64>) () ())) ())
#s(alt -3 (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -3 binary64)) (patch (fma.f64 x x #s(literal -3 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (pow x 2) 3) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -3 binary64)) (patch (fma.f64 x x #s(literal -3 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (pow x 2) 3) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -3 binary64)) (patch (fma.f64 x x #s(literal -3 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (pow x 2) 3) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -3 binary64)) (patch (fma.f64 x x #s(literal -3 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* -3 (pow (sqrt 1/6) 2)) (taylor 0 x) (#s(alt (pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2))) (taylor 0 x) (#s(alt (pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2))) (taylor 0 x) (#s(alt (pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
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#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -3 binary64)) (patch (fma.f64 x x #s(literal -3 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -3 binary64)) (patch (fma.f64 x x #s(literal -3 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (pow (sqrt 1/6) 2)) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2))) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2))) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2))) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 1/6))) (taylor -inf x) (#s(alt (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (sqrt 1/6) (* 1/4 (/ 1 (* (pow x 2) (sqrt 1/6))))))) (taylor -inf x) (#s(alt (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt 1/6) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/6))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/6) 3))))) (pow x 2)))))) (taylor -inf x) (#s(alt (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (sqrt 1/6) (* -1 (/ (+ (* 1/128 (/ 1 (* (pow x 2) (pow (sqrt 1/6) 5)))) (* 1/32 (/ 1 (pow (sqrt 1/6) 3)))) (pow x 4)))) (/ 1/4 (* (pow x 2) (sqrt 1/6)))))) (taylor -inf x) (#s(alt (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) (patch (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@inf
((+ (* (* x 1/6) x) -1/2) (* x 1/6) (/ (- (* x x) 3) 6) (+ (* (* x x) 1/6) -1/2) (* x x) (/ 1 (/ 6 (+ (* x x) -3))) (/ 6 (+ (* x x) -3)) (+ (* x x) -3) (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (pow (/ 6 (+ (* x x) -3)) -1/2))
2.0ms
x
@0
((+ (* (* x 1/6) x) -1/2) (* x 1/6) (/ (- (* x x) 3) 6) (+ (* (* x x) 1/6) -1/2) (* x x) (/ 1 (/ 6 (+ (* x x) -3))) (/ 6 (+ (* x x) -3)) (+ (* x x) -3) (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (pow (/ 6 (+ (* x x) -3)) -1/2))
1.0ms
x
@-inf
((+ (* (* x 1/6) x) -1/2) (* x 1/6) (/ (- (* x x) 3) 6) (+ (* (* x x) 1/6) -1/2) (* x x) (/ 1 (/ 6 (+ (* x x) -3))) (/ 6 (+ (* x x) -3)) (+ (* x x) -3) (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (pow (/ 6 (+ (* x x) -3)) -1/2))

simplify117.0ms (2.9%)

Memory
-27.5MiB live, 128.0MiB allocated
Algorithm
1×egg-herbie
Rules
5 268×lower-fma.f64
5 268×lower-fma.f32
4 276×lower-*.f64
4 276×lower-*.f32
1 998×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0133874
1313858
2856858
32278841
46690840
08462770
Stop Event
1×iter limit
1×node limit
Counts
120 → 120
Calls
Call 1
Inputs
-1/2
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
-1/2
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
-1/2
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
-1/2
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
-2
(- (* -2/3 (pow x 2)) 2)
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 2/3)) 2)
(- (* (pow x 2) (- (* (pow x 2) (- (* -2/27 (pow x 2)) 2/9)) 2/3)) 2)
-3
(- (pow x 2) 3)
(- (pow x 2) 3)
(- (pow x 2) 3)
(* -3 (pow (sqrt 1/6) 2))
(+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2)))
(+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2)))
(+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2)))
(sqrt -1/2)
(+ (sqrt -1/2) (* 1/12 (/ (pow x 2) (sqrt -1/2))))
(+ (sqrt -1/2) (* (pow x 2) (+ (* -1/288 (/ (pow x 2) (pow (sqrt -1/2) 3))) (* 1/12 (/ 1 (sqrt -1/2))))))
(+ (sqrt -1/2) (* (pow x 2) (+ (* (pow x 2) (- (* 1/3456 (/ (pow x 2) (pow (sqrt -1/2) 5))) (* 1/288 (/ 1 (pow (sqrt -1/2) 3))))) (* 1/12 (/ 1 (sqrt -1/2))))))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(/ 6 (pow x 2))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (/ 54 (pow x 4)))) (pow x 2))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (+ (* 162 (/ 1 (pow x 6))) (/ 54 (pow x 4))))) (pow x 2))
(pow x 2)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (pow (sqrt 1/6) 2))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(* x (sqrt 1/6))
(* x (- (sqrt 1/6) (* 1/4 (/ 1 (* (pow x 2) (sqrt 1/6))))))
(* x (+ (sqrt 1/6) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/6))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/6) 3))))) (pow x 2)))))
(* x (- (+ (sqrt 1/6) (* -1 (/ (+ (* 1/128 (/ 1 (* (pow x 2) (pow (sqrt 1/6) 5)))) (* 1/32 (/ 1 (pow (sqrt 1/6) 3)))) (pow x 4)))) (/ 1/4 (* (pow x 2) (sqrt 1/6)))))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(/ 6 (pow x 2))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (/ 54 (pow x 4)))) (pow x 2))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (+ (* 162 (/ 1 (pow x 6))) (/ 54 (pow x 4))))) (pow x 2))
(pow x 2)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (pow (sqrt 1/6) 2))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(* -1 (* x (sqrt 1/6)))
(* -1 (* x (- (sqrt 1/6) (* 1/4 (/ 1 (* (pow x 2) (sqrt 1/6)))))))
(* -1 (* x (+ (sqrt 1/6) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/6))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/6) 3))))) (pow x 2))))))
(* -1 (* x (- (+ (sqrt 1/6) (* -1 (/ (+ (* 1/128 (/ 1 (* (pow x 2) (pow (sqrt 1/6) 5)))) (* 1/32 (/ 1 (pow (sqrt 1/6) 3)))) (pow x 4)))) (/ 1/4 (* (pow x 2) (sqrt 1/6))))))
Outputs
-1/2
#s(literal -1/2 binary64)
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
-1/2
#s(literal -1/2 binary64)
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
-1/2
#s(literal -1/2 binary64)
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
-2
#s(literal -2 binary64)
(- (* -2/3 (pow x 2)) 2)
(fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -2 binary64))
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 2/3)) 2)
(fma.f64 (fma.f64 #s(literal -2/9 binary64) (*.f64 x x) #s(literal -2/3 binary64)) (*.f64 x x) #s(literal -2 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -2/27 (pow x 2)) 2/9)) 2/3)) 2)
(fma.f64 (fma.f64 (fma.f64 #s(literal -2/27 binary64) (*.f64 x x) #s(literal -2/9 binary64)) (*.f64 x x) #s(literal -2/3 binary64)) (*.f64 x x) #s(literal -2 binary64))
-3
#s(literal -3 binary64)
(- (pow x 2) 3)
(fma.f64 x x #s(literal -3 binary64))
(- (pow x 2) 3)
(fma.f64 x x #s(literal -3 binary64))
(- (pow x 2) 3)
(fma.f64 x x #s(literal -3 binary64))
(* -3 (pow (sqrt 1/6) 2))
#s(literal -1/2 binary64)
(+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(sqrt -1/2)
(sqrt.f64 #s(literal -1/2 binary64))
(+ (sqrt -1/2) (* 1/12 (/ (pow x 2) (sqrt -1/2))))
(fma.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal -1/2 binary64))) #s(literal 1/12 binary64)) x (sqrt.f64 #s(literal -1/2 binary64)))
(+ (sqrt -1/2) (* (pow x 2) (+ (* -1/288 (/ (pow x 2) (pow (sqrt -1/2) 3))) (* 1/12 (/ 1 (sqrt -1/2))))))
(fma.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal -1/2 binary64))) x) (fma.f64 #s(literal 1/144 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (sqrt.f64 #s(literal -1/2 binary64)))
(+ (sqrt -1/2) (* (pow x 2) (+ (* (pow x 2) (- (* 1/3456 (/ (pow x 2) (pow (sqrt -1/2) 5))) (* 1/288 (/ 1 (pow (sqrt -1/2) 3))))) (* 1/12 (/ 1 (sqrt -1/2))))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 #s(literal 1/3456 binary64) (pow.f64 (sqrt.f64 #s(literal -1/2 binary64)) #s(literal 5 binary64))) (*.f64 x x) (/.f64 #s(literal 1/144 binary64) (sqrt.f64 #s(literal -1/2 binary64)))) (*.f64 x x) (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal -1/2 binary64)))) (*.f64 x x) (sqrt.f64 #s(literal -1/2 binary64)))
(* 1/6 (pow x 2))
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 (pow x 2))
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* 1/6 (pow x 2))
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/6 (pow x 2))
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(/ 6 (pow x 2))
(/.f64 (/.f64 #s(literal 6 binary64) x) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (/ 54 (pow x 4)))) (pow x 2))
(/.f64 (+.f64 (+.f64 (/.f64 #s(literal 54 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 6 binary64)) (/.f64 #s(literal 18 binary64) (*.f64 x x))) (*.f64 x x))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (+ (* 162 (/ 1 (pow x 6))) (/ 54 (pow x 4))))) (pow x 2))
(/.f64 (+.f64 (+.f64 (/.f64 #s(literal 162 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 54 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 18 binary64) (*.f64 x x)))) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (pow (sqrt 1/6) 2))
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* x (sqrt 1/6))
(*.f64 (sqrt.f64 #s(literal 1/6 binary64)) x)
(* x (- (sqrt 1/6) (* 1/4 (/ 1 (* (pow x 2) (sqrt 1/6))))))
(fma.f64 (sqrt.f64 #s(literal 1/6 binary64)) x (/.f64 #s(literal -1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/6 binary64)) x)))
(* x (+ (sqrt 1/6) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/6))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/6) 3))))) (pow x 2)))))
(fma.f64 (sqrt.f64 #s(literal 1/6 binary64)) x (/.f64 (-.f64 (/.f64 #s(literal -3/16 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/6 binary64)) x) x)) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/6 binary64)))) x))
(* x (- (+ (sqrt 1/6) (* -1 (/ (+ (* 1/128 (/ 1 (* (pow x 2) (pow (sqrt 1/6) 5)))) (* 1/32 (/ 1 (pow (sqrt 1/6) 3)))) (pow x 4)))) (/ 1/4 (* (pow x 2) (sqrt 1/6)))))
(fma.f64 (-.f64 (sqrt.f64 #s(literal 1/6 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (/.f64 (/.f64 (/.f64 #s(literal 1/128 binary64) (pow.f64 (sqrt.f64 #s(literal 1/6 binary64)) #s(literal 5 binary64))) x) x)) (pow.f64 x #s(literal 4 binary64)))) x (/.f64 #s(literal -1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/6 binary64)) x)))
(* 1/6 (pow x 2))
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 (pow x 2))
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* 1/6 (pow x 2))
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/6 (pow x 2))
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(/ 6 (pow x 2))
(/.f64 (/.f64 #s(literal 6 binary64) x) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (/ 54 (pow x 4)))) (pow x 2))
(/.f64 (+.f64 (+.f64 (/.f64 #s(literal 54 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 6 binary64)) (/.f64 #s(literal 18 binary64) (*.f64 x x))) (*.f64 x x))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (+ (* 162 (/ 1 (pow x 6))) (/ 54 (pow x 4))))) (pow x 2))
(/.f64 (+.f64 (+.f64 (/.f64 #s(literal 162 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 54 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 18 binary64) (*.f64 x x)))) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (pow (sqrt 1/6) 2))
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* -1 (* x (sqrt 1/6)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 1/6 binary64)))
(* -1 (* x (- (sqrt 1/6) (* 1/4 (/ 1 (* (pow x 2) (sqrt 1/6)))))))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal 1/6 binary64)) x (/.f64 #s(literal -1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/6 binary64)) x))))
(* -1 (* x (+ (sqrt 1/6) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/6))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/6) 3))))) (pow x 2))))))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal 1/6 binary64)) x (/.f64 (-.f64 (/.f64 #s(literal -3/16 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/6 binary64)) x) x)) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/6 binary64)))) x)))
(* -1 (* x (- (+ (sqrt 1/6) (* -1 (/ (+ (* 1/128 (/ 1 (* (pow x 2) (pow (sqrt 1/6) 5)))) (* 1/32 (/ 1 (pow (sqrt 1/6) 3)))) (pow x 4)))) (/ 1/4 (* (pow x 2) (sqrt 1/6))))))
(fma.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (/.f64 (/.f64 (/.f64 #s(literal 1/128 binary64) (pow.f64 (sqrt.f64 #s(literal 1/6 binary64)) #s(literal 5 binary64))) x) x)) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal 1/6 binary64))) x (/.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/6 binary64))) x))

rewrite185.0ms (4.7%)

Memory
44.5MiB live, 272.8MiB allocated
Rules
4 166×lower-fma.f32
4 160×lower-fma.f64
3 676×lower-*.f32
3 672×lower-*.f64
2 134×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02163
03256
114056
266756
3582556
0837356
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
10 → 1 179
Calls
Call 1
Inputs
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(*.f64 x #s(literal 1/6 binary64))
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(*.f64 x x)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))))
(/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))
(fma.f64 x x #s(literal -3 binary64))
(pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64))
Outputs
(*.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/6 binary64) #s(literal -9/2 binary64)) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (fma.f64 (*.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64))))
(*.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/6 binary64) #s(literal -9/2 binary64)) (hypot.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)) (-.f64 (fma.f64 (*.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(*.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/6 binary64) #s(literal -3/2 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -27 binary64))) (+.f64 (fma.f64 #s(literal -3 binary64) (*.f64 x x) #s(literal 9 binary64)) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/6 binary64) #s(literal -3/2 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64))) (fma.f64 x x #s(literal -3 binary64)))
(*.f64 (/.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -1/12 binary64) (*.f64 x x) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64)) (-.f64 (*.f64 #s(literal 1/1296 binary64) (pow.f64 x #s(literal 8 binary64))) (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)))) (-.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) (*.f64 (*.f64 x x) #s(literal 1/12 binary64))))
(*.f64 (/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64)) (fma.f64 #s(literal 1/46656 binary64) (pow.f64 x #s(literal 12 binary64)) (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal 1/4 binary64)) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/1296 binary64) (pow.f64 x #s(literal 8 binary64)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal 1/4 binary64)) (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)))))))
(*.f64 (pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 x x #s(literal 3 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64))) (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)))
(*.f64 (*.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -3/4 binary64)) (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal 1/8 binary64))) (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal 1/8 binary64)))
(*.f64 (*.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -3/4 binary64)) (pow.f64 #s(literal 6 binary64) #s(literal -1/4 binary64))) (pow.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) (pow.f64 #s(literal 6 binary64) #s(literal -1/2 binary64))) (pow.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -3/4 binary64))) (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal 1/4 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64))) (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64))) (pow.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal 1/4 binary64))) #s(literal -1 binary64)))
(*.f64 (*.f64 (pow.f64 #s(literal 6 binary64) #s(literal -1/2 binary64)) (pow.f64 #s(literal 6 binary64) #s(literal -1/2 binary64))) (fma.f64 x x #s(literal -3 binary64)))
(*.f64 (pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -3/4 binary64)) #s(literal 1 binary64)) (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal 1/4 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 3 binary64) (*.f64 x x)) #s(literal 1 binary64)) #s(literal -1/6 binary64))
(*.f64 (pow.f64 (pow.f64 #s(literal 6 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 27 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 3 binary64)) #s(literal 9 binary64)) #s(literal -1 binary64)))
(*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/6 binary64) #s(literal -9/2 binary64)) (pow.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 3 binary64)) #s(literal 9 binary64)) #s(literal -1 binary64)))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/6 binary64) #s(literal -3/2 binary64)) (pow.f64 (fma.f64 x x #s(literal 3 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -3/4 binary64)) (/.f64 (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -3/4 binary64)) (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal 1/8 binary64)) (*.f64 (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal 1/8 binary64)) (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -3/4 binary64))))
(*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (-.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)))
(*.f64 (pow.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal 1/4 binary64))) #s(literal -1 binary64)) (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64)))
(*.f64 #s(literal -1/6 binary64) (/.f64 (-.f64 #s(literal 3 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(*.f64 #s(literal -1/6 binary64) (pow.f64 (-.f64 #s(literal 3 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(*.f64 #s(literal -1/6 binary64) (-.f64 #s(literal 3 binary64) (*.f64 x x)))
(*.f64 (neg.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64))) (pow.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64))) (pow.f64 (neg.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal 1/4 binary64)))) #s(literal -1 binary64)))
(*.f64 (*.f64 #s(literal -1/6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1 binary64))
(*.f64 (pow.f64 #s(literal 6 binary64) #s(literal -1/4 binary64)) (*.f64 (pow.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -3/4 binary64))))
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(fma.f64 (*.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) x) (/.f64 x (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64)))))
(fma.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/6 binary64)) (/.f64 #s(literal 1/6 binary64) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64)))))
(fma.f64 #s(literal 1/36 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64)))))
(fma.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) (/.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64)))))
(fma.f64 #s(literal -1/6 binary64) (*.f64 (neg.f64 x) x) #s(literal -1/2 binary64))
(fma.f64 (*.f64 (neg.f64 x) x) #s(literal -1/6 binary64) #s(literal -1/2 binary64))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/36 binary64) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64)))))
(fma.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64)))))
(fma.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64)))))
(fma.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) (/.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64)))))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(fma.f64 (*.f64 #s(literal 1/6 binary64) x) (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64)))))
(fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/6 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64)))))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(fma.f64 x (/.f64 (*.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) x) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64)))))
(fma.f64 x (*.f64 #s(literal 1/6 binary64) x) #s(literal -1/2 binary64))
(-.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/36 binary64) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(-.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))) (/.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))))
(-.f64 (/.f64 (*.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal 1/4 binary64)))) (/.f64 #s(literal 1/8 binary64) (fma.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal 1/4 binary64)))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (fma.f64 x x #s(literal 3 binary64)) #s(literal 6 binary64))) (/.f64 #s(literal 9 binary64) (*.f64 (fma.f64 x x #s(literal 3 binary64)) #s(literal 6 binary64))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 3 binary64)) #s(literal 9 binary64)) #s(literal 6 binary64))) (/.f64 #s(literal 27 binary64) (*.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 3 binary64)) #s(literal 9 binary64)) #s(literal 6 binary64))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 3 binary64))) #s(literal 6 binary64)) (/.f64 (/.f64 #s(literal 9 binary64) (fma.f64 x x #s(literal 3 binary64))) #s(literal 6 binary64)))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 3 binary64)) #s(literal 9 binary64))) #s(literal 6 binary64)) (/.f64 (/.f64 #s(literal 27 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 3 binary64)) #s(literal 9 binary64))) #s(literal 6 binary64)))
(-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/36 binary64) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64))))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/6 binary64) (fma.f64 x x #s(literal -3 binary64))))
(-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)))))
(exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal -2 binary64)) (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal -2 binary64)))) #s(literal -1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal 1/4 binary64))) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))))
(+.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) #s(literal -1/2 binary64))
(+.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 (neg.f64 x) x)) #s(literal -1/2 binary64))
(+.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/36 binary64) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64)))))
(+.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)))
(+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 (neg.f64 x) x)))
(+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))
(*.f64 (*.f64 (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal 1/4 binary64)) (pow.f64 #s(literal 6 binary64) #s(literal -1/4 binary64))) (pow.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/4 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 #s(literal 6 binary64) #s(literal -1/2 binary64))) (pow.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/2 binary64)))
(*.f64 (*.f64 (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal 1/8 binary64))) (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 6 binary64) #s(literal -1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 6 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64))) #s(literal -1/2 binary64)) (pow.f64 (fma.f64 x x #s(literal 3 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 27 binary64))) #s(literal -1/2 binary64)) (pow.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 3 binary64)) #s(literal 9 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) (pow.f64 #s(literal -6 binary64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(literal -6 binary64) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal -6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal 1/8 binary64)) (*.f64 (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal 1/8 binary64)) (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 #s(literal 6 binary64) #s(literal -1/4 binary64)) (*.f64 (pow.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal 6 binary64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(literal 6 binary64) #s(literal -1/2 binary64)) (pow.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))))
(pow.f64 (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal -2 binary64)) #s(literal -1/4 binary64))
(pow.f64 (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal -1/2 binary64))) (log.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))))))
(exp.f64 (*.f64 (log.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64)) #s(literal -2 binary64))) #s(literal -1/4 binary64)))
(exp.f64 (log.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64))))

eval211.0ms (5.3%)

Memory
-4.7MiB live, 298.2MiB allocated
Compiler

Compiled 28 264 to 2 106 computations (92.5% saved)

prune98.0ms (2.5%)

Memory
-8.3MiB live, 77.4MiB allocated
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1 56521 567
Fresh213
Picked235
Done000
Total1 56961 575
Accuracy
100.0%
Counts
1 575 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.9%
(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
✓99.9%
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
✓99.9%
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
▶51.9%
(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
▶51.9%
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
✓48.5%
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
Compiler

Compiled 32 to 28 computations (12.5% saved)

simplify5.0ms (0.1%)

Memory
4.1MiB live, 4.1MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 x #s(literal 6 binary64))
cost-diff0
(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
cost-diff0
(*.f64 x x)
cost-diff0
#s(approx (- (* x x) 3) (*.f64 x x))
cost-diff0
(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
cost-diff0
(*.f64 x x)
cost-diff0
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
cost-diff0
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
Rules
24×lower-*.f32
20×lower-*.f64
14×lower-fma.f32
12×lower-fma.f64
12×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02064
02764
13762
24362
34560
44960
55460
05457
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
#s(literal 1/6 binary64)
(*.f64 x x)
x
(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
#s(approx (- (* x x) 3) (*.f64 x x))
(*.f64 x x)
x
#s(literal 6 binary64)
(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
(/.f64 x #s(literal 6 binary64))
x
#s(literal 6 binary64)
#s(literal -1/2 binary64)
Outputs
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
#s(literal 1/6 binary64)
(*.f64 x x)
x
(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
#s(approx (- (* x x) 3) (*.f64 x x))
(*.f64 x x)
x
#s(literal 6 binary64)
(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
(/.f64 x #s(literal 6 binary64))
x
#s(literal 6 binary64)
#s(literal -1/2 binary64)

localize61.0ms (1.5%)

Memory
4.5MiB live, 42.6MiB allocated
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
accuracy0
(/.f64 x #s(literal 6 binary64))
accuracy0.046875
(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
accuracy0
(*.f64 x x)
accuracy0.0625
(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
accuracy0.2936325195371061
#s(approx (- (* x x) 3) (*.f64 x x))
accuracy0
(*.f64 x x)
accuracy0.0859375
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
accuracy0.2929687500001692
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
Samples
36.0ms131×0valid
14.0ms125×0invalid
Compiler

Compiled 53 to 19 computations (64.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 41.0ms
ival-div: 23.0ms (55.8% of total)
ival-mult: 5.0ms (12.1% of total)
const: 3.0ms (7.3% of total)
ival-pow2: 3.0ms (7.3% of total)
ival-pow: 3.0ms (7.3% of total)
ival-add: 2.0ms (4.9% of total)
ival-sub: 1.0ms (2.4% of total)
exact: 1.0ms (2.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory
6.1MiB live, 6.1MiB allocated
Counts
7 → 84
Calls
Call 1
Inputs
#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) #<representation:binary64>) () ())
#s(alt (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) #<representation:binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())
#s(alt (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) (patch (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) #<representation:binary64>) () ())
#s(alt #s(approx (- (* x x) 3) (*.f64 x x)) (patch #s(approx (- (* x x) 3) (*.f64 x x)) #<representation:binary64>) () ())
#s(alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) #<representation:binary64>) () ())
#s(alt (/.f64 x #s(literal 6 binary64)) (patch (/.f64 x #s(literal 6 binary64)) #<representation:binary64>) () ())
Outputs
#s(alt (* -3 (pow (sqrt 1/6) 2)) (taylor 0 x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2))) (taylor 0 x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2))) (taylor 0 x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2))) (taylor 0 x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt -1/2 (taylor 0 x) (#s(alt (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) (patch (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) (patch (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) (patch (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) (patch (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt -3 (taylor 0 x) (#s(alt #s(approx (- (* x x) 3) (*.f64 x x)) (patch #s(approx (- (* x x) 3) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (- (pow x 2) 3) (taylor 0 x) (#s(alt #s(approx (- (* x x) 3) (*.f64 x x)) (patch #s(approx (- (* x x) 3) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (- (pow x 2) 3) (taylor 0 x) (#s(alt #s(approx (- (* x x) 3) (*.f64 x x)) (patch #s(approx (- (* x x) 3) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (- (pow x 2) 3) (taylor 0 x) (#s(alt #s(approx (- (* x x) 3) (*.f64 x x)) (patch #s(approx (- (* x x) 3) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt -1/2 (taylor 0 x) (#s(alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor 0 x) (#s(alt (/.f64 x #s(literal 6 binary64)) (patch (/.f64 x #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor 0 x) (#s(alt (/.f64 x #s(literal 6 binary64)) (patch (/.f64 x #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor 0 x) (#s(alt (/.f64 x #s(literal 6 binary64)) (patch (/.f64 x #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor 0 x) (#s(alt (/.f64 x #s(literal 6 binary64)) (patch (/.f64 x #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (pow (sqrt 1/6) 2)) (taylor inf x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2))) (taylor inf x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2))) (taylor inf x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2))) (taylor inf x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor inf x) (#s(alt (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor inf x) (#s(alt (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor inf x) (#s(alt (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor inf x) (#s(alt (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) (patch (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) (patch (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) (patch (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) (patch (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt #s(approx (- (* x x) 3) (*.f64 x x)) (patch #s(approx (- (* x x) 3) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (- (* x x) 3) (*.f64 x x)) (patch #s(approx (- (* x x) 3) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (- (* x x) 3) (*.f64 x x)) (patch #s(approx (- (* x x) 3) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (- (* x x) 3) (*.f64 x x)) (patch #s(approx (- (* x x) 3) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor inf x) (#s(alt (/.f64 x #s(literal 6 binary64)) (patch (/.f64 x #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor inf x) (#s(alt (/.f64 x #s(literal 6 binary64)) (patch (/.f64 x #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor inf x) (#s(alt (/.f64 x #s(literal 6 binary64)) (patch (/.f64 x #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor inf x) (#s(alt (/.f64 x #s(literal 6 binary64)) (patch (/.f64 x #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (pow (sqrt 1/6) 2)) (taylor -inf x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2))) (taylor -inf x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2))) (taylor -inf x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2))) (taylor -inf x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) (patch (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) (patch (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) (patch (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) (patch (/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (- (* x x) 3) (*.f64 x x)) (patch #s(approx (- (* x x) 3) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (- (* x x) 3) (*.f64 x x)) (patch #s(approx (- (* x x) 3) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (- (* x x) 3) (*.f64 x x)) (patch #s(approx (- (* x x) 3) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (- (* x x) 3) (*.f64 x x)) (patch #s(approx (- (* x x) 3) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (/.f64 x #s(literal 6 binary64)) (patch (/.f64 x #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (/.f64 x #s(literal 6 binary64)) (patch (/.f64 x #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (/.f64 x #s(literal 6 binary64)) (patch (/.f64 x #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (/.f64 x #s(literal 6 binary64)) (patch (/.f64 x #s(literal 6 binary64)) #<representation:binary64>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@inf
((pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (* 1/6 (* x x)) (* x x) (/ (- (* x x) 3) 6) (- (* x x) 3) (+ (* (/ x 6) x) -1/2) (/ x 6))
1.0ms
x
@-inf
((pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (* 1/6 (* x x)) (* x x) (/ (- (* x x) 3) 6) (- (* x x) 3) (+ (* (/ x 6) x) -1/2) (/ x 6))
1.0ms
x
@0
((pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (* 1/6 (* x x)) (* x x) (/ (- (* x x) 3) 6) (- (* x x) 3) (+ (* (/ x 6) x) -1/2) (/ x 6))

simplify102.0ms (2.6%)

Memory
-0.4MiB live, 76.8MiB allocated
Algorithm
1×egg-herbie
Rules
4 158×lower-*.f64
4 158×lower-*.f32
2 862×lower-neg.f32
2 862×lower-neg.f64
2 792×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
029502
169406
2187406
3474406
41766406
53125406
64629406
08385370
Stop Event
1×iter limit
1×node limit
Counts
84 → 84
Calls
Call 1
Inputs
(* -3 (pow (sqrt 1/6) 2))
(+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2)))
(+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2)))
(+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2)))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
-1/2
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
-3
(- (pow x 2) 3)
(- (pow x 2) 3)
(- (pow x 2) 3)
-1/2
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* (pow x 2) (pow (sqrt 1/6) 2))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* (pow x 2) (pow (sqrt 1/6) 2))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
Outputs
(* -3 (pow (sqrt 1/6) 2))
#s(literal -1/2 binary64)
(+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2)))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2)))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2)))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
-1/2
#s(literal -1/2 binary64)
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
-3
#s(literal -3 binary64)
(- (pow x 2) 3)
(fma.f64 x x #s(literal -3 binary64))
(- (pow x 2) 3)
(fma.f64 x x #s(literal -3 binary64))
(- (pow x 2) 3)
(fma.f64 x x #s(literal -3 binary64))
-1/2
#s(literal -1/2 binary64)
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* (pow x 2) (pow (sqrt 1/6) 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* (pow x 2) (pow (sqrt 1/6) 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))

rewrite181.0ms (4.6%)

Memory
13.3MiB live, 124.6MiB allocated
Rules
3 388×lower-*.f32
3 384×lower-*.f64
3 326×lower-fma.f32
3 324×lower-fma.f64
2 180×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02054
02752
111250
259849
3553549
0804047
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
7 → 255
Calls
Call 1
Inputs
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
(*.f64 x x)
(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
#s(approx (- (* x x) 3) (*.f64 x x))
(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
(/.f64 x #s(literal 6 binary64))
Outputs
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x))
(*.f64 (/.f64 x #s(literal 1 binary64)) (*.f64 #s(literal 1/6 binary64) x))
(*.f64 (*.f64 x #s(literal -1/6 binary64)) (neg.f64 x))
(*.f64 (*.f64 (neg.f64 x) x) #s(literal -1/6 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x))
(*.f64 (neg.f64 x) (*.f64 #s(literal -1/6 binary64) x))
(*.f64 (neg.f64 x) (*.f64 x #s(literal -1/6 binary64)))
(*.f64 (*.f64 #s(literal 1/6 binary64) x) x)
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) (/.f64 x (pow.f64 x #s(literal -1 binary64))))
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
(*.f64 x (*.f64 #s(literal 1/6 binary64) x))
(pow.f64 (/.f64 (/.f64 (/.f64 #s(literal 6 binary64) x) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 6 binary64) x) x) #s(literal -1 binary64))
(pow.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) #s(literal 1 binary64))
(/.f64 (neg.f64 (*.f64 (neg.f64 x) x)) #s(literal 6 binary64))
(/.f64 (*.f64 (neg.f64 x) x) #s(literal -6 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 #s(literal 6 binary64) x) x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 6 binary64) x) x))
(/.f64 (neg.f64 x) (/.f64 #s(literal -6 binary64) x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(literal 6 binary64) x) x)))
(/.f64 (*.f64 #s(literal 1/6 binary64) x) (pow.f64 x #s(literal -1 binary64)))
(/.f64 (*.f64 x x) #s(literal 6 binary64))
(/.f64 x (/.f64 #s(literal 6 binary64) x))
(neg.f64 (*.f64 x (*.f64 x #s(literal -1/6 binary64))))
(neg.f64 (*.f64 (*.f64 x #s(literal -1/6 binary64)) x))
(neg.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 #s(literal 6 binary64) x) x)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (log.f64 #s(literal 1/6 binary64))) #s(literal 1 binary64)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 x))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (neg.f64 #s(approx (- (* x x) 3) (*.f64 x x)))) #s(literal -1/6 binary64))
(*.f64 (pow.f64 (/.f64 #s(literal 6 binary64) #s(approx (- (* x x) 3) (*.f64 x x))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 6 binary64) #s(approx (- (* x x) 3) (*.f64 x x))) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1/6 binary64) (neg.f64 #s(approx (- (* x x) 3) (*.f64 x x))))
(*.f64 #s(literal 1 binary64) (*.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 1/6 binary64)))
(*.f64 (neg.f64 #s(approx (- (* x x) 3) (*.f64 x x))) #s(literal -1/6 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal -1/6 binary64)))
(*.f64 (*.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 1/6 binary64)) #s(literal 1 binary64))
(*.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) (pow.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 1 binary64)))
(*.f64 #s(literal 1/6 binary64) #s(approx (- (* x x) 3) (*.f64 x x)))
(pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) #s(approx (- (* x x) 3) (*.f64 x x))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 6 binary64) #s(approx (- (* x x) 3) (*.f64 x x))) #s(literal -1 binary64))
(pow.f64 (*.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 1/6 binary64)) #s(literal 1 binary64))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 #s(approx (- (* x x) 3) (*.f64 x x)))) #s(literal -6 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) #s(approx (- (* x x) 3) (*.f64 x x))))
(/.f64 (neg.f64 #s(approx (- (* x x) 3) (*.f64 x x))) #s(literal -6 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -6 binary64) #s(approx (- (* x x) 3) (*.f64 x x))))
(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
(/.f64 #s(literal 1/6 binary64) (pow.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 6 binary64) #s(approx (- (* x x) 3) (*.f64 x x)))))
(neg.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal -1/6 binary64))))
(neg.f64 (*.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal -1/6 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal -1/6 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 6 binary64) #s(approx (- (* x x) 3) (*.f64 x x)))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) #s(approx (- (* x x) 3) (*.f64 x x)))
(*.f64 #s(literal -1 binary64) (neg.f64 #s(approx (- (* x x) 3) (*.f64 x x))))
#s(approx (- (* x x) 3) (*.f64 x x))
(neg.f64 (neg.f64 #s(approx (- (* x x) 3) (*.f64 x x))))
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (- (* x x) 3) (*.f64 x x))))
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(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 1/6 binary64) (fma.f64 x x #s(literal -3 binary64)))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (*.f64 #s(literal 1/6 binary64) (fma.f64 x x #s(literal -3 binary64)))))
(+.f64 (/.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1/2 binary64)))))
(+.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x))
(*.f64 (pow.f64 (/.f64 #s(literal 6 binary64) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 6 binary64) x) #s(literal -1/2 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) #s(literal -1/6 binary64))
(*.f64 #s(literal -1/6 binary64) (neg.f64 x))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) x))
(*.f64 (neg.f64 x) #s(literal -1/6 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/6 binary64)))
(*.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal 1/6 binary64) x)
(*.f64 x #s(literal 1/6 binary64))
(pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) x) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 6 binary64) x) #s(literal -1 binary64))
(pow.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1 binary64))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) #s(literal -6 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) x))
(/.f64 (neg.f64 x) #s(literal -6 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -6 binary64) x))
(/.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal -1 binary64)))
(/.f64 x #s(literal 6 binary64))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 6 binary64) x)))
(neg.f64 (*.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/6 binary64))))
(neg.f64 (*.f64 x #s(literal -1/6 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x #s(literal -1/6 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 6 binary64) x)) #s(literal -1 binary64)))

eval61.0ms (1.5%)

Memory
12.1MiB live, 93.9MiB allocated
Compiler

Compiled 4 300 to 685 computations (84.1% saved)

prune12.0ms (0.3%)

Memory
-6.2MiB live, 31.3MiB allocated
Pruning

6 alts after pruning (1 fresh and 5 done)

PrunedKeptTotal
New3581359
Fresh000
Picked033
Done123
Total3596365
Accuracy
100.0%
Counts
365 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.9%
(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
✓99.9%
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
✓51.9%
(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
▶51.9%
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x))
✓51.9%
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
✓48.5%
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
Compiler

Compiled 32 to 28 computations (12.5% saved)

simplify4.0ms (0.1%)

Memory
7.2MiB live, 7.2MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 #s(literal 1/6 binary64) x)
cost-diff0
(*.f64 (*.f64 #s(literal 1/6 binary64) x) x)
cost-diff0
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x))
Rules
20×lower-*.f32
16×lower-*.f64
10×lower-fma.f64
10×lower-fma.f32
8×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01427
01627
12125
22525
32723
43123
53623
03622
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x))
(*.f64 (*.f64 #s(literal 1/6 binary64) x) x)
(*.f64 #s(literal 1/6 binary64) x)
#s(literal 1/6 binary64)
x
Outputs
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x))
(*.f64 (*.f64 #s(literal 1/6 binary64) x) x)
(*.f64 #s(literal 1/6 binary64) x)
#s(literal 1/6 binary64)
x

localize46.0ms (1.2%)

Memory
-37.1MiB live, 55.3MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0.046875
(*.f64 (*.f64 #s(literal 1/6 binary64) x) x)
accuracy0.15625
(*.f64 #s(literal 1/6 binary64) x)
accuracy0.2929687500001692
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x))
Samples
18.0ms125×0invalid
13.0ms131×0valid
Compiler

Compiled 23 to 14 computations (39.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 25.0ms
ival-add: 9.0ms (36% of total)
ival-mult: 4.0ms (16% of total)
const: 3.0ms (12% of total)
ival-pow2: 3.0ms (12% of total)
ival-pow: 3.0ms (12% of total)
ival-div: 2.0ms (8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory
6.7MiB live, 6.7MiB allocated
Counts
3 → 36
Calls
Call 1
Inputs
#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) #<representation:binary64>) () ())
#s(alt (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) (patch (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) #<representation:binary64>) () ())
#s(alt (*.f64 #s(literal 1/6 binary64) x) (patch (*.f64 #s(literal 1/6 binary64) x) #<representation:binary64>) () ())
Outputs
#s(alt (* -3 (pow (sqrt 1/6) 2)) (taylor 0 x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) #<representation:binary64>) () ())) ())
#s(alt (+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2))) (taylor 0 x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) #<representation:binary64>) () ())) ())
#s(alt (+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2))) (taylor 0 x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) #<representation:binary64>) () ())) ())
#s(alt (+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2))) (taylor 0 x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor 0 x) (#s(alt (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) (patch (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor 0 x) (#s(alt (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) (patch (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor 0 x) (#s(alt (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) (patch (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor 0 x) (#s(alt (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) (patch (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/6 binary64) x) (patch (*.f64 #s(literal 1/6 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/6 binary64) x) (patch (*.f64 #s(literal 1/6 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/6 binary64) x) (patch (*.f64 #s(literal 1/6 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/6 binary64) x) (patch (*.f64 #s(literal 1/6 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (pow (sqrt 1/6) 2)) (taylor inf x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2))) (taylor inf x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2))) (taylor inf x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2))) (taylor inf x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor inf x) (#s(alt (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) (patch (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor inf x) (#s(alt (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) (patch (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor inf x) (#s(alt (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) (patch (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor inf x) (#s(alt (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) (patch (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor inf x) (#s(alt (*.f64 #s(literal 1/6 binary64) x) (patch (*.f64 #s(literal 1/6 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor inf x) (#s(alt (*.f64 #s(literal 1/6 binary64) x) (patch (*.f64 #s(literal 1/6 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor inf x) (#s(alt (*.f64 #s(literal 1/6 binary64) x) (patch (*.f64 #s(literal 1/6 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor inf x) (#s(alt (*.f64 #s(literal 1/6 binary64) x) (patch (*.f64 #s(literal 1/6 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (pow (sqrt 1/6) 2)) (taylor -inf x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2))) (taylor -inf x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2))) (taylor -inf x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2))) (taylor -inf x) (#s(alt #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) (patch #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) (patch (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) (patch (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) (patch (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) (patch (*.f64 (*.f64 #s(literal 1/6 binary64) x) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/6 binary64) x) (patch (*.f64 #s(literal 1/6 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/6 binary64) x) (patch (*.f64 #s(literal 1/6 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/6 binary64) x) (patch (*.f64 #s(literal 1/6 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/6 binary64) x) (patch (*.f64 #s(literal 1/6 binary64) x) #<representation:binary64>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
((pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (* (* 1/6 x) x) (* 1/6 x))
1.0ms
x
@inf
((pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (* (* 1/6 x) x) (* 1/6 x))
1.0ms
x
@0
((pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (* (* 1/6 x) x) (* 1/6 x))

simplify129.0ms (3.2%)

Memory
-9.7MiB live, 104.9MiB allocated
Algorithm
1×egg-herbie
Rules
3 880×lower-*.f64
3 880×lower-*.f32
2 620×lower-/.f32
2 620×lower-/.f64
2 186×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
016202
134170
293170
3235170
4587170
5852170
61131170
73531170
84413170
95634170
106064170
116096170
126142170
136999170
147336170
157552170
167795170
08036161
Stop Event
1×iter limit
1×node limit
Counts
36 → 36
Calls
Call 1
Inputs
(* -3 (pow (sqrt 1/6) 2))
(+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2)))
(+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2)))
(+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2)))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* (pow x 2) (pow (sqrt 1/6) 2))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* (pow x 2) (pow (sqrt 1/6) 2))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
Outputs
(* -3 (pow (sqrt 1/6) 2))
#s(literal -1/2 binary64)
(+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2)))
(*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))
(+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2)))
(*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))
(+ (* -3 (pow (sqrt 1/6) 2)) (* (pow x 2) (pow (sqrt 1/6) 2)))
(*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* (pow x 2) (pow (sqrt 1/6) 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* (pow x 2) (pow (sqrt 1/6) 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))
(* (pow x 2) (+ (* -3 (/ (pow (sqrt 1/6) 2) (pow x 2))) (pow (sqrt 1/6) 2)))
(*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))

rewrite145.0ms (3.7%)

Memory
46.6MiB live, 197.5MiB allocated
Rules
3 480×lower-/.f64
3 480×lower-/.f32
3 256×lower-fma.f64
3 256×lower-fma.f32
3 252×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01425
01623
16221
230021
3233721
0868420
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
3 → 7
Calls
Call 1
Inputs
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x))
(*.f64 (*.f64 #s(literal 1/6 binary64) x) x)
(*.f64 #s(literal 1/6 binary64) x)
Outputs
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x))
(*.f64 (*.f64 #s(literal 1/6 binary64) x) x)
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(*.f64 x (*.f64 #s(literal 1/6 binary64) x))
(*.f64 #s(literal 1/6 binary64) x)
(*.f64 x #s(literal 1/6 binary64))

eval19.0ms (0.5%)

Memory
-21.4MiB live, 26.0MiB allocated
Compiler

Compiled 287 to 26 computations (90.9% saved)

prune29.0ms (0.7%)

Memory
-19.8MiB live, 18.1MiB allocated
Pruning

6 alts after pruning (0 fresh and 6 done)

PrunedKeptTotal
New43043
Fresh000
Picked011
Done055
Total43649
Accuracy
100.0%
Counts
49 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.9%
(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
✓99.9%
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
✓51.9%
(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
✓51.9%
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x))
✓51.9%
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
✓48.5%
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
Compiler

Compiled 113 to 65 computations (42.5% saved)

regimes16.0ms (0.4%)

Memory
35.0MiB live, 35.0MiB allocated
Counts
12 → 1
Calls
Call 1
Inputs
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
#s(approx (/ (- (* x x) 3) 6) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64)) (*.f64 (fma.f64 x x #s(literal 3 binary64)) #s(literal 6 binary64)))
(pow.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
Outputs
(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
Calls

4 calls:

4.0ms
x
4.0ms
(*.f64 x x)
3.0ms
(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
3.0ms
(-.f64 (*.f64 x x) #s(literal 3 binary64))
Results
AccuracySegmentsBranch
99.9%1x
99.9%1(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
99.9%1(-.f64 (*.f64 x x) #s(literal 3 binary64))
99.9%1(*.f64 x x)
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes14.0ms (0.3%)

Memory
-11.6MiB live, 26.8MiB allocated
Counts
7 → 1
Calls
Call 1
Inputs
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
#s(approx (/ (- (* x x) 3) 6) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
Outputs
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
Calls

4 calls:

5.0ms
(*.f64 x x)
3.0ms
x
3.0ms
(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
2.0ms
(-.f64 (*.f64 x x) #s(literal 3 binary64))
Results
AccuracySegmentsBranch
99.9%1x
99.9%1(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
99.9%1(-.f64 (*.f64 x x) #s(literal 3 binary64))
99.9%1(*.f64 x x)
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes10.0ms (0.2%)

Memory
-17.7MiB live, 21.2MiB allocated
Counts
4 → 2
Calls
Call 1
Inputs
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
#s(approx (/ (- (* x x) 3) 6) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x))
Outputs
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x))
Calls

4 calls:

4.0ms
x
2.0ms
(*.f64 x x)
2.0ms
(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
2.0ms
(-.f64 (*.f64 x x) #s(literal 3 binary64))
Results
AccuracySegmentsBranch
98.7%2x
98.7%2(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
98.7%2(-.f64 (*.f64 x x) #s(literal 3 binary64))
98.7%2(*.f64 x x)
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes7.0ms (0.2%)

Memory
18.0MiB live, 18.0MiB allocated
Counts
3 → 2
Calls
Call 1
Inputs
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
#s(approx (/ (- (* x x) 3) 6) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
#s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
Outputs
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
#s(approx (/ (- (* x x) 3) 6) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
Calls

4 calls:

2.0ms
x
2.0ms
(*.f64 x x)
2.0ms
(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
1.0ms
(-.f64 (*.f64 x x) #s(literal 3 binary64))
Results
AccuracySegmentsBranch
98.6%2x
98.6%2(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
98.6%2(-.f64 (*.f64 x x) #s(literal 3 binary64))
98.6%2(*.f64 x x)
Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes5.0ms (0.1%)

Memory
12.6MiB live, 12.6MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
Outputs
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
Calls

4 calls:

1.0ms
x
1.0ms
(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
1.0ms
(*.f64 x x)
1.0ms
(-.f64 (*.f64 x x) #s(literal 3 binary64))
Results
AccuracySegmentsBranch
48.5%1x
48.5%1(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
48.5%1(-.f64 (*.f64 x x) #s(literal 3 binary64))
48.5%1(*.f64 x x)
Compiler

Compiled 16 to 13 computations (18.8% saved)

bsearch0.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.691708358352011
13803.147775425134
Compiler

Compiled 10 to 10 computations (0% saved)

bsearch11.0ms (0.3%)

Memory
-22.7MiB live, 21.4MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
10.0ms
0.691708358352011
13803.147775425134
Samples
4.0ms128×0valid
Compiler

Compiled 58 to 82 computations (-41.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 2.0ms
ival-sub: 1.0ms (56.3% of total)
ival-div: 1.0ms (56.3% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

simplify27.0ms (0.7%)

Memory
-15.7MiB live, 62.7MiB allocated
Algorithm
1×egg-herbie
Rules
6×*-commutative-binary64-*.f64
2×1-exp-binary32-exp.f32
2×1-exp-binary64-exp.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03081
13681
Stop Event
1×saturated
Calls
Call 1
Inputs
(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(if (<=.f64 (*.f64 x x) #s(literal 1 binary64)) #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)))
(if (<=.f64 (*.f64 x x) #s(literal 3 binary64)) #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) #s(approx (/ (- (* x x) 3) 6) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))))
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
Outputs
(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1/2 binary64))
(if (<=.f64 (*.f64 x x) #s(literal 1 binary64)) #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) #s(approx (pow (pow (/ 6 (+ (* x x) -3)) -1/2) 2) (*.f64 (*.f64 #s(literal 1/6 binary64) x) x)))
(if (<=.f64 (*.f64 x x) #s(literal 3 binary64)) #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) #s(approx (/ (- (* x x) 3) 6) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))))
(if (<=.f64 (*.f64 x x) #s(literal 3 binary64)) #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) #s(approx (/ (- (* x x) 3) 6) (*.f64 (*.f64 x x) #s(literal 1/6 binary64))))
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))

soundness979.0ms (24.6%)

Memory
26.1MiB live, 657.4MiB allocated
Rules
5 268×lower-fma.f64
5 268×lower-fma.f32
5 168×lower-/.f32
5 166×lower-/.f64
4 388×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0133874
1313858
2856858
32278841
46690840
08462770
02163
03256
114056
266756
3582556
0837356
02054
02752
111250
259849
3553549
0804047
019162
143162
298162
3236162
4759162
51590162
62334162
73514162
84236162
95345162
106402162
117126162
08039144
0615
0915
14215
223015
3183115
0868513
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
Compiler

Compiled 116 to 80 computations (31% saved)

preprocess70.0ms (1.7%)

Memory
6.9MiB live, 126.3MiB allocated
Remove

(abs x)

Compiler

Compiled 122 to 72 computations (41% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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