Numeric.Integration.TanhSinh:nonNegative from integration-0.2.1

Time bar (total: 5.2s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
50%50%50%0%0%0%0%2
75%75%25%0%0%0%0%3
87.5%87.5%12.5%0%0%0%0%4
93.8%93.7%6.2%0%0%0%0%5
96.9%96.8%3.1%0%0%0%0%6
98.4%98.4%1.6%0%0%0%0%7
99.2%99.2%0.8%0%0%0%0%8
99.6%99.6%0.4%0%0%0%0%9
99.8%99.8%0.2%0%0%0%0%10
99.9%99.9%0.1%0%0%0%0%11
100%99.9%0%0%0%0%0%12
Compiler

Compiled 7 to 6 computations (14.3% saved)

sample615.0ms (11.9%)

Memory
28.8MiB live, 752.7MiB allocated
Samples
351.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 124.0ms
ival-sub: 56.0ms (45% of total)
ival-div: 56.0ms (45% of total)
ival-true: 5.0ms (4% of total)
exact: 4.0ms (3.2% of total)
ival-assert: 3.0ms (2.4% of total)
Bogosity

explain44.0ms (0.9%)

Memory
-4.1MiB live, 79.4MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(/.f64 x (-.f64 #s(literal 1 binary64) x))
00-0-(-.f64 #s(literal 1 binary64) x)
00-0-#s(literal 1 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
19.0ms512×0valid
Compiler

Compiled 29 to 16 computations (44.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-sub: 6.0ms (60.6% of total)
ival-div: 3.0ms (30.3% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess21.0ms (0.4%)

Memory
1.8MiB live, 38.5MiB allocated
Algorithm
egg-herbie
Rules
44×associate-*l*
42×times-frac
36×lower-+.f64
36×lower-+.f32
34×unsub-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0615
12011
24710
310010
419510
528410
629510
730910
832210
045
065
1105
2145
3195
4265
5365
6515
7745
8965
91045
101065
01065
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))
Outputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))
Compiler

Compiled 5 to 4 computations (20% saved)

eval0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(/.f64 x (-.f64 #s(literal 1 binary64) x))
Compiler

Compiled 5 to 4 computations (20% saved)

simplify34.0ms (0.7%)

Memory
-28.5MiB live, 8.6MiB allocated
Algorithm
egg-herbie
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
cost-diff0
(-.f64 #s(literal 1 binary64) x)
cost-diff0
(/.f64 x (-.f64 #s(literal 1 binary64) x))
Rules
36×lower-+.f64
36×lower-+.f32
26×sub-neg
26×lower--.f32
24×lower--.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0410
0610
11010
21410
31910
42610
53610
65110
77410
89610
910410
1010610
010610
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))
x
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
Outputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))
x
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)

localize12.0ms (0.2%)

Memory
19.6MiB live, 19.6MiB allocated
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
accuracy0
(-.f64 #s(literal 1 binary64) x)
accuracy0.01171875
(/.f64 x (-.f64 #s(literal 1 binary64) x))
Samples
8.0ms256×0valid
Compiler

Compiled 12 to 6 computations (50% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-div: 2.0ms (59.6% of total)
ival-sub: 1.0ms (29.8% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series1.0ms (0%)

Memory
1.9MiB live, 1.9MiB allocated
Counts
2 → 24
Calls
Call 1
Inputs
#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation:binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation:binary64>) () ())
Outputs
#s(alt x (taylor 0 x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 x)))) (taylor 0 x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 (* x (+ 1 x)))))) (taylor 0 x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation:binary64>) () ())) ())
#s(alt -1 (taylor inf x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) (taylor inf x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation:binary64>) () ())) ())
#s(alt -1 (taylor -inf x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) (taylor -inf x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1) (taylor -inf x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation:binary64>) () ())) ())
Calls

3 calls:

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

simplify164.0ms (3.2%)

Memory
-24.2MiB live, 97.2MiB allocated
Algorithm
egg-herbie
Rules
4 624×lower-fma.f64
4 624×lower-fma.f32
1 546×unsub-neg
1 096×lower-*.f64
1 096×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033135
193120
2220114
3545112
41047112
51955112
63384112
74540112
84656112
94656112
104818112
114893112
124893112
04893109
Stop Event
iter limit
saturated
Counts
24 → 23
Calls
Call 1
Inputs
x
(* x (+ 1 x))
(* x (+ 1 (* x (+ 1 x))))
(* x (+ 1 (* x (+ 1 (* x (+ 1 x))))))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
Outputs
x
(* x (+ 1 x))
(fma.f64 x x x)
(* x (+ 1 (* x (+ 1 x))))
(fma.f64 (fma.f64 x x x) x x)
(* x (+ 1 (* x (+ 1 (* x (+ 1 x))))))
(*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) x) (-.f64 x #s(literal -1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
-1
#s(literal -1 binary64)
(* -1 (+ 1 (/ 1 x)))
(-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x))
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
(*.f64 (-.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(* -1 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
-1
#s(literal -1 binary64)
(* -1 (+ 1 (/ 1 x)))
(-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x))
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
(*.f64 (-.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)

rewrite222.0ms (4.3%)

Memory
-3.3MiB live, 278.5MiB allocated
Rules
3 858×lower-/.f32
3 856×lower-/.f64
3 778×lower-fma.f64
3 778×lower-fma.f32
2 920×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048
068
1298
21838
316128
093478
Stop Event
iter limit
node limit
iter limit
Counts
2 → 425
Calls
Call 1
Inputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
Outputs
(*.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (hypot.f64 (*.f64 x x) x)) #s(literal -1 binary64)) (pow.f64 (fma.f64 x x x) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (hypot.f64 (fma.f64 x x x) (pow.f64 x #s(literal 3/2 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x x))
(*.f64 (pow.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (fma.f64 (fma.f64 x x x) x x))
(*.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x x))) (-.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(*.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(*.f64 (*.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(*.f64 (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (+.f64 (pow.f64 (fma.f64 x x x) #s(literal 3 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 (fma.f64 x x x) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) x) #s(literal -1/2 binary64)))
(*.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))))
(*.f64 (*.f64 x (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x))) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))))
(*.f64 (*.f64 x (+.f64 (pow.f64 (fma.f64 x x x) #s(literal 3 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (fma.f64 x x x) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(*.f64 (fma.f64 (fma.f64 x x x) x x) (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(*.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 x x x))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 (fma.f64 x x x) x x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (fma.f64 (fma.f64 x x x) x x))
(*.f64 (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (neg.f64 x))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)
(*.f64 #s(literal -1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) x)))
(*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))
(*.f64 (fma.f64 x x x) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (neg.f64 x) (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)))
(*.f64 (neg.f64 x) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 x (fma.f64 x x #s(literal 1 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) x)))
(*.f64 x (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)))
(*.f64 x (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(pow.f64 (exp.f64 (-.f64 (log1p.f64 x) (log.f64 x))) #s(literal -1 binary64))
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(-.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -2 binary64)) (+.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))) (/.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))))
(-.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -3 binary64)) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (+.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))))))) (/.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (+.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))))))))
(-.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -3 binary64)) (+.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) #s(literal 2 binary64)) (*.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))))) (/.f64 (*.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -3 binary64))) (+.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) #s(literal 2 binary64)) (*.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))))))
(-.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
(-.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 x x #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 3 binary64))))) (/.f64 (pow.f64 x #s(literal 9 binary64)) (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 3 binary64))))))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (hypot.f64 (*.f64 x x) x) #s(literal 1 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (hypot.f64 (*.f64 x x) x) #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (*.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))) (-.f64 #s(literal -1 binary64) x))
(-.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (neg.f64 (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))) (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))))
(-.f64 (/.f64 (pow.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (neg.f64 (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))) (/.f64 (/.f64 (pow.f64 x #s(literal 9 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))))
(-.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(-.f64 (/.f64 (pow.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) (/.f64 (/.f64 (pow.f64 x #s(literal 9 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(-.f64 (/.f64 (pow.f64 (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) #s(literal -1 binary64)))
(-.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal -1 binary64) x)) (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal -1 binary64) x))
(-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (/.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal -1 binary64) x)) #s(literal -1 binary64)))
(-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))))
(-.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(-.f64 (neg.f64 x) #s(literal -1 binary64))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) x))
(-.f64 #s(literal 1 binary64) (neg.f64 x))
(-.f64 #s(literal 1 binary64) x)
(exp.f64 (neg.f64 (*.f64 (log1p.f64 x) #s(literal -1 binary64))))
(exp.f64 (*.f64 (*.f64 (log1p.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (neg.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x)))))
(+.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))))
(+.f64 (neg.f64 x) #s(literal 1 binary64))
(+.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) (neg.f64 x))
(+.f64 #s(literal 1 binary64) x)
(+.f64 x #s(literal 1 binary64))

eval190.0ms (3.7%)

Memory
17.2MiB live, 128.6MiB allocated
Compiler

Compiled 10 184 to 1 290 computations (87.3% saved)

prune8.0ms (0.2%)

Memory
28.5MiB live, 28.5MiB allocated
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New4444448
Fresh000
Picked011
Done000
Total4445449
Accuracy
100.0%
Counts
449 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
72.6%
(/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (*.f64 x x)))
100.0%
(/.f64 x (-.f64 #s(literal 1 binary64) x))
48.4%
#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
47.6%
#s(approx (/ x (- 1 x)) (fma.f64 x x x))
52.8%
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify882.0ms (17.1%)

Memory
-22.4MiB live, 221.0MiB allocated
Algorithm
egg-herbie
Localize:

Found 10 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 x x x)
cost-diff0
(neg.f64 (fma.f64 x x x))
cost-diff128
(+.f64 #s(literal -1 binary64) (*.f64 x x))
cost-diff704
(/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (*.f64 x x)))
cost-diff0
(fma.f64 x x x)
cost-diff0
(fma.f64 (fma.f64 x x x) x x)
cost-diff0
#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
cost-diff0
(fma.f64 x x x)
cost-diff0
#s(approx (/ x (- 1 x)) (fma.f64 x x x))
cost-diff0
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
Rules
20 294×lower-fma.f32
20 290×lower-fma.f64
2 986×lower-*.f32
2 984×lower-*.f64
1 588×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01478
02178
13978
28678
321372
450272
5170472
6600872
0806971
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (/ x (- 1 x)) (fma.f64 x x x))
(fma.f64 x x x)
x
#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
(fma.f64 (fma.f64 x x x) x x)
(fma.f64 x x x)
x
(/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (*.f64 x x)))
(neg.f64 (fma.f64 x x x))
(fma.f64 x x x)
x
(+.f64 #s(literal -1 binary64) (*.f64 x x))
#s(literal -1 binary64)
(*.f64 x x)
Outputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (/ x (- 1 x)) (fma.f64 x x x))
(fma.f64 x x x)
x
#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
(fma.f64 (fma.f64 x x x) x x)
(fma.f64 x x x)
x
(/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (*.f64 x x)))
(/.f64 x (-.f64 #s(literal 1 binary64) x))
(neg.f64 (fma.f64 x x x))
(*.f64 (-.f64 #s(literal -1 binary64) x) x)
(fma.f64 x x x)
x
(+.f64 #s(literal -1 binary64) (*.f64 x x))
(fma.f64 x x #s(literal -1 binary64))
#s(literal -1 binary64)
(*.f64 x x)

localize210.0ms (4.1%)

Memory
16.4MiB live, 55.7MiB allocated
Localize:

Found 10 expressions of interest:

NewMetricScoreProgram
accuracy0
(+.f64 #s(literal -1 binary64) (*.f64 x x))
accuracy0
(*.f64 x x)
accuracy0
(neg.f64 (fma.f64 x x x))
accuracy17.405851766180156
(/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (*.f64 x x)))
accuracy0
(fma.f64 x x x)
accuracy0.05078125
(fma.f64 (fma.f64 x x x) x x)
accuracy32.99373111196749
#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
accuracy0
(fma.f64 x x x)
accuracy33.52754776234219
#s(approx (/ x (- 1 x)) (fma.f64 x x x))
accuracy30.208077028476232
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
Samples
200.0ms256×0valid
Compiler

Compiled 72 to 14 computations (80.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 192.0ms
ival-sub: 181.0ms (94.2% of total)
ival-div: 3.0ms (1.6% of total)
ival-add: 3.0ms (1.6% of total)
ival-mult: 3.0ms (1.6% of total)
ival-neg: 1.0ms (0.5% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series42.0ms (0.8%)

Memory
-25.8MiB live, 12.3MiB allocated
Counts
9 → 108
Calls
Call 1
Inputs
#s(alt #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) (patch #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #<representation:binary64>) () ())
#s(alt #s(approx (/ x (- 1 x)) (fma.f64 x x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 x x x)) #<representation:binary64>) () ())
#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation:binary64>) () ())
#s(alt #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) #<representation:binary64>) () ())
#s(alt (fma.f64 (fma.f64 x x x) x x) (patch (fma.f64 (fma.f64 x x x) x x) #<representation:binary64>) () ())
#s(alt (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (*.f64 x x))) (patch (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (*.f64 x x))) #<representation:binary64>) () ())
#s(alt (+.f64 #s(literal -1 binary64) (*.f64 x x)) (patch (+.f64 #s(literal -1 binary64) (*.f64 x x)) #<representation:binary64>) () ())
#s(alt (neg.f64 (fma.f64 x x x)) (patch (neg.f64 (fma.f64 x x x)) #<representation:binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())
Outputs
#s(alt x (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) (patch #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) (patch #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 x)))) (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) (patch #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 (* x (+ 1 x)))))) (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) (patch #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #<representation:binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 x x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 x x x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 x x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 x x x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 x)))) (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 x x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 x x x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 (* x (+ 1 x)))))) (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 x x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 x x x)) #<representation:binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation:binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 x)))) (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 (* x (+ 1 x)))))) (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) #<representation:binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (fma.f64 (fma.f64 x x x) x x) (patch (fma.f64 (fma.f64 x x x) x x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 x x x) x x) (patch (fma.f64 (fma.f64 x x x) x x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 x)))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 x x x) x x) (patch (fma.f64 (fma.f64 x x x) x x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 x)))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 x x x) x x) (patch (fma.f64 (fma.f64 x x x) x x) #<representation:binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (*.f64 x x))) (patch (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (*.f64 x x))) (patch (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
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#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>) () ())) ())
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#s(alt (- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1) (taylor -inf x) (#s(alt #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) (patch #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #<representation:binary64>) () ())) ())
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#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (neg.f64 (fma.f64 x x x)) (patch (neg.f64 (fma.f64 x x x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (pow x 2) (+ 1 (/ 1 x)))) (taylor -inf x) (#s(alt (neg.f64 (fma.f64 x x x)) (patch (neg.f64 (fma.f64 x x x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (pow x 2) (+ 1 (/ 1 x)))) (taylor -inf x) (#s(alt (neg.f64 (fma.f64 x x x)) (patch (neg.f64 (fma.f64 x x x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (pow x 2) (+ 1 (/ 1 x)))) (taylor -inf x) (#s(alt (neg.f64 (fma.f64 x x x)) (patch (neg.f64 (fma.f64 x 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>) () ())) ())
Calls

3 calls:

TimeVariablePointExpression
38.0ms
x
@-inf
((/ x (- 1 x)) (/ x (- 1 x)) (+ (* x x) x) (/ x (- 1 x)) (+ (* (+ (* x x) x) x) x) (/ (neg (+ (* x x) x)) (+ -1 (* x x))) (+ -1 (* x x)) (neg (+ (* x x) x)) (* x x))
1.0ms
x
@inf
((/ x (- 1 x)) (/ x (- 1 x)) (+ (* x x) x) (/ x (- 1 x)) (+ (* (+ (* x x) x) x) x) (/ (neg (+ (* x x) x)) (+ -1 (* x x))) (+ -1 (* x x)) (neg (+ (* x x) x)) (* x x))
1.0ms
x
@0
((/ x (- 1 x)) (/ x (- 1 x)) (+ (* x x) x) (/ x (- 1 x)) (+ (* (+ (* x x) x) x) x) (/ (neg (+ (* x x) x)) (+ -1 (* x x))) (+ -1 (* x x)) (neg (+ (* x x) x)) (* x x))

simplify295.0ms (5.7%)

Memory
28.9MiB live, 145.3MiB allocated
Algorithm
egg-herbie
Rules
12 030×lower-fma.f64
12 030×lower-fma.f32
2 958×lower-*.f64
2 958×lower-*.f32
1 532×unsub-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
041664
1129640
2366603
31145595
42989595
56208595
08133542
Stop Event
iter limit
node limit
Counts
108 → 102
Calls
Call 1
Inputs
x
(* x (+ 1 x))
(* x (+ 1 (* x (+ 1 x))))
(* x (+ 1 (* x (+ 1 (* x (+ 1 x))))))
x
(* x (+ 1 x))
(* x (+ 1 (* x (+ 1 x))))
(* x (+ 1 (* x (+ 1 (* x (+ 1 x))))))
x
(* x (+ 1 x))
(* x (+ 1 x))
(* x (+ 1 x))
x
(* x (+ 1 x))
(* x (+ 1 (* x (+ 1 x))))
(* x (+ 1 (* x (+ 1 (* x (+ 1 x))))))
x
(* x (+ 1 x))
(* x (+ 1 (* x (+ 1 x))))
(* x (+ 1 (* x (+ 1 x))))
x
(* x (+ 1 x))
(* x (+ 1 (* x (+ 1 x))))
(* x (+ 1 (* x (+ 1 (* x (+ 1 x))))))
-1
(- (pow x 2) 1)
(- (pow x 2) 1)
(- (pow x 2) 1)
(* -1 x)
(* x (- (* -1 x) 1))
(* x (- (* -1 x) 1))
(* x (- (* -1 x) 1))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))))
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* -1 (pow x 2))
(* -1 (* (pow x 2) (+ 1 (/ 1 x))))
(* -1 (* (pow x 2) (+ 1 (/ 1 x))))
(* -1 (* (pow x 2) (+ 1 (/ 1 x))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 x)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)))
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* -1 (pow x 2))
(* -1 (* (pow x 2) (+ 1 (/ 1 x))))
(* -1 (* (pow x 2) (+ 1 (/ 1 x))))
(* -1 (* (pow x 2) (+ 1 (/ 1 x))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
Outputs
x
(* x (+ 1 x))
(fma.f64 x x x)
(* x (+ 1 (* x (+ 1 x))))
(fma.f64 (fma.f64 x x x) x x)
(* x (+ 1 (* x (+ 1 (* x (+ 1 x))))))
(*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) x) (-.f64 x #s(literal -1 binary64)))
x
(* x (+ 1 x))
(fma.f64 x x x)
(* x (+ 1 (* x (+ 1 x))))
(fma.f64 (fma.f64 x x x) x x)
(* x (+ 1 (* x (+ 1 (* x (+ 1 x))))))
(*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) x) (-.f64 x #s(literal -1 binary64)))
x
(* x (+ 1 x))
(fma.f64 x x x)
(* x (+ 1 x))
(fma.f64 x x x)
(* x (+ 1 x))
(fma.f64 x x x)
x
(* x (+ 1 x))
(fma.f64 x x x)
(* x (+ 1 (* x (+ 1 x))))
(fma.f64 (fma.f64 x x x) x x)
(* x (+ 1 (* x (+ 1 (* x (+ 1 x))))))
(*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) x) (-.f64 x #s(literal -1 binary64)))
x
(* x (+ 1 x))
(fma.f64 x x x)
(* x (+ 1 (* x (+ 1 x))))
(fma.f64 (fma.f64 x x x) x x)
(* x (+ 1 (* x (+ 1 x))))
(fma.f64 (fma.f64 x x x) x x)
x
(* x (+ 1 x))
(fma.f64 x x x)
(* x (+ 1 (* x (+ 1 x))))
(fma.f64 (fma.f64 x x x) x x)
(* x (+ 1 (* x (+ 1 (* x (+ 1 x))))))
(*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) x) (-.f64 x #s(literal -1 binary64)))
-1
#s(literal -1 binary64)
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(* -1 x)
(neg.f64 x)
(* x (- (* -1 x) 1))
(*.f64 (-.f64 #s(literal -1 binary64) x) x)
(* x (- (* -1 x) 1))
(*.f64 (-.f64 #s(literal -1 binary64) x) x)
(* x (- (* -1 x) 1))
(*.f64 (-.f64 #s(literal -1 binary64) 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)
-1
#s(literal -1 binary64)
(* -1 (+ 1 (/ 1 x)))
(/.f64 (-.f64 #s(literal -1 binary64) x) x)
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) x) x))
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
(-.f64 (/.f64 (fma.f64 (-.f64 #s(literal -1 binary64) x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(* -1 (+ 1 (/ 1 x)))
(/.f64 (-.f64 #s(literal -1 binary64) x) x)
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) x) x))
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
(-.f64 (/.f64 (fma.f64 (-.f64 #s(literal -1 binary64) x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(fma.f64 x x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(fma.f64 x x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(fma.f64 x x x)
-1
#s(literal -1 binary64)
(* -1 (+ 1 (/ 1 x)))
(/.f64 (-.f64 #s(literal -1 binary64) x) x)
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) x) x))
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
(-.f64 (/.f64 (fma.f64 (-.f64 #s(literal -1 binary64) x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(* (pow x 3) (+ 1 (/ 1 x)))
(*.f64 (fma.f64 x x x) x)
(* (pow x 3) (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 x x x) x x)
(* (pow x 3) (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 x x x) x x)
-1
#s(literal -1 binary64)
(* -1 (+ 1 (/ 1 x)))
(/.f64 (-.f64 #s(literal -1 binary64) x) x)
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) x) x))
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
(-.f64 (/.f64 (fma.f64 (-.f64 #s(literal -1 binary64) x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (* (pow x 2) (+ 1 (/ 1 x))))
(*.f64 (-.f64 #s(literal -1 binary64) x) x)
(* -1 (* (pow x 2) (+ 1 (/ 1 x))))
(*.f64 (-.f64 #s(literal -1 binary64) x) x)
(* -1 (* (pow x 2) (+ 1 (/ 1 x))))
(*.f64 (-.f64 #s(literal -1 binary64) 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)
-1
#s(literal -1 binary64)
(* -1 (+ 1 (/ 1 x)))
(/.f64 (-.f64 #s(literal -1 binary64) x) x)
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) x) x))
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
(-.f64 (/.f64 (fma.f64 (-.f64 #s(literal -1 binary64) x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(* -1 (+ 1 (/ 1 x)))
(/.f64 (-.f64 #s(literal -1 binary64) x) x)
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) x) x))
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
(-.f64 (/.f64 (fma.f64 (-.f64 #s(literal -1 binary64) x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(fma.f64 x x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(fma.f64 x x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(fma.f64 x x x)
-1
#s(literal -1 binary64)
(* -1 (+ 1 (/ 1 x)))
(/.f64 (-.f64 #s(literal -1 binary64) x) x)
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) x) x))
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
(-.f64 (/.f64 (fma.f64 (-.f64 #s(literal -1 binary64) x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(* (pow x 3) (+ 1 (/ 1 x)))
(*.f64 (fma.f64 x x x) x)
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)))
(fma.f64 (fma.f64 x x x) x x)
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)))
(fma.f64 (fma.f64 x x x) x x)
-1
#s(literal -1 binary64)
(* -1 (+ 1 (/ 1 x)))
(/.f64 (-.f64 #s(literal -1 binary64) x) x)
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) x) x))
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
(-.f64 (/.f64 (fma.f64 (-.f64 #s(literal -1 binary64) x) x #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* -1 (* (pow x 2) (+ 1 (/ 1 x))))
(*.f64 (-.f64 #s(literal -1 binary64) x) x)
(* -1 (* (pow x 2) (+ 1 (/ 1 x))))
(*.f64 (-.f64 #s(literal -1 binary64) x) x)
(* -1 (* (pow x 2) (+ 1 (/ 1 x))))
(*.f64 (-.f64 #s(literal -1 binary64) 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)

rewrite413.0ms (8%)

Memory
-15.8MiB live, 387.2MiB allocated
Rules
7 442×lower-fma.f32
7 438×lower-fma.f64
4 732×lower-*.f32
4 730×lower-*.f64
4 166×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01465
02165
19659
270259
0832058
Stop Event
iter limit
node limit
iter limit
Counts
9 → 799
Calls
Call 1
Inputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) (fma.f64 x x x))
(fma.f64 x x x)
#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
(fma.f64 (fma.f64 x x x) x x)
(/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (*.f64 x x)))
(+.f64 #s(literal -1 binary64) (*.f64 x x))
(neg.f64 (fma.f64 x x x))
(*.f64 x x)
Outputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) (fma.f64 x x x))
(*.f64 (/.f64 (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64)))) (*.f64 x (fma.f64 (fma.f64 x x x) x x)))
(*.f64 (/.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (hypot.f64 (pow.f64 (neg.f64 x) #s(literal 3/2 binary64)) x) #s(literal 2 binary64)))) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) (pow.f64 x #s(literal 3 binary64))))
(*.f64 (/.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (hypot.f64 (pow.f64 (neg.f64 x) #s(literal 3/2 binary64)) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (hypot.f64 (pow.f64 (neg.f64 x) #s(literal 3/2 binary64)) x) (-.f64 (hypot.f64 (pow.f64 (neg.f64 x) #s(literal 3/2 binary64)) x) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(*.f64 (/.f64 (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal 4 binary64))) (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x x))
(*.f64 (*.f64 #s(literal 1 binary64) (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (-.f64 (hypot.f64 (*.f64 x x) x) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) x)
(*.f64 (*.f64 x (-.f64 x (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) x))))
(*.f64 (pow.f64 (fma.f64 x x (neg.f64 x)) #s(literal -1 binary64)) (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal 4 binary64))))
(*.f64 (pow.f64 (-.f64 (hypot.f64 (*.f64 x x) x) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x x)))
(*.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (hypot.f64 (*.f64 x x) x) (pow.f64 x #s(literal 3 binary64))))))
(*.f64 (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64)) (neg.f64 x))
(*.f64 (+.f64 #s(literal 1 binary64) x) x)
(*.f64 (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal 4 binary64))) (*.f64 (pow.f64 (fma.f64 x x (neg.f64 x)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 x x (neg.f64 x)) #s(literal -1 binary64)))
(*.f64 (-.f64 (hypot.f64 (*.f64 x x) x) (pow.f64 x #s(literal 3 binary64))) (*.f64 (fma.f64 x x x) (pow.f64 (-.f64 (hypot.f64 (*.f64 x x) x) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64))))
(*.f64 (-.f64 (hypot.f64 (*.f64 x x) x) (pow.f64 x #s(literal 3 binary64))) (/.f64 (fma.f64 x x x) (-.f64 (hypot.f64 (*.f64 x x) x) (pow.f64 x #s(literal 3 binary64)))))
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (*.f64 (pow.f64 (-.f64 (hypot.f64 (*.f64 x x) x) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (-.f64 (hypot.f64 (*.f64 x x) x) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)))
(*.f64 (neg.f64 x) (-.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (*.f64 x (-.f64 #s(literal -1 binary64) x)) #s(literal -1 binary64))
(*.f64 (fma.f64 x x x) (*.f64 (fma.f64 x x (neg.f64 x)) (pow.f64 (fma.f64 x x (neg.f64 x)) #s(literal -1 binary64))))
(*.f64 (fma.f64 x x x) (/.f64 (fma.f64 x x (neg.f64 x)) (fma.f64 x x (neg.f64 x))))
(*.f64 (fma.f64 x x x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 #s(literal -1 binary64) x)))
(*.f64 #s(literal 1 binary64) (fma.f64 x x x))
(*.f64 x (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x x)) #s(literal -1 binary64))
(/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal 1 binary64)))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 x x (neg.f64 x)) #s(literal -1 binary64))) (hypot.f64 (*.f64 x x) x))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 x x (neg.f64 x)) #s(literal -1 binary64))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 8 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (-.f64 (hypot.f64 (*.f64 x x) x) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 18 binary64)) (pow.f64 x #s(literal 9 binary64))) (pow.f64 (-.f64 (hypot.f64 (*.f64 x x) x) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64))) (-.f64 (hypot.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 x #s(literal 9 binary64))))
(/.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (-.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (neg.f64 x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (neg.f64 x)))) (*.f64 (*.f64 x (/.f64 x (fma.f64 x x (neg.f64 x)))) (*.f64 x (/.f64 x (fma.f64 x x (neg.f64 x)))))) (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (neg.f64 x))) (*.f64 x (/.f64 x (fma.f64 x x (neg.f64 x))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (neg.f64 x))) #s(literal 3 binary64)) (pow.f64 (*.f64 x (/.f64 x (fma.f64 x x (neg.f64 x)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (neg.f64 x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (neg.f64 x))) (fma.f64 (*.f64 x (/.f64 x (fma.f64 x x (neg.f64 x)))) (*.f64 x (/.f64 x (fma.f64 x x (neg.f64 x)))) (*.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (neg.f64 x))) (*.f64 x (/.f64 x (fma.f64 x x (neg.f64 x))))))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 x (-.f64 #s(literal -1 binary64) x)) #s(literal 3 binary64))) (pow.f64 (fma.f64 x x x) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (neg.f64 x) #s(literal 3 binary64))) (-.f64 (hypot.f64 (*.f64 x x) x) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (fma.f64 x x x) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (fma.f64 x x x) #s(literal 2 binary64)) #s(literal 0 binary64))))
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(fma.f64 (/.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (hypot.f64 (pow.f64 (neg.f64 x) #s(literal 3/2 binary64)) x) #s(literal 2 binary64)))) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) (pow.f64 x #s(literal 3 binary64))) #s(literal 0 binary64))
(fma.f64 (/.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (+.f64 (pow.f64 (hypot.f64 (pow.f64 (neg.f64 x) #s(literal 3/2 binary64)) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (hypot.f64 (pow.f64 (neg.f64 x) #s(literal 3/2 binary64)) x) (-.f64 (hypot.f64 (pow.f64 (neg.f64 x) #s(literal 3/2 binary64)) x) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))) #s(literal 0 binary64))
(fma.f64 (*.f64 (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64)) #s(literal 1 binary64)) x #s(literal 0 binary64))
(fma.f64 (neg.f64 (pow.f64 (fma.f64 x x x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x x)) #s(literal 0 binary64))
(fma.f64 (neg.f64 (pow.f64 (fma.f64 x x x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x x) #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64) (*.f64 x x)) (pow.f64 (fma.f64 x x (neg.f64 x)) #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (-.f64 (hypot.f64 (*.f64 x x) x) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64)) x #s(literal 0 binary64))
(fma.f64 (*.f64 (neg.f64 x) x) #s(literal 1 binary64) (neg.f64 x))
(fma.f64 (+.f64 #s(literal 1 binary64) x) (neg.f64 x) #s(literal 0 binary64))
(fma.f64 (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal 4 binary64))) (*.f64 (pow.f64 (fma.f64 x x (neg.f64 x)) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal 4 binary64))) (neg.f64 (pow.f64 (fma.f64 x x (neg.f64 x)) #s(literal -1 binary64))) #s(literal 0 binary64))
(fma.f64 (fma.f64 (neg.f64 x) x (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x x)) #s(literal 0 binary64))
(fma.f64 (-.f64 (hypot.f64 (*.f64 x x) x) (pow.f64 x #s(literal 3 binary64))) (/.f64 (fma.f64 x x x) (neg.f64 (-.f64 (hypot.f64 (*.f64 x x) x) (pow.f64 x #s(literal 3 binary64))))) #s(literal 0 binary64))
(fma.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (*.f64 (pow.f64 (-.f64 (hypot.f64 (*.f64 x x) x) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (pow.f64 (-.f64 (hypot.f64 (*.f64 x x) x) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64))) #s(literal 0 binary64))
(fma.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (hypot.f64 (*.f64 x x) x) (pow.f64 x #s(literal 3 binary64))))) #s(literal 0 binary64))
(fma.f64 (neg.f64 x) (+.f64 #s(literal 1 binary64) x) #s(literal 0 binary64))
(fma.f64 (neg.f64 x) #s(literal 1 binary64) (*.f64 (neg.f64 x) x))
(fma.f64 (neg.f64 x) x (neg.f64 x))
(fma.f64 (*.f64 x x) #s(literal -1 binary64) (neg.f64 x))
(fma.f64 (*.f64 x (-.f64 #s(literal -1 binary64) x)) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (fma.f64 x x x) (/.f64 (fma.f64 x x (neg.f64 x)) (fma.f64 (neg.f64 x) x x)) #s(literal 0 binary64))
(fma.f64 (fma.f64 x x x) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 x x) (neg.f64 x))
(fma.f64 #s(literal -1 binary64) (fma.f64 x x x) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) x (*.f64 (neg.f64 x) x))
(fma.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x) (neg.f64 x))
(fma.f64 #s(literal 1 binary64) (neg.f64 x) (*.f64 (neg.f64 x) x))
(fma.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal -1 binary64) x)) #s(literal 0 binary64))
(fma.f64 x (-.f64 #s(literal -1 binary64) x) #s(literal 0 binary64))
(fma.f64 x (-.f64 (neg.f64 x) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 x (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 x (neg.f64 x) (neg.f64 x))
(fma.f64 x #s(literal -1 binary64) (*.f64 (neg.f64 x) x))
(-.f64 (fma.f64 (neg.f64 x) x #s(literal 0 binary64)) x)
(-.f64 (fma.f64 #s(literal -1 binary64) x #s(literal 0 binary64)) (*.f64 x x))
(-.f64 (/.f64 #s(literal 0 binary64) (pow.f64 (fma.f64 x x x) #s(literal 2 binary64))) (/.f64 (pow.f64 (fma.f64 x x x) #s(literal 3 binary64)) (pow.f64 (fma.f64 x x x) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x x)) (/.f64 (*.f64 x x) (fma.f64 (neg.f64 x) x x)))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 x x x)) (/.f64 (pow.f64 (fma.f64 x x x) #s(literal 2 binary64)) (fma.f64 x x x)))
(-.f64 (*.f64 (neg.f64 x) x) x)
(-.f64 (neg.f64 x) (*.f64 x x))
(-.f64 #s(literal 0 binary64) (fma.f64 x x x))
(+.f64 (-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (neg.f64 x)))) (*.f64 x (/.f64 x (fma.f64 x x (neg.f64 x)))))
(+.f64 (*.f64 (neg.f64 x) x) (neg.f64 x))
(+.f64 (neg.f64 x) (*.f64 (neg.f64 x) x))
(+.f64 #s(literal 0 binary64) (*.f64 x (-.f64 #s(literal -1 binary64) x)))
(+.f64 (*.f64 x (-.f64 #s(literal -1 binary64) x)) #s(literal 0 binary64))
(*.f64 (*.f64 (neg.f64 x) #s(literal -1 binary64)) x)
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (*.f64 (neg.f64 x) x) #s(literal -1 binary64))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) x))
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 x) x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval165.0ms (3.2%)

Memory
23.6MiB live, 374.6MiB allocated
Compiler

Compiled 23 393 to 2 694 computations (88.5% saved)

prune70.0ms (1.4%)

Memory
2.1MiB live, 80.6MiB allocated
Pruning

6 alts after pruning (2 fresh and 4 done)

PrunedKeptTotal
New1 23521 237
Fresh000
Picked134
Done011
Total1 23661 242
Accuracy
100.0%
Counts
1 242 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
72.6%
(/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
100.0%
(/.f64 x (-.f64 #s(literal 1 binary64) x))
48.4%
#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
47.6%
#s(approx (/ x (- 1 x)) (fma.f64 x x x))
3.4%
#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))
52.8%
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
Compiler

Compiled 35 to 24 computations (31.4% saved)

simplify223.0ms (4.3%)

Memory
-31.2MiB live, 206.6MiB allocated
Algorithm
egg-herbie
Localize:

Found 7 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x x)
cost-diff0
(-.f64 #s(literal 1 binary64) (*.f64 x x))
cost-diff0
(fma.f64 x x x)
cost-diff704
(/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
cost-diff0
(*.f64 x x)
cost-diff0
#s(approx (+ (* x x) x) (*.f64 x x))
cost-diff0
#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))
Rules
17 388×lower-fma.f32
17 386×lower-fma.f64
2 408×lower-*.f32
2 406×lower-*.f64
1 854×lower--.f32
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
01250
01650
12750
23950
35850
48450
515450
639345
7150445
8340645
9679345
0806845
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))
#s(approx (+ (* x x) x) (*.f64 x x))
(*.f64 x x)
x
(/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(fma.f64 x x x)
x
(-.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)
Outputs
#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))
#s(approx (+ (* x x) x) (*.f64 x x))
(*.f64 x x)
x
(/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 x (-.f64 #s(literal 1 binary64) x))
(fma.f64 x x x)
x
(-.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)

localize22.0ms (0.4%)

Memory
36.3MiB live, 36.3MiB allocated
Localize:

Found 7 expressions of interest:

NewMetricScoreProgram
accuracy0
(fma.f64 x x x)
accuracy0
(-.f64 #s(literal 1 binary64) (*.f64 x x))
accuracy0
(*.f64 x x)
accuracy17.405851766180156
(/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
accuracy0
(*.f64 x x)
accuracy29.47571049562406
#s(approx (+ (* x x) x) (*.f64 x x))
accuracy33.52754776234219
#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))
Samples
15.0ms256×0valid
Compiler

Compiled 42 to 10 computations (76.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
ival-sub: 3.0ms (34.2% of total)
ival-div: 3.0ms (34.2% of total)
ival-mult: 2.0ms (22.8% of total)
ival-add: 1.0ms (11.4% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series7.0ms (0.1%)

Memory
-31.8MiB live, 5.0MiB allocated
Counts
6 → 72
Calls
Call 1
Inputs
#s(alt #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) (patch #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) #<representation:binary64>) () ())
#s(alt #s(approx (+ (* x x) x) (*.f64 x x)) (patch #s(approx (+ (* x x) x) (*.f64 x x)) #<representation:binary64>) () ())
#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation:binary64>) () ())
#s(alt (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation:binary64>) () ())
#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation:binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (*.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (*.f64 x x)) #<representation:binary64>) () ())
Outputs
#s(alt x (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) (patch #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) (patch #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 x)))) (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) (patch #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 (* x (+ 1 x)))))) (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) (patch #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt #s(approx (+ (* x x) x) (*.f64 x x)) (patch #s(approx (+ (* x x) x) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt #s(approx (+ (* x x) x) (*.f64 x x)) (patch #s(approx (+ (* x x) x) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt #s(approx (+ (* x x) x) (*.f64 x x)) (patch #s(approx (+ (* x x) x) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt #s(approx (+ (* x x) x) (*.f64 x x)) (patch #s(approx (+ (* x x) x) (*.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 x (taylor 0 x) (#s(alt (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 x)))) (taylor 0 x) (#s(alt (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 (* x (+ 1 x)))))) (taylor 0 x) (#s(alt (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation:binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (*.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (*.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (*.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (*.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt -1 (taylor inf x) (#s(alt #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) (patch #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (+ 1 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) (patch #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) (taylor inf x) (#s(alt #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) (patch #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) (patch #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt #s(approx (+ (* x x) x) (*.f64 x x)) (patch #s(approx (+ (* x x) x) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (+ (* x x) x) (*.f64 x x)) (patch #s(approx (+ (* x x) x) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (+ (* x x) x) (*.f64 x x)) (patch #s(approx (+ (* x x) x) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (+ (* x x) x) (*.f64 x x)) (patch #s(approx (+ (* x x) x) (*.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 (taylor inf x) (#s(alt (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) (taylor inf x) (#s(alt (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (*.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (*.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (*.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (*.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt -1 (taylor -inf x) (#s(alt #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) (patch #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) (patch #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) (taylor -inf x) (#s(alt #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) (patch #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1) (taylor -inf x) (#s(alt #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) (patch #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (+ (* x x) x) (*.f64 x x)) (patch #s(approx (+ (* x x) x) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) x) (*.f64 x x)) (patch #s(approx (+ (* x x) x) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) x) (*.f64 x x)) (patch #s(approx (+ (* x x) x) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt #s(approx (+ (* x x) x) (*.f64 x x)) (patch #s(approx (+ (* x x) x) (*.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 (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation:binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (*.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (*.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (*.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (*.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (*.f64 x x)) #<representation:binary64>) () ())) ())
Calls

3 calls:

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

simplify210.0ms (4.1%)

Memory
19.6MiB live, 277.7MiB allocated
Algorithm
egg-herbie
Rules
15 050×lower-fma.f64
15 050×lower-fma.f32
3 720×lower-*.f64
3 720×lower-*.f32
2 042×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
031391
192370
2220358
3532354
41394354
54307354
67825354
08157326
Stop Event
iter limit
node limit
Counts
72 → 68
Calls
Call 1
Inputs
x
(* x (+ 1 x))
(* x (+ 1 (* x (+ 1 x))))
(* x (+ 1 (* x (+ 1 (* x (+ 1 x))))))
x
(* x (+ 1 x))
(* x (+ 1 x))
(* x (+ 1 x))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
x
(* x (+ 1 x))
(* x (+ 1 (* x (+ 1 x))))
(* x (+ 1 (* x (+ 1 (* x (+ 1 x))))))
x
(* x (+ 1 x))
(* x (+ 1 x))
(* x (+ 1 x))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
Outputs
x
(* x (+ 1 x))
(fma.f64 x x x)
(* x (+ 1 (* x (+ 1 x))))
(fma.f64 (fma.f64 x x x) x x)
(* x (+ 1 (* x (+ 1 (* x (+ 1 x))))))
(*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) x) (-.f64 x #s(literal -1 binary64)))
x
(* x (+ 1 x))
(fma.f64 x x x)
(* x (+ 1 x))
(fma.f64 x x x)
(* x (+ 1 x))
(fma.f64 x 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)
x
(* x (+ 1 x))
(fma.f64 x x x)
(* x (+ 1 (* x (+ 1 x))))
(fma.f64 (fma.f64 x x x) x x)
(* x (+ 1 (* x (+ 1 (* x (+ 1 x))))))
(*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) x) (-.f64 x #s(literal -1 binary64)))
x
(* x (+ 1 x))
(fma.f64 x x x)
(* x (+ 1 x))
(fma.f64 x x x)
(* x (+ 1 x))
(fma.f64 x x x)
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
-1
#s(literal -1 binary64)
(* -1 (+ 1 (/ 1 x)))
(-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) x) x))
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
(*.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(fma.f64 x x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(fma.f64 x x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(fma.f64 x 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)
-1
#s(literal -1 binary64)
(* -1 (+ 1 (/ 1 x)))
(-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) x) x))
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
(*.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(fma.f64 x x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(fma.f64 x x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(fma.f64 x x x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
-1
#s(literal -1 binary64)
(* -1 (+ 1 (/ 1 x)))
(-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) x) x))
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
(*.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(fma.f64 x x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(fma.f64 x x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(fma.f64 x 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)
-1
#s(literal -1 binary64)
(* -1 (+ 1 (/ 1 x)))
(-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) x) x))
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
(*.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(fma.f64 x x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(fma.f64 x x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(fma.f64 x x x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))

rewrite155.0ms (3%)

Memory
-12.6MiB live, 247.6MiB allocated
Rules
5 108×lower-fma.f32
5 106×lower-fma.f64
2 844×lower-*.f32
2 842×lower-*.f64
2 362×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01244
01644
17139
250939
3581939
0950038
Stop Event
iter limit
node limit
iter limit
Counts
6 → 581
Calls
Call 1
Inputs
#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))
#s(approx (+ (* x x) x) (*.f64 x x))
(*.f64 x x)
(/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(fma.f64 x x x)
(-.f64 #s(literal 1 binary64) (*.f64 x x))
Outputs
#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))
#s(approx (+ (* x x) x) (*.f64 x x))
(*.f64 (*.f64 (neg.f64 x) #s(literal -1 binary64)) x)
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 x) x))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1 binary64) (*.f64 (log.f64 x) #s(literal 1 binary64))))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 x))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.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 (*.f64 (fma.f64 x x x) (/.f64 x (-.f64 #s(literal 1 binary64) x))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64)))) (hypot.f64 (fma.f64 x x x) (pow.f64 x #s(literal 3/2 binary64))))
(*.f64 (/.f64 (*.f64 (fma.f64 x x x) (/.f64 x (-.f64 #s(literal 1 binary64) x))) (hypot.f64 (*.f64 x x) x)) (fma.f64 x x x))
(*.f64 (/.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 1 binary64))) (pow.f64 (hypot.f64 (fma.f64 x x x) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 2 binary64))) (hypot.f64 (fma.f64 x x x) (pow.f64 x #s(literal 3/2 binary64))))
(*.f64 (/.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 1 binary64))) (+.f64 (pow.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (-.f64 (hypot.f64 (hypot.f64 (*.f64 x x) x) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 7 binary64)))))
(*.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(*.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal -1 binary64)))
(*.f64 (/.f64 x (fma.f64 x x #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 x (fma.f64 x x #s(literal -1 binary64))) (-.f64 x #s(literal 1 binary64)))
(*.f64 (/.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (/.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x))))
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(/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x)) #s(literal -2 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (-.f64 (*.f64 (neg.f64 x) x) #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -3 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64))) #s(literal 3 binary64))) (+.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64))) #s(literal 2 binary64)) (*.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64)))))))
(/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x)) #s(literal -3 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x))) #s(literal 3 binary64))) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x))) #s(literal 2 binary64)) (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x)))))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))) (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 8 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 12 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x x) #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 12 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 18 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x)))
(/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) x) #s(literal 2 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x))) (*.f64 (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x)) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x)) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 8 binary64))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 18 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x)) (+.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 12 binary64))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x x) #s(literal 4 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 12 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x))))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x)))
(/.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (neg.f64 (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x)))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)))
(neg.f64 (fma.f64 x x #s(literal -1 binary64)))
(fma.f64 (pow.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 (pow.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)) (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 8 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 12 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x x) #s(literal 4 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 (pow.f64 (+.f64 (pow.f64 (fma.f64 x x x) #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (hypot.f64 (hypot.f64 (*.f64 x x) x) (fma.f64 x x x)) #s(literal 1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x)))))
(fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 12 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 18 binary64)))) (+.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 (*.f64 (neg.f64 x) #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x x) #s(literal 4 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x)))))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) #s(literal 1 binary64))
(fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x)) #s(literal 1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) x) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (*.f64 (neg.f64 x) x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 1 binary64) (hypot.f64 (*.f64 x x) x)) (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 (neg.f64 x) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(fma.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 (*.f64 x x) #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x))) (neg.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x)))))
(fma.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 x (neg.f64 x) #s(literal 1 binary64))
(fma.f64 x x #s(literal 1 binary64))
(-.f64 (/.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64))) #s(literal 1 binary64)))
(-.f64 (/.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x))) #s(literal 1 binary64)) (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x))) #s(literal 1 binary64)))
(-.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x))))
(-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(exp.f64 (*.f64 (*.f64 (log1p.f64 (*.f64 x x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(+.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x))) (neg.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (hypot.f64 (*.f64 x x) x)))))
(+.f64 (*.f64 (neg.f64 x) x) #s(literal 1 binary64))
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x))
(+.f64 #s(literal 1 binary64) (*.f64 x x))

eval84.0ms (1.6%)

Memory
34.1MiB live, 178.5MiB allocated
Compiler

Compiled 11 550 to 1 402 computations (87.9% saved)

prune22.0ms (0.4%)

Memory
10.8MiB live, 54.0MiB allocated
Pruning

6 alts after pruning (0 fresh and 6 done)

PrunedKeptTotal
New6800680
Fresh000
Picked022
Done044
Total6806686
Accuracy
100.0%
Counts
686 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
72.6%
(/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
100.0%
(/.f64 x (-.f64 #s(literal 1 binary64) x))
48.4%
#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
47.6%
#s(approx (/ x (- 1 x)) (fma.f64 x x x))
3.4%
#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))
52.8%
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
Compiler

Compiled 81 to 42 computations (48.1% saved)

regimes8.0ms (0.2%)

Memory
-14.8MiB live, 24.1MiB allocated
Counts
7 → 1
Calls
Call 1
Inputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))
#s(approx (/ x (- 1 x)) (fma.f64 x x x))
#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
(/.f64 x (-.f64 #s(literal 1 binary64) x))
(/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (*.f64 x x)))
Outputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))
Calls

2 calls:

4.0ms
(/.f64 x (-.f64 #s(literal 1 binary64) x))
3.0ms
x
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(/.f64 x (-.f64 #s(literal 1 binary64) x))
Compiler

Compiled 6 to 5 computations (16.7% saved)

regimes6.0ms (0.1%)

Memory
-21.0MiB live, 18.1MiB allocated
Counts
4 → 2
Calls
Call 1
Inputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))
#s(approx (/ x (- 1 x)) (fma.f64 x x x))
#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
Outputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
Calls

2 calls:

2.0ms
x
2.0ms
(/.f64 x (-.f64 #s(literal 1 binary64) x))
Results
AccuracySegmentsBranch
98.3%3x
98.3%2(/.f64 x (-.f64 #s(literal 1 binary64) x))
Compiler

Compiled 6 to 5 computations (16.7% saved)

regimes2.0ms (0%)

Memory
8.6MiB live, 8.6MiB allocated
Counts
3 → 2
Calls
Call 1
Inputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))
#s(approx (/ x (- 1 x)) (fma.f64 x x x))
Outputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) (fma.f64 x x x))
Calls

1 calls:

2.0ms
(/.f64 x (-.f64 #s(literal 1 binary64) x))
Results
AccuracySegmentsBranch
98.1%2(/.f64 x (-.f64 #s(literal 1 binary64) x))
Compiler

Compiled 5 to 4 computations (20% saved)

regimes3.0ms (0.1%)

Memory
14.4MiB live, 14.4MiB allocated
Counts
2 → 2
Calls
Call 1
Inputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))
Outputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))
Calls

2 calls:

2.0ms
x
1.0ms
(/.f64 x (-.f64 #s(literal 1 binary64) x))
Results
AccuracySegmentsBranch
52.8%1x
54.5%2(/.f64 x (-.f64 #s(literal 1 binary64) x))
Compiler

Compiled 6 to 5 computations (16.7% saved)

regimes3.0ms (0.1%)

Memory
12.0MiB live, 12.0MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

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

2 calls:

1.0ms
x
1.0ms
(/.f64 x (-.f64 #s(literal 1 binary64) x))
Results
AccuracySegmentsBranch
52.8%1x
52.8%1(/.f64 x (-.f64 #s(literal 1 binary64) x))
Compiler

Compiled 6 to 5 computations (16.7% saved)

bsearch0.0ms (0%)

Memory
1.5MiB live, 1.5MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
-0.9999999881462803
-0.014506679273036845
Compiler

Compiled 8 to 8 computations (0% saved)

bsearch0.0ms (0%)

Memory
1.1MiB live, 1.1MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
-0.9999999881462803
-0.014506679273036845
Compiler

Compiled 8 to 8 computations (0% saved)

bsearch0.0ms (0%)

Memory
1.1MiB live, 1.1MiB allocated
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
-1.713936958502001e-140
-3.2155140305889393e-158
Compiler

Compiled 8 to 8 computations (0% saved)

simplify44.0ms (0.8%)

Memory
-30.9MiB live, 77.5MiB allocated
Algorithm
egg-herbie
Rules
+-commutative-binary64-+.f64
sub-neg-binary64-neg.f64-+.f64--.f64
1-exp-binary32-exp.f32
*-commutative-binary64-*.f64
1-exp-binary64-exp.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02495
12995
23295
33495
43595
Stop Event
saturated
Calls
Call 1
Inputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) (fma.f64 x x x)))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -4290498537581631/429049853758163107186368799942587076079339706258956588087153966199096448962353503257659977541340909686081019461967553627320124249982290238285876768194691072 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))))
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
Outputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) (fma.f64 x x x)))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -4290498537581631/429049853758163107186368799942587076079339706258956588087153966199096448962353503257659977541340909686081019461967553627320124249982290238285876768194691072 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x))))
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

soundness911.0ms (17.7%)

Memory
-26.7MiB live, 207.7MiB allocated
Rules
12 030×lower-fma.f64
12 030×lower-fma.f32
4 624×lower-fma.f64
4 624×lower-fma.f32
2 958×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033135
193120
2220114
3545112
41047112
51955112
63384112
74540112
84656112
94656112
104818112
114893112
124893112
04893109
041664
1129640
2366603
31145595
42989595
56208595
08133542
Stop Event
done
iter limit
node limit
iter limit
saturated
Compiler

Compiled 74 to 36 computations (51.4% saved)

preprocess63.0ms (1.2%)

Memory
14.8MiB live, 53.0MiB allocated
Compiler

Compiled 120 to 48 computations (60% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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