sqrt times

Time bar (total: 3.6s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

Memory
1.9MiB live, 1.9MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%50%0%0%50%0%2
50%25%25%0%0%50%0%3
66.7%25%12.5%0%0%62.5%0%4
80%25%6.2%0%0%68.7%0%5
88.9%25%3.1%0%0%71.8%0%6
94.1%25%1.6%0%0%73.4%0%7
97%25%0.8%0%0%74.2%0%8
98.5%25%0.4%0%0%74.6%0%9
99.2%25%0.2%0%0%74.8%0%10
99.6%25%0.1%0%0%74.9%0%11
99.8%25%0%0%0%74.9%0%12
Compiler

Compiled 9 to 8 computations (11.1% saved)

sample612.0ms (16.9%)

Memory
52.1MiB live, 730.9MiB allocated
Samples
394.0ms8 246×0valid
1.0ms10×1valid
1.0ms14×0invalid
Precisions
Click to see histograms. Total time spent on operations: 249.0ms
ival-sqrt: 127.0ms (51.1% of total)
ival-sub: 56.0ms (22.5% of total)
ival-mult: 52.0ms (20.9% of total)
ival-true: 6.0ms (2.4% of total)
exact: 5.0ms (2% of total)
ival-assert: 3.0ms (1.2% of total)
adjust: 0.0ms (0% of total)
Bogosity

explain97.0ms (2.7%)

Memory
-5.8MiB live, 158.6MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
00-0-(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
00-0-(sqrt.f64 x)
00-0-(-.f64 x #s(literal 1 binary64))
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
29.0ms512×0valid
Compiler

Compiled 83 to 40 computations (51.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 17.0ms
ival-sqrt: 7.0ms (41.5% of total)
ival-sub: 5.0ms (29.7% of total)
ival-mult: 3.0ms (17.8% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess13.0ms (0.4%)

Memory
22.3MiB live, 22.3MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0819
12219
23817
35917
47717
59717
611617
713117
813217
067
0107
1167
2177
0177
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Outputs
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.2%
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0.2%)

Memory
-33.5MiB live, 5.1MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 x)
cost-diff0
(-.f64 x #s(literal 1 binary64))
cost-diff0
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
cost-diff0
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
01018
11618
21718
01718
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
(-.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(sqrt.f64 x)
Outputs
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
(-.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(sqrt.f64 x)

localize18.0ms (0.5%)

Memory
23.7MiB live, 23.7MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(-.f64 x #s(literal 1 binary64))
accuracy0
(sqrt.f64 x)
accuracy0.00390625
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
accuracy0.48046875
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Samples
13.0ms256×0valid
Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-sqrt: 3.0ms (43.6% of total)
ival-sub: 2.0ms (29.1% of total)
ival-mult: 2.0ms (29.1% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory
5.2MiB live, 5.2MiB allocated
Counts
4 → 28
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
(-.f64 x #s(literal 1 binary64))
(sqrt.f64 x)
Outputs
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))
(+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
-1
(- x 1)
(sqrt x)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))
(* x (- 1 (/ 1 x)))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* x (- (/ 1 x) 1)))
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x))
1.0ms
x
@0
((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x))
1.0ms
x
@inf
((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x))

simplify292.0ms (8%)

Memory
-4.0MiB live, 112.5MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0150448
1442387
21561366
34077348
08270324
Stop Event
1×iter limit
1×node limit
Counts
28 → 27
Calls
Call 1
Inputs
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))
(+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
-1
(- x 1)
(sqrt x)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))
(* x (- 1 (/ 1 x)))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* x (- (/ 1 x) 1)))
Outputs
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) (*.f64 x x))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (sqrt.f64 #s(literal -1 binary64)))
-1
#s(literal -1 binary64)
(- x 1)
(-.f64 x #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(-.f64 x #s(literal 1/2 binary64))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64)))
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal -1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
(* x (- 1 (/ 1 x)))
(-.f64 x #s(literal 1 binary64))
(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(-.f64 x #s(literal 1/2 binary64))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
(* -1 (* x (- (/ 1 x) 1)))
(-.f64 x #s(literal 1 binary64))

rewrite271.0ms (7.5%)

Memory
-10.6MiB live, 201.9MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
01015
13415
216115
3138815
0839315
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 368
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
(-.f64 x #s(literal 1 binary64))
(sqrt.f64 x)
Outputs
(*.f64 (sqrt.f64 (/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) x) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64))))) (sqrt.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) x) (+.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (fma.f64 (-.f64 x #s(literal -1 binary64)) (-.f64 (-.f64 x #s(literal -1 binary64)) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (pow.f64 (/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
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(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 9 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x x (-.f64 #s(literal 1 binary64) (neg.f64 x)))) (/.f64 (pow.f64 (+.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) (neg.f64 x)))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64))) (fma.f64 x x (-.f64 x #s(literal -1 binary64)))) (/.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (fma.f64 x x (-.f64 x #s(literal -1 binary64)))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 9 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x x (-.f64 x #s(literal -1 binary64)))) (/.f64 (pow.f64 (+.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (fma.f64 x x (-.f64 x #s(literal -1 binary64)))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) (neg.f64 x)))) #s(literal 1 binary64)) (/.f64 (pow.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) (neg.f64 x))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (-.f64 x #s(literal -1 binary64)))) #s(literal 1 binary64)) (/.f64 (pow.f64 (fma.f64 x x (-.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(-.f64 (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (/.f64 (*.f64 x x) (-.f64 #s(literal -1 binary64) x)))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) (neg.f64 x)))) (pow.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) (neg.f64 x))) #s(literal -1 binary64)))
(-.f64 (*.f64 (/.f64 x (-.f64 x #s(literal -1 binary64))) x) (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (-.f64 x #s(literal -1 binary64)))) (pow.f64 (fma.f64 x x (-.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (-.f64 x #s(literal 1 binary64))))
(-.f64 x #s(literal 1 binary64))
(exp.f64 (*.f64 (neg.f64 (log.f64 (-.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64)))
(exp.f64 (log.f64 (-.f64 x #s(literal 1 binary64))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) (neg.f64 x)))) (neg.f64 (pow.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) (neg.f64 x))) #s(literal -1 binary64))))
(+.f64 (*.f64 (/.f64 x (-.f64 x #s(literal -1 binary64))) x) (neg.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal -1 binary64))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (-.f64 x #s(literal -1 binary64)))) (neg.f64 (pow.f64 (fma.f64 x x (-.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))))
(+.f64 #s(literal -1 binary64) x)
(+.f64 x #s(literal -1 binary64))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1/4 binary64) (*.f64 (log.f64 x) #s(literal 1/4 binary64))))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))

eval49.0ms (1.3%)

Memory
-21.5MiB live, 99.5MiB allocated
Compiler

Compiled 8 819 to 1 550 computations (82.4% saved)

prune8.0ms (0.2%)

Memory
28.1MiB live, 28.1MiB allocated
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New3855390
Fresh000
Picked101
Done000
Total3865391
Accuracy
100.0%
Counts
391 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶55.3%
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
▶99.9%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64))))
▶99.7%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
▶99.3%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
▶98.2%
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Compiler

Compiled 120 to 96 computations (20% saved)

simplify62.0ms (1.7%)

Memory
0.1MiB live, 37.9MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
cost-diff0
(-.f64 x #s(literal 1 binary64))
cost-diff0
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
cost-diff0
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
cost-diff0
(/.f64 #s(literal -1/8 binary64) x)
cost-diff0
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
cost-diff0
(-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
cost-diff0
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
cost-diff0
(-.f64 x #s(literal 1/2 binary64))
cost-diff0
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
cost-diff0
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
cost-diff0
(/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x)
cost-diff0
(-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64))
cost-diff0
(-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64)))
cost-diff0
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
027133
039133
160133
292133
3158133
4271133
5581133
61012133
71333133
82110133
92367133
102467133
112473133
02473133
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64))))
(-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64)))
x
(-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64))
(/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x)
(+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64))
(/.f64 #s(literal 1/16 binary64) x)
#s(literal 1/16 binary64)
#s(literal 1/8 binary64)
#s(literal -1/2 binary64)
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
x
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
(-.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
x
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/8 binary64) x)
#s(literal -1/8 binary64)
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(-.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal -1/2 binary64))))
(-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64)))
(-.f64 x (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal -1/2 binary64)))
x
(-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64))
(-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal -1/2 binary64))
(/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x)
(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
(+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64))
(-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))
(/.f64 #s(literal 1/16 binary64) x)
#s(literal 1/16 binary64)
#s(literal 1/8 binary64)
#s(literal -1/2 binary64)
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
x
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
(-.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
x
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/8 binary64) x)
#s(literal -1/8 binary64)
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(-.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)

localize63.0ms (1.7%)

Memory
5.6MiB live, 125.4MiB allocated
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
accuracy0
(-.f64 x #s(literal 1 binary64))
accuracy0
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
accuracy28.62355893762732
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
accuracy0
(/.f64 #s(literal -1/8 binary64) x)
accuracy0
(-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
accuracy0
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
accuracy0.1939880237928831
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
accuracy0
(-.f64 x #s(literal 1/2 binary64))
accuracy0.4676840339617501
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
accuracy1.1718791321026982
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
accuracy0
(-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64)))
accuracy0
(+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64))
accuracy0.015625
(/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x)
accuracy0.05649389987209212
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64))))
Samples
49.0ms256×0valid
Compiler

Compiled 242 to 52 computations (78.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 32.0ms
ival-sqrt: 11.0ms (34.3% of total)
ival-sub: 9.0ms (28.1% of total)
ival-div: 5.0ms (15.6% of total)
ival-mult: 5.0ms (15.6% of total)
ival-add: 1.0ms (3.1% of total)
exact: 1.0ms (3.1% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series27.0ms (0.7%)

Memory
-28.4MiB live, 8.3MiB allocated
Counts
15 → 48
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64))))
(-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64)))
(-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64))
(/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
(-.f64 x #s(literal 1/2 binary64))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
(/.f64 #s(literal -1/8 binary64) x)
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(-.f64 x #s(literal 1 binary64))
(+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64))
Outputs
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(/ -1/16 (pow x 2))
(/ (- (* -1/8 x) 1/16) (pow x 2))
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))
(/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))
(/ 1/16 (pow x 2))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(/ (+ 1/16 (* x (+ 1/8 (* 1/2 x)))) (pow x 2))
-1/2
(- x 1/2)
(/ -1/8 x)
(/ (- (* -1/2 x) 1/8) x)
(/ (- (* x (- x 1/2)) 1/8) x)
(/ 1/8 x)
(/ (+ 1/8 (* 1/2 x)) x)
(* -1 x)
(* x (- x 1))
-1
(- x 1)
(/ 1/16 x)
(/ (+ 1/16 (* 1/8 x)) x)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
1/2
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x))))
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* x (- 1 (/ 1 x)))
1/8
(+ 1/8 (* 1/16 (/ 1 x)))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
(* -1 (* x (- (/ 1 x) 1)))
Calls

3 calls:

TimeVariablePointExpression
23.0ms
x
@-inf
((* (sqrt (- x 1)) (sqrt x)) (- x (- (/ (+ (/ 1/16 x) 1/8) x) -1/2)) (- (/ (+ (/ 1/16 x) 1/8) x) -1/2) (/ (+ (/ 1/16 x) 1/8) x) (* (sqrt (- x 1)) (sqrt x)) (* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (* (sqrt (- x 1)) (sqrt x)) (- x (- 1/2 (/ -1/8 x))) (- 1/2 (/ -1/8 x)) (/ -1/8 x) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) (+ (/ 1/16 x) 1/8))
2.0ms
x
@0
((* (sqrt (- x 1)) (sqrt x)) (- x (- (/ (+ (/ 1/16 x) 1/8) x) -1/2)) (- (/ (+ (/ 1/16 x) 1/8) x) -1/2) (/ (+ (/ 1/16 x) 1/8) x) (* (sqrt (- x 1)) (sqrt x)) (* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (* (sqrt (- x 1)) (sqrt x)) (- x (- 1/2 (/ -1/8 x))) (- 1/2 (/ -1/8 x)) (/ -1/8 x) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) (+ (/ 1/16 x) 1/8))
1.0ms
x
@inf
((* (sqrt (- x 1)) (sqrt x)) (- x (- (/ (+ (/ 1/16 x) 1/8) x) -1/2)) (- (/ (+ (/ 1/16 x) 1/8) x) -1/2) (/ (+ (/ 1/16 x) 1/8) x) (* (sqrt (- x 1)) (sqrt x)) (* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (* (sqrt (- x 1)) (sqrt x)) (- x (- 1/2 (/ -1/8 x))) (- 1/2 (/ -1/8 x)) (/ -1/8 x) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) (+ (/ 1/16 x) 1/8))

simplify124.0ms (3.4%)

Memory
32.2MiB live, 115.3MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0154411
1415388
21342346
35387330
08177319
Stop Event
1×iter limit
1×node limit
Counts
48 → 47
Calls
Call 1
Inputs
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(/ -1/16 (pow x 2))
(/ (- (* -1/8 x) 1/16) (pow x 2))
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))
(/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))
(/ 1/16 (pow x 2))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(/ (+ 1/16 (* x (+ 1/8 (* 1/2 x)))) (pow x 2))
-1/2
(- x 1/2)
(/ -1/8 x)
(/ (- (* -1/2 x) 1/8) x)
(/ (- (* x (- x 1/2)) 1/8) x)
(/ 1/8 x)
(/ (+ 1/8 (* 1/2 x)) x)
(* -1 x)
(* x (- x 1))
-1
(- x 1)
(/ 1/16 x)
(/ (+ 1/16 (* 1/8 x)) x)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
1/2
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x))))
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* x (- 1 (/ 1 x)))
1/8
(+ 1/8 (* 1/16 (/ 1 x)))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
(* -1 (* x (- (/ 1 x) 1)))
Outputs
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (*.f64 x x))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(/ -1/16 (pow x 2))
(/.f64 #s(literal -1/16 binary64) (*.f64 x x))
(/ (- (* -1/8 x) 1/16) (pow x 2))
(/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))
(-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x))
(/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))
(/.f64 (-.f64 (fma.f64 (-.f64 x #s(literal 1/2 binary64)) x #s(literal -1/8 binary64)) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(/.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) x #s(literal 1/16 binary64)) x) x)
(/ (+ 1/16 (* x (+ 1/8 (* 1/2 x)))) (pow x 2))
(/.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/8 binary64)) x #s(literal 1/16 binary64)) x) x)
-1/2
#s(literal -1/2 binary64)
(- x 1/2)
(-.f64 x #s(literal 1/2 binary64))
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ (- (* -1/2 x) 1/8) x)
(-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
(/ (- (* x (- x 1/2)) 1/8) x)
(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ (+ 1/8 (* 1/2 x)) x)
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
(* -1 x)
(neg.f64 x)
(* x (- x 1))
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
-1
#s(literal -1 binary64)
(- x 1)
(-.f64 x #s(literal 1 binary64))
(/ 1/16 x)
(/.f64 #s(literal 1/16 binary64) x)
(/ (+ 1/16 (* 1/8 x)) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) x #s(literal 1/16 binary64)) x)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(-.f64 x #s(literal 1/2 binary64))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/8 (/ 1 x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
(+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x))))
(-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64))
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(* x (- 1 (/ 1 x)))
(-.f64 x #s(literal 1 binary64))
1/8
#s(literal 1/8 binary64)
(+ 1/8 (* 1/16 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64))
(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(-.f64 x #s(literal 1/2 binary64))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/2 binary64))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))
(-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64)))
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(-.f64 #s(literal 1/2 binary64) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
(-.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64)) x)
(* -1 (* x (- (/ 1 x) 1)))
(-.f64 x #s(literal 1 binary64))

rewrite219.0ms (6%)

Memory
-1.2MiB live, 200.9MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
027118
039114
1161114
21273114
08243114
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
15 → 486
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64))))
(-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64)))
(-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64))
(/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
(-.f64 x #s(literal 1/2 binary64))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
(/.f64 #s(literal -1/8 binary64) x)
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(-.f64 x #s(literal 1 binary64))
(+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64))
Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64))))
(*.f64 (-.f64 (*.f64 x x) (pow.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (+.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) x) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) (+.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) x) (*.f64 x x)) #s(literal -1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)))) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (+.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (+.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) x)) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 x x) (+.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) x)) (/.f64 (*.f64 x x) (+.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) x)) (fma.f64 (/.f64 (pow.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (+.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) x)) (/.f64 (pow.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (+.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) x)) (*.f64 (/.f64 (*.f64 x x) (+.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) x)) (/.f64 (pow.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (+.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) x))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) (+.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) x) (*.f64 x x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) (+.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) x) (*.f64 x x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) (+.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) x) (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) (+.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) x) (*.f64 x x))) (fma.f64 (/.f64 (pow.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) (+.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) x) (*.f64 x x))) (/.f64 (pow.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) (+.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) x) (*.f64 x x))) (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) (+.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) x) (*.f64 x x))) (/.f64 (pow.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) (+.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) x) (*.f64 x x)))))))
(/.f64 (-.f64 (pow.f64 (-.f64 x (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (+.f64 (pow.f64 (-.f64 x (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (-.f64 x (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 x x) (*.f64 (neg.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64))) x))))
(/.f64 (+.f64 #s(literal -1/8 binary64) (pow.f64 (-.f64 x (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (-.f64 x (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (-.f64 x (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 x (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (neg.f64 (-.f64 (-.f64 x (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) #s(literal -1/2 binary64))))
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(pow.f64 (pow.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/64 binary64) (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64))) (/.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64))) (fma.f64 (/.f64 #s(literal 1/64 binary64) (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64))) (/.f64 #s(literal 1/64 binary64) (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64))) (*.f64 (/.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64))) (/.f64 #s(literal 1/64 binary64) (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/64 binary64) (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/256 binary64) #s(literal -1/64 binary64)))) (neg.f64 (neg.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/4096 binary64) (pow.f64 x #s(literal -3 binary64)) #s(literal 1/512 binary64)))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/256 binary64) (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/128 binary64) x))))))
(/.f64 (-.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64))) (*.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) #s(literal 1/64 binary64))) (*.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64))))
(/.f64 (-.f64 #s(literal 1/64 binary64) (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64))) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/256 binary64) #s(literal -1/64 binary64))) (neg.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/4096 binary64) (pow.f64 x #s(literal -3 binary64)) #s(literal 1/512 binary64))) (neg.f64 (+.f64 #s(literal 1/64 binary64) (/.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/16 binary64) x)) #s(literal 1/128 binary64)) x))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/4096 binary64) (pow.f64 x #s(literal -3 binary64)) #s(literal 1/512 binary64))) (neg.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/256 binary64) (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/128 binary64) x)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/256 binary64) #s(literal -1/64 binary64)) (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) #s(literal -1 binary64))))
(/.f64 (fma.f64 #s(literal 1/4096 binary64) (pow.f64 x #s(literal -3 binary64)) #s(literal 1/512 binary64)) (+.f64 #s(literal 1/64 binary64) (/.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/16 binary64) x)) #s(literal 1/128 binary64)) x)))
(/.f64 (fma.f64 #s(literal 1/4096 binary64) (pow.f64 x #s(literal -3 binary64)) #s(literal 1/512 binary64)) (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/256 binary64) (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/128 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (-.f64 #s(literal 1/64 binary64) (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/64 binary64) (/.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/16 binary64) x)) #s(literal 1/128 binary64)) x)) (fma.f64 #s(literal 1/4096 binary64) (pow.f64 x #s(literal -3 binary64)) #s(literal 1/512 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) #s(literal -1 binary64)))
(fma.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/16 binary64) #s(literal 1/8 binary64))
(fma.f64 #s(literal -1/16 binary64) (pow.f64 (neg.f64 x) #s(literal -1 binary64)) #s(literal 1/8 binary64))
(fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal -1 binary64)) #s(literal 1/8 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64))
(-.f64 (/.f64 #s(literal 1/64 binary64) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))) (/.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
(-.f64 (/.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64))) (/.f64 #s(literal 1/64 binary64) (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64))))
(+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
(+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64))

eval105.0ms (2.9%)

Memory
-17.9MiB live, 138.2MiB allocated
Compiler

Compiled 15 704 to 2 252 computations (85.7% saved)

prune9.0ms (0.3%)

Memory
-2.7MiB live, 35.2MiB allocated
Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New5241525
Fresh000
Picked145
Done000
Total5255530
Accuracy
100.0%
Counts
530 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶55.3%
(sqrt.f64 (+.f64 (*.f64 x x) (neg.f64 x)))
✓55.3%
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
✓99.7%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
✓99.3%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
✓98.2%
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Compiler

Compiled 48 to 38 computations (20.8% saved)

simplify8.0ms (0.2%)

Memory
26.0MiB live, 26.0MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(neg.f64 x)
cost-diff0
(*.f64 x x)
cost-diff0
(sqrt.f64 (+.f64 (*.f64 x x) (neg.f64 x)))
cost-diff128
(+.f64 (*.f64 x x) (neg.f64 x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0519
0917
11517
22517
33717
45617
511517
620217
723517
823517
023517
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (*.f64 x x) (neg.f64 x)))
(+.f64 (*.f64 x x) (neg.f64 x))
(*.f64 x x)
x
(neg.f64 x)
Outputs
(sqrt.f64 (+.f64 (*.f64 x x) (neg.f64 x)))
(sqrt.f64 (fma.f64 x x (neg.f64 x)))
(+.f64 (*.f64 x x) (neg.f64 x))
(fma.f64 x x (neg.f64 x))
(*.f64 x x)
x
(neg.f64 x)

localize29.0ms (0.8%)

Memory
-40.7MiB live, 46.2MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 x x)
accuracy0
(neg.f64 x)
accuracy0.01171875
(+.f64 (*.f64 x x) (neg.f64 x))
accuracy28.62355893762732
(sqrt.f64 (+.f64 (*.f64 x x) (neg.f64 x)))
Samples
22.0ms256×0valid
Compiler

Compiled 40 to 12 computations (70% saved)

Precisions
Click to see histograms. Total time spent on operations: 16.0ms
ival-mult: 12.0ms (74.9% of total)
ival-sqrt: 2.0ms (12.5% of total)
ival-add: 1.0ms (6.2% of total)
ival-neg: 1.0ms (6.2% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series2.0ms (0%)

Memory
2.8MiB live, 2.8MiB allocated
Counts
4 → 15
Calls
Call 1
Inputs
(+.f64 (*.f64 x x) (neg.f64 x))
(sqrt.f64 (+.f64 (*.f64 x x) (neg.f64 x)))
(*.f64 x x)
(neg.f64 x)
Outputs
(* -1 x)
(* x (- x 1))
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@inf
((+ (* x x) (neg x)) (sqrt (+ (* x x) (neg x))) (* x x) (neg x))
1.0ms
x
@-inf
((+ (* x x) (neg x)) (sqrt (+ (* x x) (neg x))) (* x x) (neg x))
0.0ms
x
@0
((+ (* x x) (neg x)) (sqrt (+ (* x x) (neg x))) (* x x) (neg x))

simplify157.0ms (4.3%)

Memory
37.5MiB live, 188.6MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
075203
1209187
2657181
32061156
44818148
57595148
08837142
Stop Event
1×iter limit
1×node limit
Counts
15 → 14
Calls
Call 1
Inputs
(* -1 x)
(* x (- x 1))
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
Outputs
(* -1 x)
(neg.f64 x)
(* x (- x 1))
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(fma.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (*.f64 x x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (*.f64 x x))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(-.f64 x #s(literal 1/2 binary64))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(-.f64 (+.f64 x (/.f64 #s(literal -1/8 binary64) x)) #s(literal 1/2 binary64))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(-.f64 (-.f64 x (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x)) #s(literal 1/2 binary64))
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(-.f64 #s(literal 1/2 binary64) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(-.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
(-.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal 1/2 binary64)) x)

rewrite203.0ms (5.6%)

Memory
-25.7MiB live, 216.6MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0518
0916
13216
223315
3242215
0849412
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 539
Calls
Call 1
Inputs
(+.f64 (*.f64 x x) (neg.f64 x))
(sqrt.f64 (+.f64 (*.f64 x x) (neg.f64 x)))
(*.f64 x x)
(neg.f64 x)
Outputs
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 x x x))
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (sqrt.f64 (*.f64 x x)))
(*.f64 (sqrt.f64 (*.f64 x x)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (*.f64 x x)) (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (*.f64 x x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(*.f64 (exp.f64 (log.f64 (pow.f64 (fma.f64 x x x) #s(literal 2 binary64)))) (exp.f64 (neg.f64 (log.f64 (fma.f64 x x x)))))
(*.f64 (exp.f64 (log.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))))) (exp.f64 (neg.f64 (log.f64 (fma.f64 (fma.f64 x x x) x (pow.f64 x #s(literal 4 binary64)))))))
(*.f64 (pow.f64 (*.f64 (fma.f64 x x x) x) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(*.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/2 binary64)) x)
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (fma.f64 x x x))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x x) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 x x x) #s(literal 2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x x) (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 x #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 (fma.f64 x x x) x (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 (fma.f64 x x x) x (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 x #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 (fma.f64 x x x) x (pow.f64 x #s(literal 4 binary64))) (+.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 18 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 9 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 x (fma.f64 x x x)) #s(literal -1 binary64)) (pow.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) (fma.f64 x x x)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (fma.f64 x x x) x (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (pow.f64 (fma.f64 x x x) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 x x x) #s(literal -1 binary64)))
(*.f64 (/.f64 (pow.f64 (fma.f64 x x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 x x x) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (fma.f64 x x x) x (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64))) (fma.f64 (fma.f64 x x x) x (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 12 binary64)))) (-.f64 (pow.f64 (fma.f64 (fma.f64 x x x) x (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 7 binary64)))))
(*.f64 (/.f64 (pow.f64 (fma.f64 x x x) #s(literal 2 binary64)) (pow.f64 (fma.f64 x x x) #s(literal 2 binary64))) (fma.f64 x x x))
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x

eval76.0ms (2.1%)

Memory
23.3MiB live, 105.3MiB allocated
Compiler

Compiled 10 436 to 1 814 computations (82.6% saved)

prune11.0ms (0.3%)

Memory
-8.7MiB live, 27.4MiB allocated
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New5511552
Fresh000
Picked101
Done134
Total5534557
Accuracy
100.0%
Counts
557 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶55.3%
(sqrt.f64 (-.f64 (*.f64 x x) x))
✓99.7%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
✓99.3%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
✓98.2%
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Compiler

Compiled 41 to 32 computations (22% saved)

simplify8.0ms (0.2%)

Memory
5.5MiB live, 5.5MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x x)
cost-diff0
(-.f64 (*.f64 x x) x)
cost-diff0
(sqrt.f64 (-.f64 (*.f64 x x) x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0415
0715
1915
21415
32415
43615
55515
611415
720415
823615
923615
023615
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 (*.f64 x x) x))
(-.f64 (*.f64 x x) x)
(*.f64 x x)
x
Outputs
(sqrt.f64 (-.f64 (*.f64 x x) x))
(-.f64 (*.f64 x x) x)
(*.f64 x x)
x

localize23.0ms (0.6%)

Memory
-21.1MiB live, 16.7MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0
(*.f64 x x)
accuracy0.01171875
(-.f64 (*.f64 x x) x)
accuracy28.62355893762732
(sqrt.f64 (-.f64 (*.f64 x x) x))
Samples
18.0ms256×0valid
Compiler

Compiled 32 to 10 computations (68.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-mult: 2.0ms (39.4% of total)
ival-sqrt: 2.0ms (39.4% of total)
ival-sub: 1.0ms (19.7% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series1.0ms (0%)

Memory
2.0MiB live, 2.0MiB allocated
Counts
3 → 15
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 (*.f64 x x) x))
(-.f64 (*.f64 x x) x)
(*.f64 x x)
Outputs
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(* -1 x)
(* x (- x 1))
(pow x 2)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(* (pow x 2) (- 1 (/ 1 x)))
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@inf
((sqrt (- (* x x) x)) (- (* x x) x) (* x x))
0.0ms
x
@-inf
((sqrt (- (* x x) x)) (- (* x x) x) (* x x))
0.0ms
x
@0
((sqrt (- (* x x) x)) (- (* x x) x) (* x x))

simplify190.0ms (5.2%)

Memory
16.7MiB live, 172.4MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
075203
1209187
2661181
32071156
44904148
57680148
08907142
Stop Event
1×iter limit
1×node limit
Counts
15 → 14
Calls
Call 1
Inputs
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(* -1 x)
(* x (- x 1))
(pow x 2)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(* (pow x 2) (- 1 (/ 1 x)))
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
Outputs
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(fma.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (*.f64 x x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (*.f64 x x))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(* -1 x)
(neg.f64 x)
(* x (- x 1))
(fma.f64 x x (neg.f64 x))
(pow x 2)
(*.f64 x x)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(-.f64 x #s(literal 1/2 binary64))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(-.f64 (+.f64 x (/.f64 #s(literal -1/8 binary64) x)) #s(literal 1/2 binary64))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(-.f64 (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (-.f64 #s(literal 1/2 binary64) x))
(* (pow x 2) (- 1 (/ 1 x)))
(fma.f64 x x (neg.f64 x))
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(-.f64 #s(literal 1/2 binary64) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(-.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
(-.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal 1/2 binary64)) x)

rewrite151.0ms (4.2%)

Memory
-7.5MiB live, 184.9MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0414
0714
12514
216714
3156714
0967411
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
3 → 404
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 (*.f64 x x) x))
(-.f64 (*.f64 x x) x)
(*.f64 x x)
Outputs
(*.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (fma.f64 x x x) x (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)))) (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 x x x)))
(*.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 12 binary64))))) (sqrt.f64 (+.f64 (-.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 x #s(literal 7 binary64)) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 x #s(literal 8 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (fma.f64 x x x) (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (neg.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))
(*.f64 (sqrt.f64 (/.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))) (hypot.f64 (sqrt.f64 x) x))
(*.f64 (sqrt.f64 (/.f64 (fma.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))))) (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 x x x)))
(*.f64 (sqrt.f64 (/.f64 (fma.f64 x x x) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))))) (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (hypot.f64 (sqrt.f64 x) x))
(*.f64 (pow.f64 (hypot.f64 (sqrt.f64 x) x) #s(literal 2 binary64)) (pow.f64 (pow.f64 (fma.f64 x x x) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (fma.f64 (fma.f64 x x x) x (pow.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (fma.f64 x x x) x (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 x x x)))
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 12 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (-.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 x #s(literal 7 binary64)) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 x #s(literal 8 binary64)))))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (hypot.f64 (sqrt.f64 x) x))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)) (hypot.f64 (sqrt.f64 x) x))
(*.f64 (pow.f64 (/.f64 (fma.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)))) #s(literal 1/2 binary64)) (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 x x x)))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x x) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))
(*.f64 (pow.f64 (pow.f64 (fma.f64 x x x) #s(literal 3 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x x) #s(literal -1/4 binary64)))
(*.f64 (pow.f64 (*.f64 (fma.f64 x x x) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (fma.f64 x x x) x (pow.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 8 binary64))) #s(literal -1 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (neg.f64 x)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal -1 binary64) x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 x) (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(*.f64 (neg.f64 (hypot.f64 (*.f64 x x) x)) (/.f64 #s(literal 1 binary64) (neg.f64 (hypot.f64 (sqrt.f64 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 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 x x x)))))
(*.f64 (pow.f64 (fma.f64 x x x) #s(literal -1/2 binary64)) (hypot.f64 (*.f64 x x) x))
(*.f64 (pow.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 x x x)) #s(literal -1 binary64)) (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))
(*.f64 (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64)))
(*.f64 (hypot.f64 (sqrt.f64 x) x) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (hypot.f64 (sqrt.f64 x) x) #s(literal 1 binary64))
(*.f64 (hypot.f64 (*.f64 x x) x) (pow.f64 (fma.f64 x x x) #s(literal -1/2 binary64)))
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 x x x)) (sqrt.f64 (/.f64 (fma.f64 x x x) (fma.f64 (fma.f64 x x x) x (pow.f64 x #s(literal 4 binary64))))))
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 x x x)) (pow.f64 (/.f64 (fma.f64 x x x) (fma.f64 (fma.f64 x x x) x (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)))
(*.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 x x x)) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (hypot.f64 (sqrt.f64 x) x))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (+.f64 (log1p.f64 x) (log.f64 x)))
(pow.f64 (pow.f64 (fma.f64 x x x) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (fma.f64 x x x) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(pow.f64 (fma.f64 x x x) #s(literal 1/2 binary64))
(pow.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64))
(/.f64 (neg.f64 (neg.f64 (hypot.f64 (*.f64 x x) x))) (neg.f64 (neg.f64 (hypot.f64 (sqrt.f64 x) x))))
(/.f64 (neg.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 x x x)))))
(/.f64 (sqrt.f64 (/.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 x x x) #s(literal -1 binary64)))) (hypot.f64 (*.f64 x x) x))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 x x x) #s(literal -1 binary64)))) (hypot.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (fma.f64 x x x) x (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))) (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 18 binary64)) (pow.f64 x #s(literal 9 binary64))) (pow.f64 (fma.f64 (fma.f64 x x x) x (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))) (hypot.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 x #s(literal 9/2 binary64))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (/.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64)))) (sqrt.f64 (fma.f64 (/.f64 x (+.f64 #s(literal 1 binary64) x)) (*.f64 x x) (*.f64 (/.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))))
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(exp.f64 (-.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)) (log.f64 x)))
(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)))

eval79.0ms (2.2%)

Memory
2.2MiB live, 99.3MiB allocated
Compiler

Compiled 9 130 to 1 311 computations (85.6% saved)

prune8.0ms (0.2%)

Memory
-11.0MiB live, 27.3MiB allocated
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New4170417
Fresh000
Picked011
Done033
Total4174421
Accuracy
100.0%
Counts
421 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓55.3%
(sqrt.f64 (-.f64 (*.f64 x x) x))
✓99.7%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
✓99.3%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
✓98.2%
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Compiler

Compiled 121 to 69 computations (43% saved)

regimes6.0ms (0.2%)

Memory
15.6MiB live, 15.6MiB allocated
Counts
8 → 1
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(sqrt.f64 (-.f64 (*.f64 x x) x))
(sqrt.f64 (+.f64 (*.f64 x x) (neg.f64 x)))
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64))))
Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64))))
Calls

2 calls:

3.0ms
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
3.0ms
x
Results
AccuracySegmentsBranch
99.9%1x
99.9%1(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes8.0ms (0.2%)

Memory
-24.3MiB live, 14.0MiB allocated
Counts
7 → 1
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(sqrt.f64 (-.f64 (*.f64 x x) x))
(sqrt.f64 (+.f64 (*.f64 x x) (neg.f64 x)))
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
Calls

2 calls:

3.0ms
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
3.0ms
x
Results
AccuracySegmentsBranch
99.7%1x
99.7%1(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0.1%)

Memory
12.9MiB live, 12.9MiB allocated
Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
Calls

2 calls:

2.0ms
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
1.0ms
x
Results
AccuracySegmentsBranch
99.3%1x
99.3%1(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0.1%)

Memory
8.8MiB live, 8.8MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Calls

2 calls:

1.0ms
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
1.0ms
x
Results
AccuracySegmentsBranch
98.2%1x
98.2%1(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify33.0ms (0.9%)

Memory
-7.0MiB live, 77.4MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02454
13854
26354
310054
414354
519954
628354
743254
858054
961354
1061954
1162154
Stop Event
1×saturated
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal -1/2 binary64))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

soundness622.0ms (17.2%)

Memory
-13.3MiB live, 182.1MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0150448
1442387
21561366
34077348
08270324
Stop Event
1×done
1×iter limit
1×node limit
Compiler

Compiled 55 to 26 computations (52.7% saved)

preprocess22.0ms (0.6%)

Memory
24.3MiB live, 24.3MiB allocated
Compiler

Compiled 122 to 60 computations (50.8% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

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