sqrt times

Time bar (total: 3.5s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze1.0ms (0%)

Memory
1.9MiB live, 1.9MiB allocated; 0ms collecting garbage
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)

sample912.0ms (26.2%)

Memory
43.9MiB live, 765.0MiB allocated; 840ms collecting garbage
Samples
653.0ms8 248×0valid
1.0ms8×1valid
1.0ms12×0invalid
Precisions
Click to see histograms. Total time spent on operations: 231.0ms
ival-sqrt: 105.0ms (45.5% of total)
ival-mult: 61.0ms (26.4% of total)
ival-sub: 50.0ms (21.7% of total)
ival-true: 5.0ms (2.2% of total)
exact: 5.0ms (2.2% of total)
ival-assert: 3.0ms (1.3% of total)
adjust: 2.0ms (0.9% of total)
Bogosity

explain70.0ms (2%)

Memory
27.5MiB live, 120.3MiB allocated; 27ms collecting garbage
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
26.0ms512×0valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 14.0ms
ival-sqrt: 7.0ms (51.6% of total)
ival-sub: 3.0ms (22.1% of total)
ival-mult: 3.0ms (22.1% of total)
ival-true: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess16.0ms (0.5%)

Memory
-35.2MiB live, 23.2MiB allocated; 5ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0819
11519
21719
067
0107
1137
0137
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
0.2MiB live, 0.2MiB allocated; 0ms collecting garbage
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated; 0ms collecting garbage
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)

simplify4.0ms (0.1%)

Memory
5.5MiB live, 5.5MiB allocated; 0ms collecting garbage
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
11318
01318
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
27.2MiB live, 27.2MiB allocated; 0ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(-.f64 x #s(literal 1 binary64))
accuracy0.0
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
accuracy0.0
(sqrt.f64 x)
accuracy0.5390625
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Samples
12.0ms256×0valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-sqrt: 3.0ms (45.1% of total)
ival-sub: 2.0ms (30.1% of total)
ival-mult: 1.0ms (15% of total)
ival-true: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series10.0ms (0.3%)

Memory
-37.9MiB live, 7.9MiB allocated; 9ms collecting garbage
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
5.0ms
x
@inf
((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x))
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))

simplify187.0ms (5.4%)

Memory
42.1MiB live, 129.6MiB allocated; 14ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0150457
1495390
22202378
37444375
08362345
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 (*.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (sqrt.f64 #s(literal -1 binary64))) 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 (/.f64 (fma.f64 #s(literal 1/8 binary64) x #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 (*.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) #s(literal 1/16 binary64)) x (/.f64 (fma.f64 #s(literal 1/8 binary64) x #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))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x)
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(fma.f64 (/.f64 x x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x)
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x) x x)
(* 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 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x)
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(fma.f64 (/.f64 x x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #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))))
(fma.f64 (/.f64 (-.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 (* (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 3 binary64)))) #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 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 (neg.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) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
(* -1 (* x (- (/ 1 x) 1)))
(*.f64 (neg.f64 x) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))

rewrite235.0ms (6.7%)

Memory
-33.0MiB live, 252.4MiB allocated; 44ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
01015
13215
214815
3118915
0961413
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 354
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 (*.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)))) (*.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)))))
(*.f64 (*.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (*.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))))
(*.f64 (*.f64 (pow.f64 x #s(literal 1/4 binary64)) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)))) (*.f64 (pow.f64 x #s(literal 1/4 binary64)) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)))))
(*.f64 (*.f64 (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 x #s(literal 1/4 binary64)))) (*.f64 (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 x #s(literal 1/4 binary64)))))
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(fma.f64 (neg.f64 x) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(fma.f64 #s(literal 1 binary64) (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)))
(fma.f64 #s(literal 1 binary64) (neg.f64 x) #s(literal -1 binary64))
(fma.f64 x (/.f64 (*.f64 x x) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(fma.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)))
(fma.f64 x #s(literal -1 binary64) #s(literal -1 binary64))
(expm1.f64 (/.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(expm1.f64 (*.f64 (log.f64 x) #s(literal 1 binary64)))
(expm1.f64 (log.f64 x))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))) (neg.f64 (-.f64 x #s(literal 1 binary64)))) (/.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64)))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (-.f64 x #s(literal 1 binary64)))) (/.f64 (pow.f64 (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64)))))
(-.f64 (/.f64 (*.f64 x x) (neg.f64 (-.f64 x #s(literal 1 binary64)))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))))
(-.f64 (/.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) x)) (/.f64 (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal -2 binary64)) (-.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 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 -2 binary64)) (*.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -3 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 -2 binary64)) (*.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal -2 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)))))) (/.f64 (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal -3 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal -2 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)))))))
(-.f64 (/.f64 (fma.f64 x x (pow.f64 x #s(literal 3 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) x) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
(-.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 (*.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 9 binary64)) (*.f64 (+.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) x)) (/.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) x)) (/.f64 (pow.f64 (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #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 (-.f64 x #s(literal 1 binary64)) 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 (-.f64 x #s(literal 1 binary64)) 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 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))) (/.f64 (*.f64 (neg.f64 (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (neg.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))) (/.f64 (*.f64 (neg.f64 (*.f64 x x)) x) (neg.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))))
(-.f64 (/.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(-.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 x x) (-.f64 x #s(literal 1 binary64))))
(-.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(-.f64 (neg.f64 x) #s(literal 1 binary64))
(-.f64 x #s(literal 1 binary64))
(exp.f64 (log.f64 (-.f64 x #s(literal 1 binary64))))
(+.f64 (/.f64 (*.f64 x x) (neg.f64 (-.f64 x #s(literal 1 binary64)))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(+.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))))
(+.f64 (cosh.f64 (log.f64 (-.f64 x #s(literal 1 binary64)))) (sinh.f64 (log.f64 (-.f64 x #s(literal 1 binary64)))))
(+.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 (neg.f64 (neg.f64 x)) (neg.f64 x)) (-.f64 x #s(literal 1 binary64))))
(+.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 (neg.f64 x) x) (-.f64 x #s(literal 1 binary64))))
(+.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 x (neg.f64 x)) (-.f64 x #s(literal 1 binary64))))
(+.f64 #s(literal -1 binary64) (neg.f64 x))
(+.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(+.f64 (neg.f64 x) #s(literal -1 binary64))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (neg.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64)))) (neg.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64)))))
(*.f64 (pow.f64 (neg.f64 (neg.f64 x)) #s(literal 1/4 binary64)) (pow.f64 (neg.f64 (neg.f64 x)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)))
(*.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (neg.f64 (pow.f64 x #s(literal 1/4 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 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(/.f64 (-.f64 (*.f64 (cosh.f64 (log.f64 (sqrt.f64 x))) (cosh.f64 (log.f64 (sqrt.f64 x)))) (*.f64 (sinh.f64 (log.f64 (sqrt.f64 x))) (sinh.f64 (log.f64 (sqrt.f64 x))))) (-.f64 (cosh.f64 (log.f64 (sqrt.f64 x))) (sinh.f64 (log.f64 (sqrt.f64 x)))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (log.f64 (sqrt.f64 x))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (log.f64 (sqrt.f64 x))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (log.f64 (sqrt.f64 x))) (cosh.f64 (log.f64 (sqrt.f64 x))) (-.f64 (*.f64 (sinh.f64 (log.f64 (sqrt.f64 x))) (sinh.f64 (log.f64 (sqrt.f64 x)))) (*.f64 (cosh.f64 (log.f64 (sqrt.f64 x))) (sinh.f64 (log.f64 (sqrt.f64 x)))))))
(sqrt.f64 x)
(fabs.f64 (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 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (sqrt.f64 x)))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 x))) (sinh.f64 (log.f64 (sqrt.f64 x))))

eval38.0ms (1.1%)

Memory
46.8MiB live, 91.6MiB allocated; 4ms collecting garbage
Compiler

Compiled 7 786 to 1 459 computations (81.3% saved)

prune10.0ms (0.3%)

Memory
-16.0MiB live, 28.2MiB allocated; 5ms collecting garbage
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New3744378
Fresh000
Picked011
Done000
Total3745379
Accuracy
100.0%
Counts
379 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.2%
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶92.7%
(*.f64 (sqrt.f64 (expm1.f64 (log.f64 x))) (sqrt.f64 x))
▶98.3%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 x x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x))
▶98.0%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
▶96.4%
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Compiler

Compiled 55 to 42 computations (23.6% saved)

simplify195.0ms (5.6%)

Memory
-5.8MiB live, 185.9MiB allocated; 49ms collecting garbage
Algorithm
1×egg-herbie
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
cost-diff0
(log.f64 x)
cost-diff0
(expm1.f64 (log.f64 x))
cost-diff0
(sqrt.f64 (expm1.f64 (log.f64 x)))
cost-diff0
(*.f64 (sqrt.f64 (expm1.f64 (log.f64 x))) (sqrt.f64 x))
cost-diff0
(-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))
cost-diff0
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 x x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x))
cost-diff1
(fma.f64 (/.f64 x x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x)
cost-diff2
(/.f64 x x)
cost-diff0
(/.f64 #s(literal -1/2 binary64) x)
cost-diff0
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
cost-diff3
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x)
cost-diff0
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02396
03790
15682
212182
332582
4132082
0867482
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
x
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x)
(/.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 x x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x))
(fma.f64 (/.f64 x x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x)
(/.f64 x x)
x
(-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))
(/.f64 #s(literal -1/8 binary64) x)
#s(literal -1/8 binary64)
#s(literal 1/2 binary64)
(*.f64 (sqrt.f64 (expm1.f64 (log.f64 x))) (sqrt.f64 x))
(sqrt.f64 (expm1.f64 (log.f64 x)))
(expm1.f64 (log.f64 x))
(log.f64 x)
x
(sqrt.f64 x)
Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
x
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x)
(-.f64 x #s(literal 1/2 binary64))
(/.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 x x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (+.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x))
(fma.f64 (/.f64 x x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x)
(+.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x)
(/.f64 x x)
#s(literal 1 binary64)
x
(-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))
(/.f64 #s(literal -1/8 binary64) x)
#s(literal -1/8 binary64)
#s(literal 1/2 binary64)
(*.f64 (sqrt.f64 (expm1.f64 (log.f64 x))) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(sqrt.f64 (expm1.f64 (log.f64 x)))
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
(expm1.f64 (log.f64 x))
(-.f64 x #s(literal 1 binary64))
(log.f64 x)
x
(sqrt.f64 x)

localize112.0ms (3.2%)

Memory
-22.6MiB live, 83.8MiB allocated; 21ms collecting garbage
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(sqrt.f64 x)
accuracy0.0
(log.f64 x)
accuracy0.5390625
(*.f64 (sqrt.f64 (expm1.f64 (log.f64 x))) (sqrt.f64 x))
accuracy5.6254414611998325
(expm1.f64 (log.f64 x))
accuracy0.0
(/.f64 x x)
accuracy0.0
(/.f64 #s(literal -1/8 binary64) x)
accuracy0.00390625
(-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))
accuracy1.0564538552107297
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 x x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x))
accuracy0.0
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x)
accuracy0.0
(/.f64 #s(literal -1/2 binary64) x)
accuracy1.3092782491103812
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
accuracy2.3091239153404746
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Samples
74.0ms256×0valid
Compiler

Compiled 86 to 23 computations (73.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 63.0ms
ival-mult: 27.0ms (42.7% of total)
ival-div: 20.0ms (31.6% of total)
ival-sqrt: 5.0ms (7.9% of total)
ival-sub: 3.0ms (4.7% of total)
ival-log: 3.0ms (4.7% of total)
ival-add: 2.0ms (3.2% of total)
ival-expm1: 2.0ms (3.2% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series79.0ms (2.3%)

Memory
6.3MiB live, 94.6MiB allocated; 12ms collecting garbage
Counts
14 → 41
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
(/.f64 #s(literal -1/2 binary64) x)
(/.f64 x x)
(fma.f64 (/.f64 x x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 x x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x))
(-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (expm1.f64 (log.f64 x))) (sqrt.f64 x))
(sqrt.f64 (expm1.f64 (log.f64 x)))
(expm1.f64 (log.f64 x))
(log.f64 x)
(/.f64 #s(literal -1/8 binary64) x)
(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)))))))))
-1/2
(- x 1/2)
(/ -1/2 x)
1
(/ -1/8 x)
(/ (- (* -1/2 x) 1/8) x)
(/ (- (* x (- x 1/2)) 1/8) x)
(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)
(log x)
(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))))
(* -1 (+ 1/2 (* 1/8 (/ 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 (log (/ 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 (* (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)))
(+ (log -1) (* -1 (log (/ -1 x))))
Calls

3 calls:

TimeVariablePointExpression
33.0ms
x
@inf
((* (sqrt (- x 1)) (sqrt x)) (+ (* (/ -1/2 x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ -1/2 x) (/ x x) (+ (* (/ x x) (- (/ -1/8 x) 1/2)) x) (* (sqrt (- x 1)) (sqrt x)) (- (/ -1/8 x) 1/2) (* (sqrt (- (exp (log x)) 1)) (sqrt x)) (sqrt (- (exp (log x)) 1)) (- (exp (log x)) 1) (log x) (/ -1/8 x) (sqrt x))
24.0ms
x
@0
((* (sqrt (- x 1)) (sqrt x)) (+ (* (/ -1/2 x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ -1/2 x) (/ x x) (+ (* (/ x x) (- (/ -1/8 x) 1/2)) x) (* (sqrt (- x 1)) (sqrt x)) (- (/ -1/8 x) 1/2) (* (sqrt (- (exp (log x)) 1)) (sqrt x)) (sqrt (- (exp (log x)) 1)) (- (exp (log x)) 1) (log x) (/ -1/8 x) (sqrt x))
21.0ms
x
@-inf
((* (sqrt (- x 1)) (sqrt x)) (+ (* (/ -1/2 x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ -1/2 x) (/ x x) (+ (* (/ x x) (- (/ -1/8 x) 1/2)) x) (* (sqrt (- x 1)) (sqrt x)) (- (/ -1/8 x) 1/2) (* (sqrt (- (exp (log x)) 1)) (sqrt x)) (sqrt (- (exp (log x)) 1)) (- (exp (log x)) 1) (log x) (/ -1/8 x) (sqrt x))

simplify167.0ms (4.8%)

Memory
-5.9MiB live, 95.1MiB allocated; 12ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0176510
1554441
22335408
37015404
08565380
Stop Event
1×iter limit
1×node limit
Counts
41 → 40
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)))))))))
-1/2
(- x 1/2)
(/ -1/2 x)
1
(/ -1/8 x)
(/ (- (* -1/2 x) 1/8) x)
(/ (- (* x (- x 1/2)) 1/8) x)
(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)
(log x)
(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))))
(* -1 (+ 1/2 (* 1/8 (/ 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 (log (/ 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 (* (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)))
(+ (log -1) (* -1 (log (/ -1 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 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (sqrt.f64 #s(literal -1 binary64))) 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)))
-1/2
#s(literal -1/2 binary64)
(- x 1/2)
(-.f64 x #s(literal 1/2 binary64))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
1
#s(literal 1 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 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1/8 binary64) 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 (/.f64 (fma.f64 #s(literal 1/8 binary64) x #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 (*.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) #s(literal 1/16 binary64)) x (/.f64 (fma.f64 #s(literal 1/8 binary64) x #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))
(log x)
(log.f64 x)
(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 (/.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 x (*.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(* -1 (+ 1/2 (* 1/8 (/ 1 x))))
(-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
(* 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 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(* -1 (log (/ 1 x)))
(log.f64 x)
(* -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 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(* -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 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal -1/2 binary64)) #s(literal 1 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 x (-.f64 (/.f64 #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 3 binary64)))) #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 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 (neg.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) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
(* -1 (* x (- (/ 1 x) 1)))
(*.f64 (neg.f64 x) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))
(+ (log -1) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))

rewrite178.0ms (5.1%)

Memory
5.0MiB live, 239.8MiB allocated; 26ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02389
03779
111771
275271
0828271
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
14 → 366
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
(/.f64 #s(literal -1/2 binary64) x)
(/.f64 x x)
(fma.f64 (/.f64 x x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 x x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x))
(-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (expm1.f64 (log.f64 x))) (sqrt.f64 x))
(sqrt.f64 (expm1.f64 (log.f64 x)))
(expm1.f64 (log.f64 x))
(log.f64 x)
(/.f64 #s(literal -1/8 binary64) x)
(sqrt.f64 x)
Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
(*.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (+.f64 #s(literal 1/4 binary64) (*.f64 x (-.f64 x #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 #s(literal 1/4 binary64) (*.f64 x x))) (-.f64 x #s(literal 1/2 binary64)))
(*.f64 (/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/8 binary64)) (-.f64 #s(literal 1/16 binary64) (pow.f64 (*.f64 x (+.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (-.f64 #s(literal 1/4 binary64) (*.f64 x (+.f64 x #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/64 binary64) (pow.f64 (*.f64 x (+.f64 x #s(literal 1/2 binary64))) #s(literal 3 binary64)))) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x (+.f64 x #s(literal 1/2 binary64))) (-.f64 (*.f64 x (+.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)))))
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) #s(literal 1 binary64)) x)
(*.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) x)
(*.f64 (-.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
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(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(/.f64 (hypot.f64 (pow.f64 (cosh.f64 (log.f64 x)) #s(literal 3/2 binary64)) (pow.f64 (sinh.f64 (log.f64 x)) #s(literal 3/2 binary64))) (sqrt.f64 (+.f64 (pow.f64 (cosh.f64 (log.f64 x)) #s(literal 2 binary64)) (*.f64 (sinh.f64 (log.f64 x)) (-.f64 (sinh.f64 (log.f64 x)) (cosh.f64 (log.f64 x)))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(sqrt.f64 x)
(exp.f64 (/.f64 (log.f64 x) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (/.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (/.f64 (log.f64 x) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64))))

eval67.0ms (1.9%)

Memory
32.8MiB live, 133.6MiB allocated; 24ms collecting garbage
Compiler

Compiled 12 374 to 1 652 computations (86.6% saved)

prune8.0ms (0.2%)

Memory
-19.1MiB live, 26.5MiB allocated; 4ms collecting garbage
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New3963399
Fresh000
Picked314
Done011
Total3995404
Accuracy
100.0%
Counts
404 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.2%
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶57.1%
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
▶98.3%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
▶98.0%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
✓96.4%
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Compiler

Compiled 48 to 39 computations (18.8% saved)

simplify5.0ms (0.1%)

Memory
10.0MiB live, 10.0MiB allocated; 0ms collecting garbage
Algorithm
1×egg-herbie
Localize:

Found 9 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 1/2 binary64) x)
cost-diff0
(/.f64 #s(literal -1/8 binary64) x)
cost-diff0
(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
cost-diff0
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 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)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01763
02463
13063
23163
33363
43463
53563
63663
73863
03863
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#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 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal -1/8 binary64) x)
#s(literal -1/8 binary64)
x
(-.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 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 #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 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) x) #s(literal 1/2 binary64)))
(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
(-.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) x) #s(literal 1/2 binary64))
(/.f64 #s(literal -1/8 binary64) x)
#s(literal -1/8 binary64)
x
(-.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 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)

localize34.0ms (1%)

Memory
12.2MiB live, 58.7MiB allocated; 3ms collecting garbage
Localize:

Found 9 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(-.f64 x #s(literal 1 binary64))
accuracy0.0
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
accuracy27.473951016001372
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
accuracy0.0
(/.f64 #s(literal -1/8 binary64) x)
accuracy0.0
(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
accuracy0.0
(-.f64 #s(literal 1/2 binary64) x)
accuracy1.0564538552107297
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
accuracy0.0
(-.f64 x #s(literal 1/2 binary64))
accuracy1.3092782491103812
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
Samples
25.0ms256×0valid
Compiler

Compiled 53 to 16 computations (69.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 16.0ms
ival-sqrt: 6.0ms (36.7% of total)
ival-sub: 5.0ms (30.6% of total)
ival-mult: 3.0ms (18.3% of total)
ival-div: 2.0ms (12.2% of total)
ival-true: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory
4.9MiB live, 4.9MiB allocated; 0ms collecting garbage
Counts
9 → 33
Calls
Call 1
Inputs
#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 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal -1/8 binary64) x)
(-.f64 #s(literal 1/2 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))
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)))))))))
-1/2
(- x 1/2)
(/ -1/8 x)
(/ (- (* -1/2 x) 1/8) x)
(/ (- (* x (- x 1/2)) 1/8) x)
1/2
(+ 1/2 (* -1 x))
(* -1 x)
(* x (- x 1))
-1
(- x 1)
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 (- (* 1/2 (/ 1 x)) 1))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* 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 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 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
1.0ms
x
@-inf
((* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (* (sqrt (- x 1)) (sqrt x)) (- (/ -1/8 x) (- 1/2 x)) (/ -1/8 x) (- 1/2 x) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1))
1.0ms
x
@0
((* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (* (sqrt (- x 1)) (sqrt x)) (- (/ -1/8 x) (- 1/2 x)) (/ -1/8 x) (- 1/2 x) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1))
1.0ms
x
@inf
((* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (* (sqrt (- x 1)) (sqrt x)) (- (/ -1/8 x) (- 1/2 x)) (/ -1/8 x) (- 1/2 x) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1))

simplify143.0ms (4.1%)

Memory
-10.8MiB live, 127.8MiB allocated; 32ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0125299
1387271
21574233
35299230
08111224
Stop Event
1×iter limit
1×node limit
Counts
33 → 32
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)))))))))
-1/2
(- x 1/2)
(/ -1/8 x)
(/ (- (* -1/2 x) 1/8) x)
(/ (- (* x (- x 1/2)) 1/8) x)
1/2
(+ 1/2 (* -1 x))
(* -1 x)
(* x (- x 1))
-1
(- x 1)
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 (- (* 1/2 (/ 1 x)) 1))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* 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 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 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 (*.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (sqrt.f64 #s(literal -1 binary64))) 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)))
-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 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))
(/ (- (* x (- x 1/2)) 1/8) x)
(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1 x))
(-.f64 #s(literal 1/2 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))
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 (/.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 x (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal -1/2 binary64)))
(* x (- (* 1/2 (/ 1 x)) 1))
(-.f64 #s(literal 1/2 binary64) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 x)))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x) x)
(* x (- 1 (/ 1 x)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(* -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 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(* -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 x (-.f64 (/.f64 #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)
(* -1 (* x (- (/ 1 x) 1)))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (neg.f64 x))

rewrite197.0ms (5.7%)

Memory
-25.8MiB live, 161.7MiB allocated; 47ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01756
02454
18254
255254
0837254
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
9 → 236
Calls
Call 1
Inputs
#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 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal -1/8 binary64) x)
(-.f64 #s(literal 1/2 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))
Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
(*.f64 (/.f64 (-.f64 (*.f64 x x) #s(literal 1/4 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 x (-.f64 x #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (/.f64 (-.f64 (*.f64 x x) #s(literal 1/4 binary64)) (fma.f64 (neg.f64 x) x #s(literal 1/4 binary64))) (-.f64 #s(literal 1/2 binary64) x))
(*.f64 (/.f64 (-.f64 (*.f64 x x) #s(literal 1/4 binary64)) (-.f64 (*.f64 x x) #s(literal 1/4 binary64))) (-.f64 x #s(literal 1/2 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)) #s(literal 2 binary64)))) (-.f64 (*.f64 x (-.f64 x #s(literal 1/2 binary64))) #s(literal 1/4 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (+.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)) (-.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (-.f64 (*.f64 (*.f64 x (/.f64 x (+.f64 #s(literal 1/2 binary64) x))) (*.f64 x (/.f64 x (+.f64 #s(literal 1/2 binary64) x)))) (*.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) x)))) (fma.f64 x (/.f64 x (+.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) x))))
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(+.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x)) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x)) #s(literal 1/2 binary64))))
(*.f64 (/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))
(*.f64 (/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (fma.f64 x x #s(literal -1 binary64))) (-.f64 x #s(literal 1 binary64)))
(*.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 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (-.f64 (fma.f64 x x #s(literal -1 binary64)) x))
(*.f64 (/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) x) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) x)
(*.f64 (/.f64 x (+.f64 #s(literal 1 binary64) x)) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (+.f64 #s(literal 1 binary64) x)))
(*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 x (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1 binary64))
(*.f64 (-.f64 x #s(literal 1 binary64)) (/.f64 x #s(literal 1 binary64)))
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(*.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(*.f64 x (*.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))
(*.f64 x (-.f64 x #s(literal 1 binary64)))
(/.f64 (*.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) x) (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64)))
(/.f64 (*.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) x) (neg.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (*.f64 x (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64)))
(/.f64 (*.f64 x (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x x)) (fma.f64 x x x))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (neg.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64)))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) x)) (neg.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (+.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) x) (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1 binary64))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (neg.f64 x))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (neg.f64 x))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) (neg.f64 x))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (neg.f64 x))
(fma.f64 (*.f64 x x) #s(literal 1 binary64) (neg.f64 x))
(fma.f64 (neg.f64 x) (neg.f64 x) (neg.f64 x))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) (neg.f64 x))
(fma.f64 x x (neg.f64 x))
(-.f64 (*.f64 x x) x)
(+.f64 (*.f64 x x) (neg.f64 x))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (-.f64 x #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (-.f64 (fma.f64 x x #s(literal -1 binary64)) x))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (-.f64 x #s(literal 1 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (-.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 (*.f64 (*.f64 x (/.f64 x (+.f64 #s(literal 1 binary64) x))) (*.f64 x (/.f64 x (+.f64 #s(literal 1 binary64) 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)))) (fma.f64 x (/.f64 x (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))) (*.f64 (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))) (+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (*.f64 x (/.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 x (/.f64 x (+.f64 #s(literal 1 binary64) x))) (*.f64 x (/.f64 x (+.f64 #s(literal 1 binary64) x))) (fma.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 x (/.f64 x (+.f64 #s(literal 1 binary64) x))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (fma.f64 (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (neg.f64 (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (-.f64 (fma.f64 x x (pow.f64 x #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (*.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (*.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1 binary64)) (*.f64 (+.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) x))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(neg.f64 (/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) x)))
(neg.f64 (/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(neg.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64))))
(neg.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (neg.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))))
(-.f64 (*.f64 x (/.f64 x (+.f64 #s(literal 1 binary64) x))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(-.f64 x #s(literal 1 binary64))

eval30.0ms (0.9%)

Memory
27.4MiB live, 71.7MiB allocated; 4ms collecting garbage
Compiler

Compiled 7 242 to 1 079 computations (85.1% saved)

prune8.0ms (0.2%)

Memory
-19.7MiB live, 25.3MiB allocated; 3ms collecting garbage
Pruning

5 alts after pruning (0 fresh and 5 done)

PrunedKeptTotal
New2610261
Fresh000
Picked033
Done022
Total2615266
Accuracy
100.0%
Counts
266 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.2%
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓57.1%
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
✓98.3%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
✓98.0%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
✓96.4%
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Compiler

Compiled 135 to 73 computations (45.9% saved)

regimes5.0ms (0.2%)

Memory
13.2MiB live, 13.2MiB allocated; 0ms collecting garbage
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 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 x x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x))
(*.f64 (sqrt.f64 (expm1.f64 (log.f64 x))) (sqrt.f64 x))
Outputs
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Calls

2 calls:

2.0ms
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
2.0ms
x
Results
AccuracySegmentsBranch
99.2%1(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
99.2%1x
Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes4.0ms (0.1%)

Memory
8.5MiB live, 8.5MiB allocated; 0ms collecting garbage
Counts
5 → 2
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 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
Outputs
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Calls

2 calls:

2.0ms
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
2.0ms
x
Results
AccuracySegmentsBranch
100.0%2(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
100.0%2x
Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes4.0ms (0.1%)

Memory
8.5MiB live, 8.5MiB allocated; 0ms collecting garbage
Counts
4 → 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 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
Calls

2 calls:

2.0ms
x
2.0ms
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Results
AccuracySegmentsBranch
98.3%1(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
98.3%1x
Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0.1%)

Memory
7.4MiB live, 7.4MiB allocated; 0ms collecting garbage
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:

1.0ms
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
1.0ms
x
Results
AccuracySegmentsBranch
98.0%1(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
98.0%1x
Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes2.0ms (0.1%)

Memory
6.1MiB live, 6.1MiB allocated; 0ms collecting garbage
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
96.4%1(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
96.4%1x
Compiler

Compiled 8 to 7 computations (12.5% saved)

bsearch7.0ms (0.2%)

Memory
-55.2MiB live, 5.2MiB allocated; 6ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×predicate-same
Steps
TimeLeftRight
6.0ms
1470075391921130.0
44640149995340910.0
Samples
4.0ms16×1valid
1.0ms16×0valid
Compiler

Compiled 40 to 38 computations (5% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.0ms
ival-sqrt: 1.0ms (82.7% of total)
adjust: 0.0ms (0% of total)
ival-mult: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-sub: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

simplify85.0ms (2.4%)

Memory
12.3MiB live, 58.2MiB allocated; 5ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02461
13561
25061
36361
49961
514661
619061
722161
825461
927961
1045961
11321361
Stop Event
1×node limit
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(if (<=.f64 x #s(literal 10000000000000000 binary64)) (sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x)) #s(approx (* (sqrt (- x 1)) (sqrt x)) x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 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
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(if (<=.f64 x #s(literal 10000000000000000 binary64)) (sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x)) #s(approx (* (sqrt (- x 1)) (sqrt x)) x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

derivations610.0ms (17.5%)

Memory
39.3MiB live, 461.6MiB allocated; 66ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02389
03779
111771
275271
0828271
0176510
1554441
22335408
37015404
08565380
0150457
1495390
22202378
37444375
08362345
0616
01015
13215
214815
3118915
0961413
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
Compiler

Compiled 61 to 25 computations (59% saved)

preprocess36.0ms (1%)

Memory
-1.3MiB live, 45.4MiB allocated; 2ms collecting garbage
Compiler

Compiled 136 to 62 computations (54.4% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Profiling

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