Main:bigenough3 from C

Time bar (total: 4.5s)

start0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

analyze2.0ms (0.1%)

Memory
6.4MiB live, 6.4MiB 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
50%50%50%0%0%0%0%2
66.7%50%25%0%0%25%0%3
80%50%12.5%0%0%37.5%0%4
88.9%50%6.2%0%0%43.7%0%5
94.1%50%3.1%0%0%46.9%0%6
97%50%1.6%0%0%48.4%0%7
98.5%50%0.8%0%0%49.2%0%8
99.2%50%0.4%0%0%49.6%0%9
99.6%50%0.2%0%0%49.8%0%10
99.8%50%0.1%0%0%49.9%0%11
99.9%50%0%0%0%49.9%0%12
Compiler

Compiled 9 to 8 computations (11.1% saved)

sample1.2s (27.6%)

Memory
40.1MiB live, 1 346.5MiB allocated; 363ms collecting garbage
Samples
656.0ms4 004×1valid
193.0ms4 252×0valid
0.0ms7×0invalid
Precisions
Click to see histograms. Total time spent on operations: 540.0ms
ival-sqrt: 236.0ms (43.7% of total)
adjust: 151.0ms (28% of total)
ival-add: 84.0ms (15.6% of total)
ival-sub: 55.0ms (10.2% of total)
ival-true: 6.0ms (1.1% of total)
exact: 5.0ms (0.9% of total)
ival-assert: 3.0ms (0.6% of total)
Bogosity

explain120.0ms (2.7%)

Memory
-16.4MiB live, 84.5MiB allocated; 13ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1270-0-(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
00-0-(+.f64 x #s(literal 1 binary64))
00-0-(sqrt.f64 x)
00-0-#s(literal 1 binary64)
00-0-(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))cancellation1270
Confusion
Predicted +Predicted -
+1270
-0129
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+12700
-00129
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
0129
1127
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
60.0ms254×1valid
12.0ms258×0valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 25.0ms
ival-sqrt: 10.0ms (40.2% of total)
adjust: 7.0ms (28.1% of total)
ival-add: 4.0ms (16.1% of total)
ival-sub: 3.0ms (12% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

preprocess13.0ms (0.3%)

Memory
9.9MiB live, 9.9MiB allocated; 0ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0819
11119
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 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶52.6%
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0.1%)

Memory
3.7MiB live, 3.7MiB 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 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
x
#s(literal 1 binary64)
(sqrt.f64 x)

localize26.0ms (0.6%)

Memory
30.2MiB live, 30.2MiB allocated; 0ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(+.f64 x #s(literal 1 binary64))
accuracy0.0
(sqrt.f64 x)
accuracy0.0078125
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy30.323675792379568
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Samples
13.0ms127×1valid
6.0ms129×0valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.0ms
ival-sqrt: 5.0ms (40.4% of total)
adjust: 3.0ms (24.2% of total)
ival-add: 2.0ms (16.2% of total)
ival-sub: 2.0ms (16.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series19.0ms (0.4%)

Memory
-38.6MiB live, 6.7MiB allocated; 4ms collecting garbage
Counts
4 → 27
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
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(+ 1 x)
(sqrt x)
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
x
(* x (+ 1 (/ 1 x)))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
Calls

3 calls:

TimeVariablePointExpression
16.0ms
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))

simplify191.0ms (4.3%)

Memory
36.4MiB live, 177.5MiB allocated; 17ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0113451
1331393
21209387
34903387
08229353
Stop Event
1×iter limit
1×node limit
Counts
27 → 26
Calls
Call 1
Inputs
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(+ 1 x)
(sqrt x)
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
x
(* x (+ 1 (/ 1 x)))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
Outputs
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 x)
(-.f64 x #s(literal -1 binary64))
(sqrt x)
(sqrt.f64 x)
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -5/128 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(*.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)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(*.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)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(*.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 (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)
x
(* x (+ 1 (/ 1 x)))
(-.f64 x #s(literal -1 binary64))
(* -1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(/.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(/.f64 (fma.f64 #s(literal 5/128 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.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)
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 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))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 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)

rewrite226.0ms (5.1%)

Memory
-5.7MiB live, 233.4MiB allocated; 35ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
01016
14216
227116
3293216
0909916
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 281
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 (-.f64 (-.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (-.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x)))
(*.f64 (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) x) (-.f64 (-.f64 #s(literal 1 binary64) x) x)) (-.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (pow.f64 (-.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x)) #s(literal 2 binary64))) (-.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x)))
(*.f64 (/.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (pow.f64 (-.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)))) (fma.f64 (-.f64 (hypot.f64 (sqrt.f64 x) x) x) (-.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x)) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
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(/.f64 (-.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64)))) #s(literal 2 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -2 binary64))) (fma.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))
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(/.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 3 binary64))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -3 binary64))) (+.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -2 binary64)) (*.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64)))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))))
(/.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) #s(literal 2 binary64)) (-.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -2 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(/.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal 2 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (*.f64 (sinh.f64 (acosh.f64 x)) (cosh.f64 (asinh.f64 (pow.f64 x #s(literal 3/2 binary64))))) (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) x)))
(/.f64 (*.f64 (cosh.f64 (asinh.f64 (pow.f64 x #s(literal 3/2 binary64)))) (sinh.f64 (acosh.f64 x))) (*.f64 (hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) x) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))))
(/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (hypot.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x #s(literal 1 binary64))) (*.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (sinh.f64 (acosh.f64 (*.f64 x x))) (sinh.f64 (acosh.f64 x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal 2 binary64)) (-.f64 x #s(literal 1 binary64))))
(/.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 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(/.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 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 x #s(literal 1 binary64)))
(/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(neg.f64 (-.f64 #s(literal 1 binary64) x))
(fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 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) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(fma.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -2 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64))
(fma.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1 binary64))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) x #s(literal 1 binary64))
(fma.f64 x (/.f64 (*.f64 x x) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(fma.f64 x #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 x #s(literal 1 binary64) #s(literal 1 binary64))
(sin.f64 (acos.f64 x))
(cosh.f64 (asinh.f64 x))
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
(-.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))
(-.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(-.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64)))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) x)
(fabs.f64 (-.f64 #s(literal 1 binary64) x))
(cos.f64 (asin.f64 x))
(hypot.f64 (fabs.f64 (hypot.f64 (sqrt.f64 x) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(hypot.f64 (hypot.f64 (sqrt.f64 x) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (fabs.f64 (hypot.f64 (sqrt.f64 x) x)))
(hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (hypot.f64 (sqrt.f64 x) x))
(exp.f64 (log1p.f64 x))
(+.f64 (cosh.f64 (log1p.f64 x)) (sinh.f64 (log1p.f64 x)))
(+.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) x)
(+.f64 x #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3/4 binary64))))
(*.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (neg.f64 (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 x #s(literal 1/4 binary64))))
(*.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) (sqrt.f64 #s(literal -1 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 (fabs.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 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/8 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(neg.f64 (sqrt.f64 x))
(sqrt.f64 x)
(fabs.f64 (sqrt.f64 x))
(exp.f64 (/.f64 (log.f64 x) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 x)) #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 (sqrt.f64 x)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (sqrt.f64 x)))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 x))) (sinh.f64 (log.f64 (sqrt.f64 x))))

eval36.0ms (0.8%)

Memory
-6.8MiB live, 82.7MiB allocated; 7ms collecting garbage
Compiler

Compiled 5 730 to 1 085 computations (81.1% saved)

prune6.0ms (0.1%)

Memory
24.0MiB live, 24.0MiB allocated; 0ms collecting garbage
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New3015306
Fresh000
Picked101
Done000
Total3025307
Accuracy
99.9%
Counts
307 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶3.5%
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
▶50.6%
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
▶52.4%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
▶49.9%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
▶52.8%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
Compiler

Compiled 136 to 110 computations (19.1% saved)

simplify14.0ms (0.3%)

Memory
-44.5MiB live, 13.7MiB allocated; 5ms collecting garbage
Algorithm
1×egg-herbie
Localize:

Found 18 expressions of interest:

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

Useful iterations: 0 (0.0ms)

IterNodesCost
024159
037159
155159
286159
3132159
4205159
5300159
6363159
7368159
0368159
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal 1/2 binary64)
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 x)
x
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(literal 1/2 binary64)
x
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 x)
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) (sqrt.f64 x))
(sqrt.f64 x)
x
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal -1/8 binary64)
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
#s(literal 1/2 binary64)
(sqrt.f64 x)
Outputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal 1/2 binary64)
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 x)
x
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(literal 1/2 binary64)
x
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 x)
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) (sqrt.f64 x))
(sqrt.f64 x)
x
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal -1/8 binary64)
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 x)

localize170.0ms (3.8%)

Memory
7.2MiB live, 185.8MiB allocated; 60ms collecting garbage
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
accuracy0.01171875
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
accuracy0.11328125
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy0.21875
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
accuracy31.947797338101932
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
accuracy0.0
(sqrt.f64 x)
accuracy30.144322171059915
#s(approx (sqrt (+ x 1)) (sqrt.f64 x))
accuracy30.323675792379568
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
accuracy0.0
(sqrt.f64 x)
accuracy0.00390625
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy0.01171875
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
accuracy30.434511672065792
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
accuracy0.0
(sqrt.f64 x)
accuracy30.01343011231706
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
accuracy30.323675792379568
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
accuracy0.0
(/.f64 #s(literal 1 binary64) x)
accuracy0.0
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
accuracy0.11328125
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy30.126039565667224
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
Samples
64.0ms127×1valid
18.0ms129×0valid
Compiler

Compiled 126 to 20 computations (84.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 51.0ms
ival-add: 22.0ms (43.3% of total)
adjust: 8.0ms (15.8% of total)
ival-mult: 7.0ms (13.8% of total)
ival-sqrt: 7.0ms (13.8% of total)
ival-div: 4.0ms (7.9% of total)
ival-sub: 3.0ms (5.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series8.0ms (0.2%)

Memory
24.6MiB live, 24.6MiB allocated; 0ms collecting garbage
Counts
15 → 47
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
(sqrt.f64 x)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
Outputs
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(sqrt (/ 1 x))
(/ 1 x)
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* -1/8 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* x (- 1/2 (sqrt (/ 1 x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(* -1 (sqrt x))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(* 1/2 (sqrt x))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* (sqrt x) (pow (sqrt -1) 2))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
Calls

3 calls:

TimeVariablePointExpression
3.0ms
x
@-inf
((- (sqrt (+ x 1)) (sqrt x)) (* (sqrt (/ 1 x)) 1/2) (sqrt (/ 1 x)) (/ 1 x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (+ (* 1/2 x) (- 1 (sqrt x))) (- 1 (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))))
3.0ms
x
@0
((- (sqrt (+ x 1)) (sqrt x)) (* (sqrt (/ 1 x)) 1/2) (sqrt (/ 1 x)) (/ 1 x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (+ (* 1/2 x) (- 1 (sqrt x))) (- 1 (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))))
2.0ms
x
@inf
((- (sqrt (+ x 1)) (sqrt x)) (* (sqrt (/ 1 x)) 1/2) (sqrt (/ 1 x)) (/ 1 x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (+ (* 1/2 x) (- 1 (sqrt x))) (- 1 (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))))

simplify176.0ms (3.9%)

Memory
9.4MiB live, 198.8MiB allocated; 25ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0144673
1424585
21613576
35880576
08179534
Stop Event
1×iter limit
1×node limit
Counts
47 → 47
Calls
Call 1
Inputs
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(sqrt (/ 1 x))
(/ 1 x)
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* -1/8 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* x (- 1/2 (sqrt (/ 1 x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(* -1 (sqrt x))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(* 1/2 (sqrt x))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* (sqrt x) (pow (sqrt -1) 2))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
Outputs
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(* -1/8 (sqrt (/ 1 (pow x 3))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 x x))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -5/128 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(*.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)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(*.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)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(*.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 (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)
(* x (- 1/2 (sqrt (/ 1 x))))
(*.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(fma.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x #s(literal 1 binary64))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(fma.f64 (neg.f64 x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(* 1/2 (sqrt x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)
(* -1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(/.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(/.f64 (fma.f64 #s(literal 5/128 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) x)
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.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)
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 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))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 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)
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(*.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x #s(literal 1 binary64))
(* (sqrt x) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 x))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(fma.f64 (neg.f64 x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 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 1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)

rewrite232.0ms (5.2%)

Memory
-14.1MiB live, 260.3MiB allocated; 85ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
024129
037129
1145121
21033119
08352116
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
15 → 323
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
(sqrt.f64 x)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
Outputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x))) (/.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x))))
(*.f64 (/.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x))) (/.f64 #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x))))
(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 (sqrt.f64 x) (sqrt.f64 x)))
(*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x)
(/.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (neg.f64 x))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 x)))
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(neg.f64 (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (neg.f64 x)))
(neg.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (neg.f64 (sqrt.f64 x))) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (neg.f64 (sqrt.f64 x))))
(*.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 x)) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 x)))
(*.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) x))
(*.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) x) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (/.f64 (sqrt.f64 x) #s(literal 1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (neg.f64 (pow.f64 x #s(literal -1/4 binary64))) (neg.f64 (pow.f64 x #s(literal -1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal -1/4 binary64))) (fabs.f64 (pow.f64 x #s(literal -1/4 binary64))))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal -1/2 binary64))) (sqrt.f64 (pow.f64 x #s(literal -1/2 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 (pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (/.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x))))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (sqrt.f64 x) (sqrt.f64 x)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64)))
(pow.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) #s(literal 1/4 binary64))
(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 (sqrt.f64 x) #s(literal -1 binary64))
(pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 x #s(literal -1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (neg.f64 x))))
(/.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 x))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 x)))
(/.f64 (sqrt.f64 x) x)
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(sqrt.f64 (/.f64 x (*.f64 x x)))
(sqrt.f64 (pow.f64 x #s(literal -1 binary64)))
(fabs.f64 (pow.f64 x #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (log.f64 (sqrt.f64 x))))
(exp.f64 (/.f64 (neg.f64 (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 x)) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (*.f64 (neg.f64 (log.f64 x)) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (neg.f64 (log.f64 x)) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64)))
(pow.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -2 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(pow.f64 x #s(literal -1 binary64))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x)
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (*.f64 (sqrt.f64 (neg.f64 x)) (neg.f64 (sqrt.f64 x))))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 x)))
(/.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (neg.f64 x))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 x) (sqrt.f64 (neg.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 x))
(/.f64 #s(literal 1 binary64) x)
(neg.f64 (/.f64 #s(literal -1 binary64) x))
(sqrt.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64))))
(exp.f64 (fma.f64 (neg.f64 (log.f64 x)) #s(literal 1/2 binary64) (*.f64 (neg.f64 (log.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (*.f64 (neg.f64 (log.f64 x)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (neg.f64 (log.f64 x)))
(+.f64 (cosh.f64 (neg.f64 (log.f64 x))) (sinh.f64 (neg.f64 (log.f64 x))))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 2 binary64)) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))) (/.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 2 binary64)) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64))))) (*.f64 (/.f64 x (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))) (/.f64 x (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))))) (+.f64 (/.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 2 binary64)) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))) (/.f64 x (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64))))))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 3 binary64)) (fma.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (fma.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) x))) (/.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 3 binary64)) (fma.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (fma.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) x)))) (*.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (fma.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) x))) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (fma.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) x))))) (+.f64 (/.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 3 binary64)) (fma.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (fma.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) x))) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (fma.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 2 binary64)) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 x (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 2 binary64)) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))) (/.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 2 binary64)) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))) (fma.f64 (/.f64 x (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))) (/.f64 x (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))) (*.f64 (/.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 2 binary64)) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))) (/.f64 x (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 3 binary64)) (fma.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (fma.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (fma.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 3 binary64)) (fma.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (fma.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) x))) (/.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 3 binary64)) (fma.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (fma.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) x))) (fma.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (fma.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) x))) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (fma.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) x))) (*.f64 (/.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 3 binary64)) (fma.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (fma.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) x))) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (fma.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) x)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 2 binary64)) x))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64))))))
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(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1/8 binary64) (*.f64 (neg.f64 (neg.f64 (sqrt.f64 x))) #s(literal 1/2 binary64)))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1/8 binary64) (*.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1/2 binary64)))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
(-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))) (/.f64 (/.f64 #s(literal 1/64 binary64) x) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))))
(-.f64 (/.f64 (*.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64))) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))))) (/.f64 (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1/8 binary64)) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))))))
(-.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) x) (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) (/.f64 (*.f64 #s(literal 1/4 binary64) x) (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))))
(-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(-.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))
(+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (fma.f64 #s(literal 1/4 binary64) x (-.f64 (/.f64 #s(literal 1/64 binary64) x) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))))) (/.f64 (*.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64))) (fma.f64 #s(literal 1/4 binary64) x (-.f64 (/.f64 #s(literal 1/64 binary64) x) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))))))
(+.f64 (/.f64 (*.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64))) (fma.f64 #s(literal 1/4 binary64) x (-.f64 (/.f64 #s(literal 1/64 binary64) x) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))))) (/.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (fma.f64 #s(literal 1/4 binary64) x (-.f64 (/.f64 #s(literal 1/64 binary64) x) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))))))
(+.f64 (neg.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (neg.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))
(+.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (neg.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))
(+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (fma.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x))) (/.f64 (*.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64))) (fma.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x))))
(+.f64 (/.f64 (*.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64))) (fma.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x))) (/.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (fma.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x))))
(+.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) x) (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) (/.f64 (neg.f64 (*.f64 #s(literal 1/4 binary64) x)) (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))))
(+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (neg.f64 (neg.f64 (sqrt.f64 x))) #s(literal 1/2 binary64)))
(+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1/2 binary64)))
(+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
(+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))

eval102.0ms (2.3%)

Memory
20.5MiB live, 115.7MiB allocated; 24ms collecting garbage
Compiler

Compiled 15 034 to 1 813 computations (87.9% saved)

prune18.0ms (0.4%)

Memory
-10.3MiB live, 36.1MiB allocated; 4ms collecting garbage
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New5086514
Fresh000
Picked235
Done000
Total5109519
Accuracy
100.0%
Counts
519 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓50.6%
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
✓52.4%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
▶3.0%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))))
49.9%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
▶52.7%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x))
▶52.7%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
▶52.4%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))
✓52.8%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
▶52.6%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x)))
Compiler

Compiled 224 to 174 computations (22.3% saved)

simplify9.0ms (0.2%)

Memory
15.5MiB live, 15.5MiB allocated; 0ms collecting garbage
Algorithm
1×egg-herbie
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 x)
cost-diff0
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
cost-diff0
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
cost-diff0
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x))
cost-diff0
(/.f64 #s(literal 1/2 binary64) x)
cost-diff0
(sqrt.f64 x)
cost-diff0
(*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x))
cost-diff0
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x)))
cost-diff0
(sqrt.f64 x)
cost-diff0
(-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x)))
cost-diff0
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))
cost-diff1
(-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))
cost-diff0
(neg.f64 (sqrt.f64 x))
cost-diff0
#s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))
cost-diff0
(fma.f64 #s(literal 1/2 binary64) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))))
cost-diff0
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))))
cost-diff0
(sqrt.f64 x)
cost-diff0
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
cost-diff0
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
025158
037158
149158
262158
379158
4100158
5108158
6124158
7148158
8160158
9166158
10170158
11172158
0172155
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
#s(literal 1/2 binary64)
(sqrt.f64 x)
x
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))))
(fma.f64 #s(literal 1/2 binary64) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))))
#s(literal 1/2 binary64)
x
#s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))
(neg.f64 (sqrt.f64 x))
(sqrt.f64 x)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))
(-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x)))
#s(literal 1 binary64)
(-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))
(sqrt.f64 x)
x
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x)))
(*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x))
(sqrt.f64 x)
x
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x))
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(sqrt.f64 x)
x
#s(literal 1/2 binary64)
Outputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
#s(literal 1/2 binary64)
(sqrt.f64 x)
x
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))))
(fma.f64 #s(literal 1/2 binary64) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))))
#s(literal 1/2 binary64)
x
#s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))
(neg.f64 (sqrt.f64 x))
(sqrt.f64 x)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x)))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(literal 1 binary64)
(-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x))
(sqrt.f64 x)
x
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (/.f64 (sqrt.f64 x) x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 (/.f64 (sqrt.f64 x) x) #s(literal 1/2 binary64))
(sqrt.f64 x)
x
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (/.f64 (sqrt.f64 x) x) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
(*.f64 (/.f64 (sqrt.f64 x) x) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(sqrt.f64 x)
x
#s(literal 1/2 binary64)

localize114.0ms (2.5%)

Memory
23.4MiB live, 112.4MiB allocated; 16ms collecting garbage
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
accuracy0.0
(sqrt.f64 x)
accuracy0.2421875
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
accuracy30.126039565667224
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x))
accuracy0.0
(/.f64 #s(literal 1/2 binary64) x)
accuracy0.0
(sqrt.f64 x)
accuracy0.33107377930532605
(*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x))
accuracy30.126039565667224
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x)))
accuracy0.0
(*.f64 #s(literal 1/2 binary64) x)
accuracy0.0
(sqrt.f64 x)
accuracy0.02734375
(-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))
accuracy30.434511672065792
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))
accuracy0.0
(neg.f64 (sqrt.f64 x))
accuracy0.01171875
(fma.f64 #s(literal 1/2 binary64) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))))
accuracy30.434511672065792
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))))
accuracy32.24508934129339
#s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))
accuracy0.0
(sqrt.f64 x)
accuracy0.28515625
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
accuracy30.126039565667224
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
Samples
58.0ms129×0valid
39.0ms127×1valid
Compiler

Compiled 113 to 20 computations (82.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 42.0ms
adjust: 9.0ms (21.5% of total)
ival-div: 7.0ms (16.7% of total)
ival-add: 7.0ms (16.7% of total)
ival-mult: 6.0ms (14.3% of total)
ival-sub: 6.0ms (14.3% of total)
ival-sqrt: 5.0ms (12% of total)
ival-neg: 2.0ms (4.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series34.0ms (0.8%)

Memory
-40.6MiB live, 12.9MiB allocated; 22ms collecting garbage
Counts
17 → 30
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(sqrt.f64 x)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))))
(fma.f64 #s(literal 1/2 binary64) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))))
#s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))
(neg.f64 (sqrt.f64 x))
(-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))
(-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x)))
(*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/2 binary64) x)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x))
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
Outputs
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(sqrt x)
(* -1 (sqrt x))
(+ (sqrt x) (* -1/2 x))
(/ 1/2 x)
(* 1/2 (sqrt x))
(* 1/2 x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* x (- 1/2 (sqrt (/ 1 x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* x (- (sqrt (/ 1 x)) 1/2))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* (sqrt x) (pow (sqrt -1) 2))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
Calls

3 calls:

TimeVariablePointExpression
28.0ms
x
@inf
((- (sqrt (+ x 1)) (sqrt x)) (/ 1/2 (sqrt x)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (+ (* 1/2 x) (- 1 (sqrt x))) (- 1 (sqrt x)) (neg (sqrt x)) (- (sqrt x) (* 1/2 x)) (- (sqrt (+ x 1)) (sqrt x)) (- 1 (- (sqrt x) (* 1/2 x))) (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (/ 1/2 x)) (/ 1/2 x) (- (sqrt (+ x 1)) (sqrt x)) (/ (* (sqrt x) 1/2) x) (* (sqrt x) 1/2) (* 1/2 x))
4.0ms
x
@-inf
((- (sqrt (+ x 1)) (sqrt x)) (/ 1/2 (sqrt x)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (+ (* 1/2 x) (- 1 (sqrt x))) (- 1 (sqrt x)) (neg (sqrt x)) (- (sqrt x) (* 1/2 x)) (- (sqrt (+ x 1)) (sqrt x)) (- 1 (- (sqrt x) (* 1/2 x))) (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (/ 1/2 x)) (/ 1/2 x) (- (sqrt (+ x 1)) (sqrt x)) (/ (* (sqrt x) 1/2) x) (* (sqrt x) 1/2) (* 1/2 x))
1.0ms
x
@0
((- (sqrt (+ x 1)) (sqrt x)) (/ 1/2 (sqrt x)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (+ (* 1/2 x) (- 1 (sqrt x))) (- 1 (sqrt x)) (neg (sqrt x)) (- (sqrt x) (* 1/2 x)) (- (sqrt (+ x 1)) (sqrt x)) (- 1 (- (sqrt x) (* 1/2 x))) (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (/ 1/2 x)) (/ 1/2 x) (- (sqrt (+ x 1)) (sqrt x)) (/ (* (sqrt x) 1/2) x) (* (sqrt x) 1/2) (* 1/2 x))

simplify196.0ms (4.4%)

Memory
28.3MiB live, 262.7MiB allocated; 38ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0102341
1268308
2832303
32877303
47194293
08522273
Stop Event
1×iter limit
1×node limit
Counts
30 → 30
Calls
Call 1
Inputs
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(sqrt x)
(* -1 (sqrt x))
(+ (sqrt x) (* -1/2 x))
(/ 1/2 x)
(* 1/2 (sqrt x))
(* 1/2 x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* x (- 1/2 (sqrt (/ 1 x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* x (- (sqrt (/ 1 x)) 1/2))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* (sqrt x) (pow (sqrt -1) 2))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
Outputs
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(sqrt x)
(sqrt.f64 x)
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(+ (sqrt x) (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* 1/2 (sqrt x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -5/128 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) x)
(* x (- 1/2 (sqrt (/ 1 x))))
(*.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(fma.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x #s(literal 1 binary64))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(fma.f64 (neg.f64 x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(* x (- (sqrt (/ 1 x)) 1/2))
(*.f64 (+.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* -1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(/.f64 (fma.f64 #s(literal -1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(/.f64 (fma.f64 #s(literal -1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 5/128 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(*.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x #s(literal 1 binary64))
(* (sqrt x) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 x))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(fma.f64 (neg.f64 x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (+.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))

rewrite188.0ms (4.2%)

Memory
-15.5MiB live, 231.1MiB allocated; 27ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
025139
037139
1120139
2796135
08366132
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
17 → 199
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(sqrt.f64 x)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))))
(fma.f64 #s(literal 1/2 binary64) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))))
#s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))
(neg.f64 (sqrt.f64 x))
(-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))
(-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x)))
(*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/2 binary64) x)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x))
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
Outputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(neg.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(*.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (neg.f64 (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 (neg.f64 (sqrt.f64 x))) (sqrt.f64 (neg.f64 (sqrt.f64 x))))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal 1/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.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 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(neg.f64 (neg.f64 (sqrt.f64 x)))
(sqrt.f64 x)
(fabs.f64 (neg.f64 (sqrt.f64 x)))
(fabs.f64 (sqrt.f64 x))
(exp.f64 (log.f64 (sqrt.f64 x)))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 x))) (sinh.f64 (log.f64 (sqrt.f64 x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))))) (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))))) (*.f64 (/.f64 (pow.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))))) (/.f64 (pow.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))))))) (+.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))))) (/.f64 (pow.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))))))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (-.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 #s(literal 1/2 binary64) x)) (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (-.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 #s(literal 1/2 binary64) x)) (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))))) (*.f64 (/.f64 (pow.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) #s(literal 3 binary64)) (fma.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (-.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 #s(literal 1/2 binary64) x)) (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))) (/.f64 (pow.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) #s(literal 3 binary64)) (fma.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (-.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 #s(literal 1/2 binary64) x)) (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))))) (-.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (-.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 #s(literal 1/2 binary64) x)) (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))) (/.f64 (pow.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) #s(literal 3 binary64)) (fma.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (-.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 #s(literal 1/2 binary64) x)) (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))))) (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))))) (fma.f64 (/.f64 (pow.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))))) (/.f64 (pow.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))))) (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))))) (/.f64 (pow.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (-.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 #s(literal 1/2 binary64) x)) (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) #s(literal 3 binary64)) (fma.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (-.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 #s(literal 1/2 binary64) x)) (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (-.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 #s(literal 1/2 binary64) x)) (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (-.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 #s(literal 1/2 binary64) x)) (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))) (-.f64 (*.f64 (/.f64 (pow.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) #s(literal 3 binary64)) (fma.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (-.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 #s(literal 1/2 binary64) x)) (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))) (/.f64 (pow.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) #s(literal 3 binary64)) (fma.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (-.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 #s(literal 1/2 binary64) x)) (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))))) (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (-.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 #s(literal 1/2 binary64) x)) (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))) (/.f64 (pow.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) #s(literal 3 binary64)) (fma.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (-.f64 #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 #s(literal 1/2 binary64) x)) (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))))))))
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(-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) x))
(-.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)))
(+.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64)) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (-.f64 (*.f64 #s(literal 1/2 binary64) x) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))))) (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (-.f64 (*.f64 #s(literal 1/2 binary64) x) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))))))
(+.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) x (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 (neg.f64 x) #s(literal -1/2 binary64)))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(*.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (/.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x))))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 (sqrt.f64 x) (sqrt.f64 x)))
(*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))
(/.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (neg.f64 x))
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
(neg.f64 (*.f64 (sqrt.f64 x) (/.f64 #s(literal -1/2 binary64) x)))
(neg.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) (sqrt.f64 x)))
(neg.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1/2 binary64)))
(/.f64 #s(literal -1/2 binary64) (neg.f64 x))
(/.f64 #s(literal 1/2 binary64) x)
(neg.f64 (/.f64 #s(literal -1/2 binary64) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(*.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (/.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x))))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 (sqrt.f64 x) (sqrt.f64 x)))
(*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))
(/.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (neg.f64 x))
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
(neg.f64 (*.f64 (sqrt.f64 x) (/.f64 #s(literal -1/2 binary64) x)))
(neg.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) (sqrt.f64 x)))
(neg.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 x)))
(*.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1/2 binary64))
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(neg.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
(sqrt.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))
(fabs.f64 (*.f64 #s(literal -1/2 binary64) x))
(fabs.f64 (*.f64 #s(literal 1/2 binary64) x))

eval37.0ms (0.8%)

Memory
19.8MiB live, 65.6MiB allocated; 3ms collecting garbage
Compiler

Compiled 8 441 to 1 033 computations (87.8% saved)

prune42.0ms (0.9%)

Memory
-40.4MiB live, 16.9MiB allocated; 6ms collecting garbage
Pruning

8 alts after pruning (2 fresh and 6 done)

PrunedKeptTotal
New2881289
Fresh011
Picked145
Done123
Total2908298
Accuracy
100.0%
Counts
298 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓50.6%
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
✓3.0%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))))
▶49.9%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
✓52.7%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x))
✓52.7%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
▶52.4%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))))
✓52.8%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
✓52.6%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x)))
Compiler

Compiled 115 to 90 computations (21.7% saved)

simplify9.0ms (0.2%)

Memory
4.3MiB live, 4.3MiB allocated; 0ms collecting garbage
Algorithm
1×egg-herbie
Localize:

Found 8 expressions of interest:

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01777
02577
13777
26077
39277
413977
520277
625977
727977
027977
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))))
(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))
#s(literal 1 binary64)
(fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))
x
#s(literal -1/2 binary64)
(sqrt.f64 x)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(sqrt.f64 x)
x
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
#s(literal -1/8 binary64)
Outputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x))))
(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))
(-.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)))
#s(literal 1 binary64)
(fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))
(fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x))
x
#s(literal -1/2 binary64)
(sqrt.f64 x)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(sqrt.f64 x)
x
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
#s(literal -1/8 binary64)

localize58.0ms (1.3%)

Memory
6.5MiB live, 52.3MiB allocated; 3ms collecting garbage
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
accuracy0.01171875
(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
accuracy0.21875
(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
accuracy0.28515625
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
accuracy31.947797338101932
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
accuracy0.0
(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))
accuracy0.0
(sqrt.f64 x)
accuracy0.02734375
(fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))
accuracy30.434511672065792
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))))
Samples
30.0ms127×1valid
12.0ms129×0valid
Compiler

Compiled 64 to 18 computations (71.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 31.0ms
adjust: 8.0ms (25.9% of total)
ival-div: 5.0ms (16.2% of total)
ival-add: 5.0ms (16.2% of total)
ival-sqrt: 5.0ms (16.2% of total)
ival-mult: 4.0ms (12.9% of total)
ival-sub: 3.0ms (9.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory
3.9MiB live, 3.9MiB allocated; 0ms collecting garbage
Counts
8 → 32
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))))
(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))
(fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))
(sqrt.f64 x)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
Outputs
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(sqrt x)
(+ (sqrt x) (* -1/2 x))
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* -1/8 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* x (- 1/2 (sqrt (/ 1 x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(* x (- (sqrt (/ 1 x)) 1/2))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(* 1/2 (sqrt x))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
Calls

3 calls:

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

simplify169.0ms (3.8%)

Memory
25.4MiB live, 112.5MiB allocated; 11ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0113415
1313388
21050381
33497381
47896381
08474355
Stop Event
1×iter limit
1×node limit
Counts
32 → 32
Calls
Call 1
Inputs
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(sqrt x)
(+ (sqrt x) (* -1/2 x))
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* -1/8 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* x (- 1/2 (sqrt (/ 1 x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(* x (- (sqrt (/ 1 x)) 1/2))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(* 1/2 (sqrt x))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
Outputs
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x))
(* -1/8 (sqrt (/ 1 (pow x 3))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 x x))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -5/128 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) x)
(* x (- 1/2 (sqrt (/ 1 x))))
(*.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(fma.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x #s(literal 1 binary64))
(* x (- (sqrt (/ 1 x)) 1/2))
(*.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) x)
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64)))
(* 1/2 (sqrt x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) x)
(* -1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(/.f64 (fma.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(/.f64 (fma.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 5/128 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) x)
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(*.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x #s(literal 1 binary64))
(* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))) x)

rewrite190.0ms (4.3%)

Memory
-4.7MiB live, 138.1MiB allocated; 14ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01769
02569
110469
280669
0853369
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
8 → 264
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))))
(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))
(fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))
(sqrt.f64 x)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
Outputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x))))
(/.f64 (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64))) (+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) x)))
(/.f64 (-.f64 (*.f64 (pow.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal -1 binary64))) (*.f64 (/.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 2 binary64)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64))) (/.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 2 binary64)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64))))) (+.f64 (pow.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 2 binary64)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))) (*.f64 (/.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64))))) (+.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 3 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 2 binary64)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (pow.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 (/.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 2 binary64)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64))) (/.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 2 binary64)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64))) (*.f64 (pow.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 2 binary64)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)))))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 (/.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x)) #s(literal 2 binary64)) x)) (neg.f64 (+.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x)) (sqrt.f64 x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x)) #s(literal 2 binary64)) (+.f64 x (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x)) (sqrt.f64 x))))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 2 binary64)))) (neg.f64 (fma.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal -1 binary64))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64))) (*.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 2 binary64)))) (*.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 3 binary64)))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x)) #s(literal 2 binary64)) x) (+.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x)) (sqrt.f64 x)))
(/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x)) #s(literal 2 binary64)) (+.f64 x (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x)) (sqrt.f64 x)))))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal -1 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 3 binary64))) (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(neg.f64 (/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)) #s(literal 1 binary64))))
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(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) x) (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (*.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x))) (*.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(/.f64 (fma.f64 (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)) (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (*.f64 (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))))) (*.f64 (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))
(/.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) x) (*.f64 #s(literal 1/4 binary64) x)) (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/64 binary64) x))) (neg.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64) (/.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))))) (neg.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (*.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64) (/.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))))) (neg.f64 (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/64 binary64) x)) (neg.f64 (neg.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/64 binary64) x)) (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64) (/.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64) (/.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (*.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64) (/.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(neg.f64 (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(-.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) x) (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) (/.f64 (*.f64 #s(literal 1/4 binary64) x) (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))))
(-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 (/.f64 #s(literal 1/64 binary64) x) (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))
(+.f64 (/.f64 (/.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (*.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))))) (/.f64 (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (*.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))))))
(+.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (*.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))))) (/.f64 (/.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (fma.f64 #s(literal 1/4 binary64) x (*.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))))))
(+.f64 (neg.f64 (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(+.f64 (/.f64 (/.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) (/.f64 (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)) (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))
(+.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)) (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) (/.f64 (/.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))
(+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 (neg.f64 (/.f64 #s(literal 1/64 binary64) x)) (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (neg.f64 (neg.f64 (sqrt.f64 x))) #s(literal 1/2 binary64)))
(+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (neg.f64 (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))))
(+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1/8 binary64) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 x)))))
(/.f64 #s(literal 1/8 binary64) (neg.f64 (sqrt.f64 x)))
(/.f64 #s(literal -1/8 binary64) (neg.f64 (neg.f64 (sqrt.f64 x))))
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
(neg.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))

eval75.0ms (1.7%)

Memory
-7.1MiB live, 91.6MiB allocated; 12ms collecting garbage
Compiler

Compiled 10 090 to 1 354 computations (86.6% saved)

prune12.0ms (0.3%)

Memory
-16.4MiB live, 28.5MiB allocated; 4ms collecting garbage
Pruning

8 alts after pruning (0 fresh and 8 done)

PrunedKeptTotal
New3300330
Fresh000
Picked022
Done066
Total3308338
Accuracy
100.0%
Counts
338 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓50.6%
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
✓3.0%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))))
✓49.9%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
✓52.7%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x))
✓52.7%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
✓52.4%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))))
✓52.8%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
✓52.6%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x)))
Compiler

Compiled 298 to 143 computations (52% saved)

regimes8.0ms (0.2%)

Memory
16.8MiB live, 16.8MiB allocated; 0ms collecting garbage
Counts
13 → 2
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
Outputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
Calls

2 calls:

4.0ms
x
3.0ms
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Results
AccuracySegmentsBranch
99.8%2(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
99.8%2x
Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes7.0ms (0.2%)

Memory
16.2MiB live, 16.2MiB allocated; 0ms collecting garbage
Counts
11 → 2
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Outputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
Calls

2 calls:

3.0ms
x
3.0ms
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Results
AccuracySegmentsBranch
99.8%2(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
99.8%2x
Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes8.0ms (0.2%)

Memory
-29.6MiB live, 15.4MiB allocated; 3ms collecting garbage
Counts
8 → 2
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x)))
Outputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
Calls

2 calls:

5.0ms
x
2.0ms
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Results
AccuracySegmentsBranch
99.7%2(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
99.7%2x
Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes4.0ms (0.1%)

Memory
10.0MiB live, 10.0MiB allocated; 0ms collecting garbage
Counts
5 → 1
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))
Outputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))))
Calls

2 calls:

2.0ms
x
2.0ms
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Results
AccuracySegmentsBranch
52.4%1(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
52.4%1x
Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0.1%)

Memory
7.5MiB live, 7.5MiB allocated; 0ms collecting garbage
Accuracy

Total -31.3b remaining (-98.8%)

Threshold costs -31.3b (-98.8%)

Counts
2 → 1
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))))
Outputs
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
Calls

2 calls:

1.0ms
x
1.0ms
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Results
AccuracySegmentsBranch
50.6%1x
50.6%1(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Compiler

Compiled 8 to 7 computations (12.5% saved)

bsearch16.0ms (0.4%)

Memory
-15.8MiB live, 31.2MiB allocated; 2ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
14.0ms
1.2628520081757724e-8
122233409.12966035
Samples
8.0ms160×0valid
Compiler

Compiled 340 to 280 computations (17.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-sqrt: 2.0ms (55% of total)
ival-sub: 1.0ms (27.5% of total)
ival-add: 1.0ms (27.5% 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)

bsearch5.0ms (0.1%)

Memory
7.5MiB live, 7.5MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
5.0ms
1.2628520081757724e-8
122233409.12966035
Samples
2.0ms48×0valid
Compiler

Compiled 300 to 270 computations (10% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.0ms
ival-sqrt: 1.0ms (90.6% of total)
ival-sub: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
ival-add: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

bsearch1.0ms (0%)

Memory
2.1MiB live, 2.1MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
1.0ms
1.2628520081757724e-8
122233409.12966035
Compiler

Compiled 280 to 250 computations (10.7% saved)

simplify11.0ms (0.2%)

Memory
17.5MiB live, 17.5MiB allocated; 0ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
031125
140125
246125
348125
Stop Event
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 x #s(literal 7385903388887613/9007199254740992 binary64)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)))
(if (<=.f64 x #s(literal 1 binary64)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal 1 binary64)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))))
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
Outputs
(if (<=.f64 x #s(literal 7385903388887613/9007199254740992 binary64)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)))
(if (<=.f64 x #s(literal 1 binary64)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal 1 binary64)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (pow.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal 1 binary64)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))))
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))

derivations643.0ms (14.4%)

Memory
-18.4MiB live, 462.7MiB allocated; 161ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0113451
1331393
21209387
34903387
08229353
024129
037129
1145121
21033119
08352116
025139
037139
1120139
2796135
08366132
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
Compiler

Compiled 125 to 33 computations (73.6% saved)

preprocess37.0ms (0.8%)

Memory
12.8MiB live, 58.2MiB allocated; 3ms collecting garbage
Compiler

Compiled 282 to 92 computations (67.4% saved)

end0.0ms (0%)

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

Profiling

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