Main:bigenough3 from C

Time bar (total: 4.3s)

start0.0ms (0%)

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

analyze1.0ms (0%)

Memory
5.5MiB live, 5.5MiB 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 (27.9%)

Memory
55.3MiB live, 1 687.3MiB allocated; 458ms collecting garbage
Samples
549.0ms3 969×1valid
274.0ms4 287×0valid
0.0ms7×0invalid
Precisions
Click to see histograms. Total time spent on operations: 590.0ms
ival-sqrt: 267.0ms (45.2% of total)
adjust: 125.0ms (21.2% of total)
ival-add: 96.0ms (16.3% of total)
ival-sub: 86.0ms (14.6% of total)
ival-true: 6.0ms (1% of total)
exact: 6.0ms (1% of total)
ival-assert: 3.0ms (0.5% of total)
Bogosity

explain133.0ms (3.1%)

Memory
11.5MiB live, 114.3MiB allocated; 18ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1371(2173.2311582455386)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))cancellation1380
Confusion
Predicted +Predicted -
+1370
-1118
Precision
0.9927536231884058
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+13700
-10118
Precision?
0.9927536231884058
Recall?
1.0
Freqs
test
numberfreq
0118
1138
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
30.0ms274×1valid
12.0ms238×0valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 27.0ms
ival-sqrt: 11.0ms (40.8% of total)
adjust: 7.0ms (26% of total)
ival-add: 4.0ms (14.8% of total)
ival-sub: 4.0ms (14.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

preprocess268.0ms (6.2%)

Memory
-27.4MiB live, 258.4MiB allocated; 51ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0819
11119
21419
32519
46119
526717
6231617
7569517
067
0107
1137
2167
3277
4617
52527
621957
754917
086357
Stop Event
1×iter limit
1×node limit
1×iter limit
1×node limit
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 x #s(literal -1 binary64))) (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
0.9MiB live, 0.9MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶49.3%
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify181.0ms (4.2%)

Memory
12.9MiB live, 155.8MiB allocated; 16ms collecting garbage
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
21618
32718
46118
525218
6219518
7549118
0863518
Stop Event
1×iter limit
1×node limit
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 x #s(literal -1 binary64))) (sqrt.f64 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
(+.f64 x #s(literal 1 binary64))
(-.f64 x #s(literal -1 binary64))
x
#s(literal 1 binary64)
(sqrt.f64 x)

localize29.0ms (0.7%)

Memory
5.7MiB live, 50.8MiB allocated; 5ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(+.f64 x #s(literal 1 binary64))
accuracy0.0
(sqrt.f64 x)
accuracy0.00390625
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy32.44743084144339
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Samples
15.0ms137×1valid
6.0ms119×0valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.0ms
ival-sqrt: 5.0ms (38.1% of total)
adjust: 3.0ms (22.8% of total)
ival-add: 2.0ms (15.2% of total)
ival-sub: 2.0ms (15.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory
6.3MiB live, 6.3MiB allocated; 0ms collecting garbage
Counts
4 → 30
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
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- 1 (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* 1/2 x)) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 1))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (+ x 1) #s(hole binary64 1))
#s(approx (+ x 1) #s(hole binary64 (+ 1 x)))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* 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))))))))))
#s(approx (+ x 1) #s(hole binary64 x))
#s(approx (+ x 1) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1/2 (sqrt (/ 1 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -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))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -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))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -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)))))))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
Calls

3 calls:

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

simplify164.0ms (3.8%)

Memory
-15.2MiB live, 132.1MiB allocated; 14ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0146634
1364576
21254555
05889519
Stop Event
1×iter limit
1×iter limit
1×node limit
Counts
30 → 30
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- 1 (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* 1/2 x)) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 1))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (+ x 1) #s(hole binary64 1))
#s(approx (+ x 1) #s(hole binary64 (+ 1 x)))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* 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))))))))))
#s(approx (+ x 1) #s(hole binary64 x))
#s(approx (+ x 1) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1/2 (sqrt (/ 1 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -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))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -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))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -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)))))))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
Outputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- 1 (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* 1/2 x)) (sqrt 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)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (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))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 (fma.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))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 1))
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (+ x 1) #s(hole binary64 1))
#s(approx (+ x 1) #s(literal 1 binary64))
#s(approx (+ x 1) #s(hole binary64 (+ 1 x)))
#s(approx (+ x 1) (-.f64 x #s(literal -1 binary64)))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (sqrt x) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* 1/2 (sqrt (/ 1 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)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt 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)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt 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))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt 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))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x 1)) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (+ x 1)) (*.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))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (+ x 1)) (*.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))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* 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))))))))))
#s(approx (sqrt (+ x 1)) (*.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))
#s(approx (+ x 1) #s(hole binary64 x))
#s(approx (+ x 1) x)
#s(approx (+ x 1) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (+ x 1) (-.f64 x #s(literal -1 binary64)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1/2 (sqrt (/ 1 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt 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)) #s(hole binary64 (* -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))))
#s(approx (- (sqrt (+ x 1)) (sqrt 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))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -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))))
#s(approx (- (sqrt (+ x 1)) (sqrt 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) (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))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x 1)) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x 1)) (*.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))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x 1)) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -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)))))))))
#s(approx (sqrt (+ x 1)) (*.f64 (fma.f64 #s(literal -1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt x) (sqrt.f64 x))

rewrite56.0ms (1.3%)

Memory
-10.1MiB live, 35.5MiB allocated; 6ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
01016
14216
030416
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
4 → 35
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 (neg.f64 (-.f64 (-.f64 x #s(literal -1 binary64)) x)) (neg.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (+.f64 (-.f64 x #s(literal -1 binary64)) x) (sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) x)))))
(/.f64 (-.f64 (-.f64 x #s(literal -1 binary64)) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
(/.f64 (-.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (+.f64 (-.f64 x #s(literal -1 binary64)) x) (sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) x))))
(-.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))) (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))))
(-.f64 (/.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3/2 binary64)) (+.f64 (+.f64 (-.f64 x #s(literal -1 binary64)) x) (sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) x)))) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (+.f64 (-.f64 x #s(literal -1 binary64)) x) (sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) x)))))
(-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))
(*.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
(exp.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) (neg.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
(*.f64 (fabs.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) (fabs.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(pow.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) (-.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) #s(literal 2 binary64))
(pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64))) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) (-.f64 x #s(literal -1 binary64))))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))
(-.f64 x #s(literal -1 binary64))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(+.f64 #s(literal 1 binary64) x)
(+.f64 x #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))

eval7.0ms (0.2%)

Memory
13.6MiB live, 13.6MiB allocated; 0ms collecting garbage
Compiler

Compiled 1 029 to 243 computations (76.4% saved)

prune6.0ms (0.1%)

Memory
10.3MiB live, 10.3MiB allocated; 0ms collecting garbage
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New54862
Fresh000
Picked011
Done000
Total54963
Accuracy
100.0%
Counts
63 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
50.4%
(/.f64 (-.f64 (-.f64 x #s(literal -1 binary64)) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
✓49.3%
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
3.5%
(-.f64 (sqrt.f64 #s(approx (+ x 1) x)) (sqrt.f64 x))
▶46.6%
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x))
▶48.4%
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
▶46.5%
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
48.4%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
▶53.9%
#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))
▶56.2%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
Compiler

Compiled 221 to 176 computations (20.4% saved)

simplify153.0ms (3.5%)

Memory
0.7MiB live, 136.0MiB allocated; 29ms collecting garbage
Localize:

Found 19 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
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
cost-diff0
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
cost-diff0
#s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
cost-diff0
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x))
cost-diff0
(sqrt.f64 x)
cost-diff0
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
cost-diff0
#s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
cost-diff0
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #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
026182
043182
163182
2110182
3231182
4487182
51304182
67047182
08599182
Stop Event
1×iter limit
1×node limit
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
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)
(sqrt.f64 x)
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
#s(literal -1/8 binary64)
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(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)))
(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
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)
(sqrt.f64 x)
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
#s(literal -1/8 binary64)
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(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))
#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)

localize110.0ms (2.5%)

Memory
-0.1MiB live, 91.4MiB allocated; 6ms collecting garbage
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy0.0234375
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
accuracy0.1171875
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy0.2421875
(/.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)
accuracy29.345285002758988
#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
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
accuracy0.0
(sqrt.f64 x)
accuracy32.44743084144339
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x))
accuracy34.26715637657702
#s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
accuracy0.0
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
accuracy0.0
(sqrt.f64 x)
accuracy32.137543363908044
#s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
accuracy32.44743084144339
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
accuracy0.0
(sqrt.f64 x)
accuracy32.367746719502236
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
accuracy32.44743084144339
(-.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))
accuracy0.1171875
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy27.94724598329485
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
Samples
75.0ms137×1valid
18.0ms119×0valid
Compiler

Compiled 140 to 23 computations (83.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 72.0ms
ival-mult: 41.0ms (56.6% of total)
adjust: 9.0ms (12.4% of total)
ival-add: 9.0ms (12.4% of total)
ival-sqrt: 7.0ms (9.7% of total)
ival-div: 4.0ms (5.5% of total)
ival-sub: 2.0ms (2.8% 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
14.3MiB live, 14.3MiB allocated; 0ms collecting garbage
Counts
17 → 58
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)
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
#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)) #s(hole binary64 (- 1 (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* 1/2 x)) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))))
#s(approx (* (sqrt (/ 1 x)) 1/2) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (sqrt (/ 1 x)) #s(hole binary64 (sqrt (/ 1 x))))
#s(approx (/ 1 x) #s(hole binary64 (/ 1 x)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 1))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 1))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) #s(hole binary64 1))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (+ (* -1/8 x) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/8 x) 1/2) #s(hole binary64 (+ 1/2 (* -1/8 x))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (* -1/8 (sqrt (/ 1 (pow x 3))))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* -1/8 (sqrt (/ 1 x)))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* 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))))))))))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 (* 1/2 x)))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 (* x (+ 1/2 (/ 1 x)))))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) #s(hole binary64 (* -1/8 (pow x 2))))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) #s(hole binary64 (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) #s(hole binary64 (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))))
#s(approx (+ (* -1/8 x) 1/2) #s(hole binary64 (* -1/8 x)))
#s(approx (+ (* -1/8 x) 1/2) #s(hole binary64 (* x (- (* 1/2 (/ 1 x)) 1/8))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* 1/2 (sqrt x))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1/2 (sqrt (/ 1 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -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))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -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))))
#s(approx (* (sqrt (/ 1 x)) 1/2) #s(hole binary64 (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
#s(approx (sqrt (/ 1 x)) #s(hole binary64 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -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)))))))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (+ (* -1/8 x) 1/2) #s(hole binary64 (* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* -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)) (sqrt (+ x 1)) (+ (* 1/2 x) 1) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ (* (+ (* -1/8 x) 1/2) x) 1) (+ (* -1/8 x) 1/2) (- (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
@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)) (sqrt (+ x 1)) (+ (* 1/2 x) 1) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ (* (+ (* -1/8 x) 1/2) x) 1) (+ (* -1/8 x) 1/2) (- (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)) (sqrt (+ x 1)) (+ (* 1/2 x) 1) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ (* (+ (* -1/8 x) 1/2) x) 1) (+ (* -1/8 x) 1/2) (- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))))

simplify157.0ms (3.6%)

Memory
-22.3MiB live, 165.0MiB allocated; 53ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02131159
15061072
217591048
06592962
Stop Event
1×iter limit
1×iter limit
1×node limit
Counts
58 → 58
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- 1 (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* 1/2 x)) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))))
#s(approx (* (sqrt (/ 1 x)) 1/2) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (sqrt (/ 1 x)) #s(hole binary64 (sqrt (/ 1 x))))
#s(approx (/ 1 x) #s(hole binary64 (/ 1 x)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 1))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 1))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) #s(hole binary64 1))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (+ (* -1/8 x) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/8 x) 1/2) #s(hole binary64 (+ 1/2 (* -1/8 x))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (* -1/8 (sqrt (/ 1 (pow x 3))))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* -1/8 (sqrt (/ 1 x)))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* 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))))))))))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 (* 1/2 x)))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 (* x (+ 1/2 (/ 1 x)))))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) #s(hole binary64 (* -1/8 (pow x 2))))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) #s(hole binary64 (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) #s(hole binary64 (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))))
#s(approx (+ (* -1/8 x) 1/2) #s(hole binary64 (* -1/8 x)))
#s(approx (+ (* -1/8 x) 1/2) #s(hole binary64 (* x (- (* 1/2 (/ 1 x)) 1/8))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* 1/2 (sqrt x))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1/2 (sqrt (/ 1 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -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))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -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))))
#s(approx (* (sqrt (/ 1 x)) 1/2) #s(hole binary64 (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
#s(approx (sqrt (/ 1 x)) #s(hole binary64 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -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)))))))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (+ (* -1/8 x) 1/2) #s(hole binary64 (* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
Outputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- 1 (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* 1/2 x)) (sqrt 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)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (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))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 (fma.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))))
#s(approx (* (sqrt (/ 1 x)) 1/2) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (* (sqrt (/ 1 x)) 1/2) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
#s(approx (sqrt (/ 1 x)) #s(hole binary64 (sqrt (/ 1 x))))
#s(approx (sqrt (/ 1 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
#s(approx (/ 1 x) #s(hole binary64 (/ 1 x)))
#s(approx (/ 1 x) (/.f64 #s(literal 1 binary64) x))
#s(approx (sqrt (+ x 1)) #s(hole binary64 1))
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (sqrt x) (sqrt.f64 x))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 1))
#s(approx (+ (* 1/2 x) 1) #s(literal 1 binary64))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (+ (* 1/2 x) 1) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) #s(hole binary64 1))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) #s(literal 1 binary64))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (+ (* -1/8 x) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/8 x) 1/2) #s(literal 1/2 binary64))
#s(approx (+ (* -1/8 x) 1/2) #s(hole binary64 (+ 1/2 (* -1/8 x))))
#s(approx (+ (* -1/8 x) 1/2) (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (* -1/8 (sqrt (/ 1 (pow x 3))))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64)))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) 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))) (*.f64 x x)))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* -1/8 (sqrt (/ 1 x)))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt 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))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* 1/2 (sqrt (/ 1 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)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt 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)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt 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))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt 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))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x 1)) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (+ x 1)) (*.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))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (+ x 1)) (*.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))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* 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))))))))))
#s(approx (sqrt (+ x 1)) (*.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))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 (* 1/2 x)))
#s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 (* x (+ 1/2 (/ 1 x)))))
#s(approx (+ (* 1/2 x) 1) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) #s(hole binary64 (* -1/8 (pow x 2))))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) #s(hole binary64 (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) #s(hole binary64 (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))))
#s(approx (+ (* (+ (* -1/8 x) 1/2) x) 1) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (+ (* -1/8 x) 1/2) #s(hole binary64 (* -1/8 x)))
#s(approx (+ (* -1/8 x) 1/2) (*.f64 #s(literal -1/8 binary64) x))
#s(approx (+ (* -1/8 x) 1/2) #s(hole binary64 (* x (- (* 1/2 (/ 1 x)) 1/8))))
#s(approx (+ (* -1/8 x) 1/2) (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) 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))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* 1/2 (sqrt x))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt 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))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1/2 (sqrt (/ 1 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt 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)) #s(hole binary64 (* -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))))
#s(approx (- (sqrt (+ x 1)) (sqrt 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))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -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))))
#s(approx (- (sqrt (+ x 1)) (sqrt 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) (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))
#s(approx (* (sqrt (/ 1 x)) 1/2) #s(hole binary64 (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
#s(approx (* (sqrt (/ 1 x)) 1/2) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
#s(approx (sqrt (/ 1 x)) #s(hole binary64 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
#s(approx (sqrt (/ 1 x)) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x 1)) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x 1)) (*.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))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x 1)) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -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)))))))))
#s(approx (sqrt (+ x 1)) (*.f64 (fma.f64 #s(literal -1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt x) (sqrt.f64 x))
#s(approx (+ (* -1/8 x) 1/2) #s(hole binary64 (* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))))
#s(approx (+ (* -1/8 x) 1/2) (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) 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))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt 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))

rewrite84.0ms (2%)

Memory
16.3MiB live, 71.4MiB allocated; 10ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
026149
043149
1177141
01306138
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
17 → 137
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)
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
#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 #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 #s(literal 1/2 binary64) (sqrt.f64 x))
(*.f64 (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/4 binary64)))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 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 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(sqrt.f64 (pow.f64 x #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64)))
(pow.f64 x #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 x))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 x)))
(/.f64 #s(literal 1 binary64) x)
(neg.f64 (/.f64 #s(literal -1 binary64) x))
(neg.f64 (/.f64 #s(literal 1 binary64) (neg.f64 x)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -1 binary64)))
(/.f64 (neg.f64 (-.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 2 binary64)) x)) (neg.f64 (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (neg.f64 (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 2 binary64)) 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 3 binary64)) (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 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 #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 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(pow.f64 x #s(literal 1/2 binary64))
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(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) #s(literal 3 binary64))) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (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 (*.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (*.f64 #s(literal 1/4 binary64) x))) (neg.f64 (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 (fma.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64) (pow.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal 1/4 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 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (*.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 (fma.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64) (pow.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) x (-.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64) (pow.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 3 binary64))) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))))
(fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.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)))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(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 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (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 (neg.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 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))))
(-.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (*.f64 (neg.f64 (pow.f64 x #s(literal -1/2 binary64))) #s(literal -1/8 binary64)))
(+.f64 (/.f64 (pow.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 3 binary64)) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))))) (/.f64 (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.f64 (*.f64 #s(literal 1/4 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) (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)))

eval26.0ms (0.6%)

Memory
2.7MiB live, 47.8MiB allocated; 3ms collecting garbage
Compiler

Compiled 5 200 to 816 computations (84.3% saved)

prune13.0ms (0.3%)

Memory
-20.8MiB live, 25.5MiB allocated; 3ms collecting garbage
Pruning

11 alts after pruning (7 fresh and 4 done)

PrunedKeptTotal
New2165221
Fresh123
Picked235
Done011
Total21911230
Accuracy
100.0%
Counts
230 → 11
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶50.4%
(/.f64 (-.f64 (-.f64 x #s(literal -1 binary64)) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
✓49.3%
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓46.6%
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x))
▶3.2%
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
✓46.5%
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
53.9%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) x) (/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x)))
▶48.4%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
53.9%
#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))
▶56.1%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
▶56.1%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
✓56.2%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
Compiler

Compiled 287 to 216 computations (24.7% saved)

simplify200.0ms (4.6%)

Memory
12.9MiB live, 150.8MiB allocated; 15ms collecting garbage
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
cost-diff0
(-.f64 x #s(literal -1 binary64))
cost-diff0
(/.f64 (-.f64 (-.f64 x #s(literal -1 binary64)) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
cost-diff4
(-.f64 (-.f64 x #s(literal -1 binary64)) 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)))
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
(*.f64 #s(literal 1/2 binary64) x)
cost-diff0
#s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))
cost-diff0
#s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)))
cost-diff0
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
cost-diff0
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
cost-diff0
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
cost-diff0
(/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
cost-diff0
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
035202
049198
169198
2101198
3162194
4295194
51222194
66386194
08932188
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
(/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (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
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
(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)))
#s(literal 1/2 binary64)
x
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 x)
#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
(/.f64 (-.f64 (-.f64 x #s(literal -1 binary64)) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
(-.f64 (-.f64 x #s(literal -1 binary64)) x)
(-.f64 x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(sqrt.f64 x)
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
Outputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x))
(/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 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)
x
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
(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)))
#s(literal 1/2 binary64)
x
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 x)
#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
(/.f64 (-.f64 (-.f64 x #s(literal -1 binary64)) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x)))
(-.f64 (-.f64 x #s(literal -1 binary64)) x)
#s(literal 1 binary64)
(-.f64 x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))
(sqrt.f64 x)
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))

localize112.0ms (2.6%)

Memory
1.8MiB live, 143.0MiB allocated; 20ms collecting garbage
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy0.00390625
(+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
accuracy0.00390625
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
accuracy0.1875
(/.f64 (-.f64 (-.f64 x #s(literal -1 binary64)) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
accuracy31.971929440337494
(-.f64 (-.f64 x #s(literal -1 binary64)) x)
accuracy0.0
(sqrt.f64 x)
accuracy0.28515625
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
accuracy27.94724598329485
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
accuracy0.0
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy0.0
(sqrt.f64 x)
accuracy0.00390625
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
accuracy33.00312321252216
#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)
accuracy28.486572039269763
#s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))
accuracy32.137543363908044
#s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)))
accuracy32.44743084144339
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
accuracy0.0
(sqrt.f64 x)
accuracy0.2421875
(/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
accuracy29.345285002758988
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
accuracy29.470530724837914
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
Samples
52.0ms137×1valid
27.0ms119×0valid
Compiler

Compiled 139 to 27 computations (80.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 60.0ms
ival-sqrt: 14.0ms (23.5% of total)
adjust: 13.0ms (21.8% of total)
ival-div: 11.0ms (18.5% of total)
ival-add: 9.0ms (15.1% of total)
ival-sub: 7.0ms (11.7% of total)
ival-mult: 5.0ms (8.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series12.0ms (0.3%)

Memory
22.9MiB live, 22.9MiB allocated; 0ms collecting garbage
Counts
19 → 98
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
(/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) 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))))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(sqrt.f64 x)
#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))
(-.f64 (-.f64 x #s(literal -1 binary64)) x)
(/.f64 (-.f64 (-.f64 x #s(literal -1 binary64)) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
(-.f64 x #s(literal -1 binary64))
(+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
Outputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- 1 (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* 1/2 x)) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (* -1/8 (sqrt (/ 1 (pow x 3))))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* -1/8 (sqrt (/ 1 x)))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)))
#s(approx (* 1/2 (sqrt x)) #s(hole binary64 (* 1/2 (sqrt x))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 1))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 1))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (* 1/2 x) #s(hole binary64 (* 1/2 x)))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) #s(hole binary64 (- 1 (sqrt x))))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) #s(hole binary64 (- (+ 1 (* 1/2 x)) (sqrt x))))
#s(approx (- 1 (sqrt x)) #s(hole binary64 (- 1 (sqrt x))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (/ 1/2 (sqrt x)) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (- (- x -1) x) #s(hole binary64 1))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ 1 (+ 1 (sqrt x)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))))
#s(approx (- x -1) #s(hole binary64 1))
#s(approx (- x -1) #s(hole binary64 (+ 1 x)))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (sqrt x))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (+ (sqrt x) (* 1/2 x)))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 1))
#s(approx (sqrt (- x -1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* 1/2 (sqrt x))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* 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))))))))))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 (* 1/2 x)))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 (* x (+ 1/2 (/ 1 x)))))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) #s(hole binary64 (* x (- 1/2 (sqrt (/ 1 x))))))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) #s(hole binary64 (* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))))
#s(approx (- 1 (sqrt x)) #s(hole binary64 (* -1 (sqrt x))))
#s(approx (- 1 (sqrt x)) #s(hole binary64 (* x (- (/ 1 x) (sqrt (/ 1 x))))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)))
#s(approx (- x -1) #s(hole binary64 x))
#s(approx (- x -1) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* 2 (sqrt x))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* 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))))))))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1/2 (sqrt (/ 1 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -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))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -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))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (* 1/2 (sqrt x)) #s(hole binary64 (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -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)))))))))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) #s(hole binary64 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) #s(hole binary64 (* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))))
#s(approx (- 1 (sqrt x)) #s(hole binary64 (* (sqrt x) (pow (sqrt -1) 2))))
#s(approx (- 1 (sqrt x)) #s(hole binary64 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1/2 (sqrt (/ 1 x)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -2 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -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)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -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
4.0ms
x
@-inf
((- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (* 1/2 (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ (* 1/2 x) 1) (* 1/2 x) (- (sqrt (+ x 1)) (sqrt x)) (+ (* 1/2 x) (- 1 (sqrt x))) (- 1 (sqrt x)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (/ 1/2 (sqrt x)) (- (- x -1) x) (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (- x -1) (+ (sqrt x) (sqrt (- x -1))) (sqrt (- x -1)))
3.0ms
x
@0
((- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (* 1/2 (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ (* 1/2 x) 1) (* 1/2 x) (- (sqrt (+ x 1)) (sqrt x)) (+ (* 1/2 x) (- 1 (sqrt x))) (- 1 (sqrt x)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (/ 1/2 (sqrt x)) (- (- x -1) x) (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (- x -1) (+ (sqrt x) (sqrt (- x -1))) (sqrt (- x -1)))
3.0ms
x
@inf
((- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (* 1/2 (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ (* 1/2 x) 1) (* 1/2 x) (- (sqrt (+ x 1)) (sqrt x)) (+ (* 1/2 x) (- 1 (sqrt x))) (- 1 (sqrt x)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (/ 1/2 (sqrt x)) (- (- x -1) x) (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (- x -1) (+ (sqrt x) (sqrt (- x -1))) (sqrt (- x -1)))

simplify168.0ms (3.9%)

Memory
-15.8MiB live, 175.0MiB allocated; 40ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03532317
18942131
232942064
088611946
Stop Event
1×iter limit
1×node limit
Counts
98 → 98
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- 1 (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* 1/2 x)) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (* -1/8 (sqrt (/ 1 (pow x 3))))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* -1/8 (sqrt (/ 1 x)))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)))
#s(approx (* 1/2 (sqrt x)) #s(hole binary64 (* 1/2 (sqrt x))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 1))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 1))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (* 1/2 x) #s(hole binary64 (* 1/2 x)))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) #s(hole binary64 (- 1 (sqrt x))))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) #s(hole binary64 (- (+ 1 (* 1/2 x)) (sqrt x))))
#s(approx (- 1 (sqrt x)) #s(hole binary64 (- 1 (sqrt x))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (/ 1/2 (sqrt x)) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (- (- x -1) x) #s(hole binary64 1))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ 1 (+ 1 (sqrt x)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))))
#s(approx (- x -1) #s(hole binary64 1))
#s(approx (- x -1) #s(hole binary64 (+ 1 x)))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (sqrt x))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (+ (sqrt x) (* 1/2 x)))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 1))
#s(approx (sqrt (- x -1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* 1/2 (sqrt x))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* 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))))))))))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 (* 1/2 x)))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 (* x (+ 1/2 (/ 1 x)))))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) #s(hole binary64 (* x (- 1/2 (sqrt (/ 1 x))))))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) #s(hole binary64 (* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))))
#s(approx (- 1 (sqrt x)) #s(hole binary64 (* -1 (sqrt x))))
#s(approx (- 1 (sqrt x)) #s(hole binary64 (* x (- (/ 1 x) (sqrt (/ 1 x))))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)))
#s(approx (- x -1) #s(hole binary64 x))
#s(approx (- x -1) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* 2 (sqrt x))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* 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))))))))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1/2 (sqrt (/ 1 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -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))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -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))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (* 1/2 (sqrt x)) #s(hole binary64 (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -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)))))))))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) #s(hole binary64 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) #s(hole binary64 (* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))))
#s(approx (- 1 (sqrt x)) #s(hole binary64 (* (sqrt x) (pow (sqrt -1) 2))))
#s(approx (- 1 (sqrt x)) #s(hole binary64 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1/2 (sqrt (/ 1 x)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -2 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -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)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -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
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- 1 (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* 1/2 x)) (sqrt 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)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (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))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 (fma.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))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (* -1/8 (sqrt (/ 1 (pow x 3))))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64)))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) 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))) (*.f64 x x)))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* -1/8 (sqrt (/ 1 x)))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt 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))
#s(approx (* 1/2 (sqrt x)) #s(hole binary64 (* 1/2 (sqrt x))))
#s(approx (* 1/2 (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 1))
#s(approx (sqrt (- x -1)) #s(literal 1 binary64))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (- x -1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (- x -1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (sqrt (- x -1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 1))
#s(approx (+ (* 1/2 x) 1) #s(literal 1 binary64))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (+ (* 1/2 x) 1) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
#s(approx (* 1/2 x) #s(hole binary64 (* 1/2 x)))
#s(approx (* 1/2 x) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) #s(hole binary64 (- 1 (sqrt x))))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) #s(hole binary64 (- (+ 1 (* 1/2 x)) (sqrt x))))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
#s(approx (- 1 (sqrt x)) #s(hole binary64 (- 1 (sqrt x))))
#s(approx (- 1 (sqrt x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (sqrt x) (sqrt.f64 x))
#s(approx (/ 1/2 (sqrt x)) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (/ 1/2 (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
#s(approx (- (- x -1) x) #s(hole binary64 1))
#s(approx (- (- x -1) x) #s(literal 1 binary64))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ 1 (+ 1 (sqrt x)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (/.f64 (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) x) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) #s(literal 1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (fma.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) #s(literal 1/8 binary64)) (pow.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64))) x (/.f64 #s(literal -1/2 binary64) (pow.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) #s(literal 4 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) #s(literal 3 binary64)))) #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) #s(literal 1/16 binary64)) (pow.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) #s(literal 1/8 binary64)) (pow.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal -1/2 binary64) (pow.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))))
#s(approx (- x -1) #s(hole binary64 1))
#s(approx (- x -1) #s(literal 1 binary64))
#s(approx (- x -1) #s(hole binary64 (+ 1 x)))
#s(approx (- x -1) (-.f64 x #s(literal -1 binary64)))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (sqrt x))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (+ (sqrt x) (* 1/2 x)))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (fma.f64 #s(literal 1/2 binary64) x (-.f64 (sqrt.f64 x) #s(literal -1 binary64))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 (sqrt.f64 x) #s(literal -1 binary64))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 (sqrt.f64 x) #s(literal -1 binary64))))
#s(approx (sqrt (- x -1)) #s(hole binary64 1))
#s(approx (sqrt (- x -1)) #s(literal 1 binary64))
#s(approx (sqrt (- x -1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (- x -1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
#s(approx (sqrt (- x -1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (- x -1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (sqrt (- x -1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (sqrt (- x -1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt 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 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt 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 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt 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 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) x))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* 1/2 (sqrt x))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (- x -1)) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (- x -1)) (*.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))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (- x -1)) (*.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))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* 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))))))))))
#s(approx (sqrt (- x -1)) (*.f64 (+.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) (*.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))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 (* 1/2 x)))
#s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (+ (* 1/2 x) 1) #s(hole binary64 (* x (+ 1/2 (/ 1 x)))))
#s(approx (+ (* 1/2 x) 1) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) #s(hole binary64 (* x (- 1/2 (sqrt (/ 1 x))))))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) (*.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) #s(hole binary64 (* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) (fma.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x #s(literal 1 binary64)))
#s(approx (- 1 (sqrt x)) #s(hole binary64 (* -1 (sqrt x))))
#s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))
#s(approx (- 1 (sqrt x)) #s(hole binary64 (* x (- (/ 1 x) (sqrt (/ 1 x))))))
#s(approx (- 1 (sqrt x)) (fma.f64 (neg.f64 x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (neg.f64 (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) x))
#s(approx (- x -1) #s(hole binary64 x))
#s(approx (- x -1) x)
#s(approx (- x -1) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (- x -1) (-.f64 x #s(literal -1 binary64)))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* 2 (sqrt x))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (*.f64 (fma.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))) x))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)))) x))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))))) x))
#s(approx (sqrt (- x -1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (- x -1)) (sqrt.f64 x))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (- x -1)) (*.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))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (- x -1)) (*.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))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* 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))))))))))
#s(approx (sqrt (- x -1)) (*.f64 (+.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) (*.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))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1/2 (sqrt (/ 1 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt 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 #s(literal -1/2 binary64) (sqrt.f64 x))) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -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))))
#s(approx (- (sqrt (+ x 1)) (sqrt 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 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -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))))
#s(approx (- (sqrt (+ x 1)) (sqrt 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) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) x))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) #s(hole binary64 (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))))
#s(approx (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) #s(hole binary64 (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x))
#s(approx (* 1/2 (sqrt x)) #s(hole binary64 (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (* 1/2 (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (- x -1)) (*.f64 (sqrt.f64 x) #s(literal 1 binary64)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (- x -1)) (*.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))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (- x -1)) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -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)))))))))
#s(approx (sqrt (- x -1)) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 #s(literal -1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) #s(hole binary64 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) (*.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) #s(hole binary64 (* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))))
#s(approx (+ (* 1/2 x) (- 1 (sqrt x))) (fma.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x #s(literal 1 binary64)))
#s(approx (- 1 (sqrt x)) #s(hole binary64 (* (sqrt x) (pow (sqrt -1) 2))))
#s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))
#s(approx (- 1 (sqrt x)) #s(hole binary64 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))))
#s(approx (- 1 (sqrt x)) (fma.f64 (neg.f64 x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt x) (*.f64 (sqrt.f64 x) #s(literal 1 binary64)))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1/2 (sqrt (/ 1 x)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (/.f64 (fma.f64 #s(literal -1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) x))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (/.f64 (fma.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (neg.f64 (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) (neg.f64 x)))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -2 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -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)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (*.f64 (fma.f64 #s(literal -1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) x))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (- x -1)) (*.f64 (sqrt.f64 x) #s(literal 1 binary64)))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (- x -1)) (*.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))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (- x -1)) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -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)))))))))
#s(approx (sqrt (- x -1)) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 #s(literal -1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x))

rewrite65.0ms (1.5%)

Memory
14.0MiB live, 60.7MiB allocated; 4ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
035183
049183
1191171
01508165
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
19 → 139
Calls
Call 1
Inputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
(/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) 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))))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(sqrt.f64 x)
#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))
(-.f64 (-.f64 x #s(literal -1 binary64)) x)
(/.f64 (-.f64 (-.f64 x #s(literal -1 binary64)) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
(-.f64 x #s(literal -1 binary64))
(+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
Outputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x))
(/.f64 (neg.f64 (neg.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) (neg.f64 x))
(/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(neg.f64 (/.f64 (neg.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) x))
(neg.f64 (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) (neg.f64 x)))
#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.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))
(/.f64 (neg.f64 (-.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) x)) (neg.f64 (+.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 3 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (fma.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x) x) (pow.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) x) (+.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x)))
(/.f64 (-.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 3 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (fma.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x) x) (pow.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) (+.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))) (/.f64 x (+.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))))
(-.f64 (/.f64 (pow.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 3 binary64)) (+.f64 (fma.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x) x) (pow.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 2 binary64)))) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (fma.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x) x) (pow.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 2 binary64)))))
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) #s(literal -1 binary64))
(*.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 x #s(literal 1/2 binary64))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) x) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 x)))
(/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (*.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 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (+.f64 x (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 x)))))
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)))) (neg.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) x))))))
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x)))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (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 1/4 binary64) (*.f64 x x)) (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) x)))))
(fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x))))
(-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) x))
(-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 (neg.f64 x) #s(literal 1/2 binary64)))
(-.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 x))
(-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x)))
(+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) x))))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64)) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) x))))))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x)) (neg.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (+.f64 (sqrt.f64 x) x) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (+.f64 (sqrt.f64 x) x) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) (/.f64 x (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (sqrt.f64 x) x) #s(literal 1 binary64))) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (+.f64 (sqrt.f64 x) x) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 #s(literal -1 binary64) (*.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
#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) (neg.f64 (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)))
(neg.f64 (/.f64 #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x))))
(*.f64 (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x)))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))) (+.f64 x (-.f64 x #s(literal 1 binary64))))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)) (*.f64 x (-.f64 x #s(literal 1 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (*.f64 x x))) (neg.f64 (+.f64 (-.f64 x #s(literal -1 binary64)) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x (+.f64 (-.f64 x #s(literal -1 binary64)) x) (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (*.f64 x x)) (+.f64 (-.f64 x #s(literal -1 binary64)) x))
(/.f64 (-.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x (+.f64 (-.f64 x #s(literal -1 binary64)) x) (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64))))
(fma.f64 (neg.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) (neg.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) (*.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)))
(fma.f64 (fabs.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) (fabs.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) (*.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (*.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)))
(-.f64 (/.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (+.f64 (-.f64 x #s(literal -1 binary64)) x)) (/.f64 (*.f64 x x) (+.f64 (-.f64 x #s(literal -1 binary64)) x)))
(-.f64 (/.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3 binary64)) (fma.f64 x (+.f64 (-.f64 x #s(literal -1 binary64)) x) (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 (-.f64 x #s(literal -1 binary64)) x) (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)))))
(-.f64 (-.f64 x #s(literal -1 binary64)) x)
(-.f64 x (-.f64 x #s(literal 1 binary64)))
(+.f64 (-.f64 x #s(literal -1 binary64)) (*.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)))
(*.f64 (/.f64 (-.f64 (-.f64 x #s(literal -1 binary64)) x) (-.f64 x (-.f64 x #s(literal -1 binary64)))) (-.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
(*.f64 (/.f64 (-.f64 (-.f64 x #s(literal -1 binary64)) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3/2 binary64)))) (-.f64 (+.f64 (-.f64 x #s(literal -1 binary64)) x) (sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) x))))
(/.f64 (-.f64 (*.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))) (/.f64 (-.f64 x #s(literal -1 binary64)) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x)))) (*.f64 (/.f64 x (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))) (/.f64 x (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))))) (+.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))) (/.f64 x (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))) #s(literal 3 binary64)) (pow.f64 (/.f64 x (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))) (/.f64 (-.f64 x #s(literal -1 binary64)) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))) (fma.f64 (/.f64 x (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))) (/.f64 x (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))) (*.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))) (/.f64 x (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x)))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (+.f64 (-.f64 x #s(literal -1 binary64)) x) (sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) x)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (-.f64 x #s(literal -1 binary64)) x))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x)))))
(/.f64 (-.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))) (*.f64 (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x)) x)) (*.f64 (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x)) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))))
(/.f64 (-.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (*.f64 x x)) (*.f64 (+.f64 (-.f64 x #s(literal -1 binary64)) x) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))))
(/.f64 (-.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (*.f64 (fma.f64 x (+.f64 (-.f64 x #s(literal -1 binary64)) x) (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64))) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))))
(/.f64 (-.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (+.f64 (-.f64 x #s(literal -1 binary64)) x) (sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) x))))
(/.f64 (neg.f64 (-.f64 (-.f64 x #s(literal -1 binary64)) x)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))))
(/.f64 (-.f64 (-.f64 x #s(literal -1 binary64)) x) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x)))
(neg.f64 (/.f64 (neg.f64 (-.f64 (-.f64 x #s(literal -1 binary64)) x)) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))))
(neg.f64 (/.f64 (-.f64 (-.f64 x #s(literal -1 binary64)) x) (neg.f64 (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x)))))
(-.f64 (/.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3/2 binary64)) (+.f64 (+.f64 (-.f64 x #s(literal -1 binary64)) x) (sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) x)))) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (+.f64 (-.f64 x #s(literal -1 binary64)) x) (sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) x)))))
(-.f64 (/.f64 x (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))) (/.f64 (-.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))))
(-.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))) (/.f64 x (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))))
(-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))
(*.f64 (neg.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) (neg.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
(*.f64 (fabs.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) (fabs.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(pow.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) #s(literal 2 binary64))
(pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64))) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (-.f64 x #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 3 binary64)) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal -1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(-.f64 x #s(literal -1 binary64))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(+.f64 #s(literal 1 binary64) x)
(+.f64 x #s(literal 1 binary64))
(/.f64 (neg.f64 (-.f64 x (-.f64 x #s(literal -1 binary64)))) (neg.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))))
(/.f64 (neg.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3/2 binary64)))) (neg.f64 (-.f64 (+.f64 (-.f64 x #s(literal -1 binary64)) x) (sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) x)))))
(/.f64 (-.f64 x (-.f64 x #s(literal -1 binary64))) (-.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
(/.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3/2 binary64))) (+.f64 (-.f64 x #s(literal -1 binary64)) (-.f64 x (sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) x)))))
(/.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3/2 binary64))) (-.f64 (+.f64 (-.f64 x #s(literal -1 binary64)) x) (sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) x))))
(/.f64 (-.f64 (-.f64 x #s(literal -1 binary64)) x) (-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x)))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(fma.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 x))
(fma.f64 #s(literal -1 binary64) (*.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(fma.f64 (sqrt.f64 x) #s(literal 1 binary64) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(-.f64 (/.f64 x (-.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))) (/.f64 (-.f64 x #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (-.f64 (+.f64 (-.f64 x #s(literal -1 binary64)) x) (sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) x)))) (/.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3/2 binary64)) (-.f64 (+.f64 (-.f64 x #s(literal -1 binary64)) x) (sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) x)))))
(+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))
(+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(*.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
(exp.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64)))

eval32.0ms (0.7%)

Memory
-0.8MiB live, 44.8MiB allocated; 5ms collecting garbage
Compiler

Compiled 6 426 to 906 computations (85.9% saved)

prune19.0ms (0.4%)

Memory
-25.8MiB live, 21.2MiB allocated; 2ms collecting garbage
Pruning

12 alts after pruning (4 fresh and 8 done)

PrunedKeptTotal
New2692271
Fresh022
Picked145
Done044
Total27012282
Accuracy
100.0%
Counts
282 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.7%
(/.f64 #s(approx (- (- x -1) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
✓49.3%
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓46.6%
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x))
✓3.2%
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
✓46.5%
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
▶53.9%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) x) (/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x)))
✓48.4%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
▶53.9%
#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))
✓56.1%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
✓56.1%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
▶48.4%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))
✓56.2%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
Compiler

Compiled 184 to 144 computations (21.7% saved)

simplify158.0ms (3.6%)

Memory
34.9MiB live, 125.8MiB allocated; 19ms collecting garbage
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 x)
cost-diff0
(+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
cost-diff0
#s(approx (- (- x -1) x) #s(literal 1 binary64))
cost-diff0
(/.f64 #s(approx (- (- x -1) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
cost-diff0
(sqrt.f64 x)
cost-diff0
(/.f64 (sqrt.f64 x) x)
cost-diff0
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) x) (/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x)))
cost-diff2
(fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) x) (/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x))
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
(-.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))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
029175
045171
167171
294171
3158163
4275163
5886163
64634163
08872160
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
#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 (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)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) x) (/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) x) (/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x))
#s(literal 1/2 binary64)
(/.f64 (sqrt.f64 x) x)
(sqrt.f64 x)
x
(/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x)
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
#s(literal -1/8 binary64)
(/.f64 #s(approx (- (- x -1) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
#s(approx (- (- x -1) x) #s(literal 1 binary64))
#s(literal 1 binary64)
(+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(sqrt.f64 x)
x
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
(-.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
Outputs
#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 binary64) (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x))))
(-.f64 #s(literal 1 binary64) (-.f64 (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)))
#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 (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)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) x) (/.f64 (/.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))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) x) (/.f64 (/.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)
#s(literal 1/2 binary64)
(/.f64 (sqrt.f64 x) x)
(sqrt.f64 x)
x
(/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x)
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
#s(literal -1/8 binary64)
(/.f64 #s(approx (- (- x -1) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
(/.f64 #s(approx (- (- x -1) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x)))
#s(approx (- (- x -1) x) #s(literal 1 binary64))
#s(literal 1 binary64)
(+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))
(sqrt.f64 x)
x
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
(-.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)

localize128.0ms (3%)

Memory
-20.5MiB live, 173.0MiB allocated; 20ms collecting garbage
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
accuracy0.0
#s(approx (- (- x -1) x) #s(literal 1 binary64))
accuracy0.00390625
(+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
accuracy0.00390625
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
accuracy0.1875
(/.f64 #s(approx (- (- x -1) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
accuracy0.171875
(/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x)
accuracy0.26953125
(/.f64 (sqrt.f64 x) x)
accuracy0.28515625
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
accuracy29.345285002758988
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) x) (/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x)))
accuracy0.0234375
(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
accuracy0.2421875
(/.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))
accuracy29.345285002758988
#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
(sqrt.f64 x)
accuracy0.00390625
(-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x)))
accuracy0.01171875
(-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))
accuracy33.00312321252216
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))
Samples
69.0ms137×1valid
23.0ms119×0valid
Compiler

Compiled 143 to 27 computations (81.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 72.0ms
ival-div: 22.0ms (30.4% of total)
ival-sqrt: 15.0ms (20.7% of total)
adjust: 13.0ms (18% of total)
ival-sub: 8.0ms (11% of total)
ival-add: 7.0ms (9.7% of total)
ival-mult: 6.0ms (8.3% of total)
exact: 1.0ms (1.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series9.0ms (0.2%)

Memory
19.3MiB live, 19.3MiB allocated; 0ms collecting garbage
Counts
16 → 83
Calls
Call 1
Inputs
(-.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)))
(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)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) x) (/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) x) (/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x)))
(/.f64 (sqrt.f64 x) x)
(/.f64 #s(approx (- (- x -1) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
#s(approx (- (- x -1) x) #s(literal 1 binary64))
(+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
(/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x)
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
Outputs
#s(approx (- (sqrt x) (* 1/2 x)) #s(hole binary64 (sqrt x)))
#s(approx (- (sqrt x) (* 1/2 x)) #s(hole binary64 (+ (sqrt x) (* -1/2 x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- 1 (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* 1/2 x)) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) #s(hole binary64 (- 1 (sqrt x))))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) #s(hole binary64 (- (+ 1 (* 1/2 x)) (sqrt x))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) #s(hole binary64 (* -1/8 (sqrt (/ 1 (pow x 3))))))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) #s(hole binary64 (* -1/8 (sqrt (/ 1 x)))))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)))
#s(approx (+ (* 1/2 (/ (sqrt x) x)) (/ (/ -1/8 (sqrt x)) x)) #s(hole binary64 (* -1/8 (sqrt (/ 1 (pow x 3))))))
#s(approx (+ (* 1/2 (/ (sqrt x) x)) (/ (/ -1/8 (sqrt x)) x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))))
#s(approx (/ (sqrt x) x) #s(hole binary64 (sqrt (/ 1 x))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ 1 (+ 1 (sqrt x)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))))
#s(approx (- (- x -1) x) #s(hole binary64 1))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (sqrt x))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (+ (sqrt x) (* 1/2 x)))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))))
#s(approx (/ -1/8 (sqrt x)) #s(hole binary64 (* -1/8 (sqrt (/ 1 x)))))
#s(approx (/ (/ -1/8 (sqrt x)) x) #s(hole binary64 (* -1/8 (sqrt (/ 1 (pow x 3))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 1))
#s(approx (sqrt (- x -1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (- (sqrt x) (* 1/2 x)) #s(hole binary64 (* x (- (sqrt (/ 1 x)) 1/2))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) #s(hole binary64 (* x (- 1/2 (sqrt (/ 1 x))))))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) #s(hole binary64 (* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) #s(hole binary64 (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) #s(hole binary64 (* 1/2 (sqrt x))))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) #s(hole binary64 (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))))
#s(approx (+ (* 1/2 (/ (sqrt x) x)) (/ (/ -1/8 (sqrt x)) x)) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (+ (* 1/2 (/ (sqrt x) x)) (/ (/ -1/8 (sqrt x)) x)) #s(hole binary64 (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* 2 (sqrt x))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* 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))))))))))
#s(approx (- (sqrt x) (* 1/2 x)) #s(hole binary64 (* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1/2 (sqrt (/ 1 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -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))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -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))))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) #s(hole binary64 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) #s(hole binary64 (* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) #s(hole binary64 (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) #s(hole binary64 (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) #s(hole binary64 (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) #s(hole binary64 (* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (+ (* 1/2 (/ (sqrt x) x)) (/ (/ -1/8 (sqrt x)) x)) #s(hole binary64 (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
#s(approx (+ (* 1/2 (/ (sqrt x) x)) (/ (/ -1/8 (sqrt x)) x)) #s(hole binary64 (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))))
#s(approx (/ (sqrt x) x) #s(hole binary64 (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1/2 (sqrt (/ 1 x)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -2 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -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)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -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
4.0ms
x
@-inf
((- (sqrt x) (* 1/2 x)) (- (sqrt (+ x 1)) (sqrt x)) (- 1 (- (sqrt x) (* 1/2 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))) (+ (* 1/2 (/ (sqrt x) x)) (/ (/ -1/8 (sqrt x)) x)) (- (sqrt (+ x 1)) (sqrt x)) (/ (sqrt x) x) (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1))) (/ -1/8 (sqrt x)) (/ (/ -1/8 (sqrt x)) x) (sqrt (- x -1)))
2.0ms
x
@0
((- (sqrt x) (* 1/2 x)) (- (sqrt (+ x 1)) (sqrt x)) (- 1 (- (sqrt x) (* 1/2 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))) (+ (* 1/2 (/ (sqrt x) x)) (/ (/ -1/8 (sqrt x)) x)) (- (sqrt (+ x 1)) (sqrt x)) (/ (sqrt x) x) (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1))) (/ -1/8 (sqrt x)) (/ (/ -1/8 (sqrt x)) x) (sqrt (- x -1)))
2.0ms
x
@inf
((- (sqrt x) (* 1/2 x)) (- (sqrt (+ x 1)) (sqrt x)) (- 1 (- (sqrt x) (* 1/2 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))) (+ (* 1/2 (/ (sqrt x) x)) (/ (/ -1/8 (sqrt x)) x)) (- (sqrt (+ x 1)) (sqrt x)) (/ (sqrt x) x) (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1))) (/ -1/8 (sqrt x)) (/ (/ -1/8 (sqrt x)) x) (sqrt (- x -1)))

simplify222.0ms (5.1%)

Memory
-0.2MiB live, 228.6MiB allocated; 22ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03382059
18701943
232881881
087071770
Stop Event
1×iter limit
1×node limit
Counts
83 → 83
Calls
Call 1
Inputs
#s(approx (- (sqrt x) (* 1/2 x)) #s(hole binary64 (sqrt x)))
#s(approx (- (sqrt x) (* 1/2 x)) #s(hole binary64 (+ (sqrt x) (* -1/2 x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- 1 (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* 1/2 x)) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) #s(hole binary64 (- 1 (sqrt x))))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) #s(hole binary64 (- (+ 1 (* 1/2 x)) (sqrt x))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) #s(hole binary64 (* -1/8 (sqrt (/ 1 (pow x 3))))))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) #s(hole binary64 (* -1/8 (sqrt (/ 1 x)))))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)))
#s(approx (+ (* 1/2 (/ (sqrt x) x)) (/ (/ -1/8 (sqrt x)) x)) #s(hole binary64 (* -1/8 (sqrt (/ 1 (pow x 3))))))
#s(approx (+ (* 1/2 (/ (sqrt x) x)) (/ (/ -1/8 (sqrt x)) x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))))
#s(approx (/ (sqrt x) x) #s(hole binary64 (sqrt (/ 1 x))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ 1 (+ 1 (sqrt x)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))))
#s(approx (- (- x -1) x) #s(hole binary64 1))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (sqrt x))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (+ (sqrt x) (* 1/2 x)))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))))
#s(approx (/ -1/8 (sqrt x)) #s(hole binary64 (* -1/8 (sqrt (/ 1 x)))))
#s(approx (/ (/ -1/8 (sqrt x)) x) #s(hole binary64 (* -1/8 (sqrt (/ 1 (pow x 3))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 1))
#s(approx (sqrt (- x -1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (- (sqrt x) (* 1/2 x)) #s(hole binary64 (* x (- (sqrt (/ 1 x)) 1/2))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) #s(hole binary64 (* x (- 1/2 (sqrt (/ 1 x))))))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) #s(hole binary64 (* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) #s(hole binary64 (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) #s(hole binary64 (* 1/2 (sqrt x))))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) #s(hole binary64 (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))))
#s(approx (+ (* 1/2 (/ (sqrt x) x)) (/ (/ -1/8 (sqrt x)) x)) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (+ (* 1/2 (/ (sqrt x) x)) (/ (/ -1/8 (sqrt x)) x)) #s(hole binary64 (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* 2 (sqrt x))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* 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))))))))))
#s(approx (- (sqrt x) (* 1/2 x)) #s(hole binary64 (* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1/2 (sqrt (/ 1 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -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))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -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))))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) #s(hole binary64 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) #s(hole binary64 (* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) #s(hole binary64 (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) #s(hole binary64 (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) #s(hole binary64 (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) #s(hole binary64 (* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (+ (* 1/2 (/ (sqrt x) x)) (/ (/ -1/8 (sqrt x)) x)) #s(hole binary64 (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
#s(approx (+ (* 1/2 (/ (sqrt x) x)) (/ (/ -1/8 (sqrt x)) x)) #s(hole binary64 (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))))
#s(approx (/ (sqrt x) x) #s(hole binary64 (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1/2 (sqrt (/ 1 x)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -2 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -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)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -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
#s(approx (- (sqrt x) (* 1/2 x)) #s(hole binary64 (sqrt x)))
#s(approx (- (sqrt x) (* 1/2 x)) (sqrt.f64 x))
#s(approx (- (sqrt x) (* 1/2 x)) #s(hole binary64 (+ (sqrt x) (* -1/2 x))))
#s(approx (- (sqrt x) (* 1/2 x)) (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- 1 (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* 1/2 x)) (sqrt 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)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (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))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 (fma.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))))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) #s(hole binary64 (- 1 (sqrt x))))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) #s(hole binary64 (- (+ 1 (* 1/2 x)) (sqrt x))))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (sqrt x) (sqrt.f64 x))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) #s(hole binary64 (* -1/8 (sqrt (/ 1 (pow x 3))))))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64)))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) 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))) (*.f64 x x)))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) #s(hole binary64 (* -1/8 (sqrt (/ 1 x)))))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt 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))
#s(approx (+ (* 1/2 (/ (sqrt x) x)) (/ (/ -1/8 (sqrt x)) x)) #s(hole binary64 (* -1/8 (sqrt (/ 1 (pow x 3))))))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64)))
#s(approx (+ (* 1/2 (/ (sqrt x) x)) (/ (/ -1/8 (sqrt x)) x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) 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))) (*.f64 x x)))
#s(approx (/ (sqrt x) x) #s(hole binary64 (sqrt (/ 1 x))))
#s(approx (/ (sqrt x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ 1 (+ 1 (sqrt x)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (/.f64 (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (fma.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) #s(literal 1/8 binary64)) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64))) x (/.f64 #s(literal -1/2 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 4 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64)))) #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) #s(literal 1/16 binary64)) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) #s(literal 1/8 binary64)) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal -1/2 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))))
#s(approx (- (- x -1) x) #s(hole binary64 1))
#s(approx (- (- x -1) x) #s(literal 1 binary64))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (sqrt x))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (+ (sqrt x) (* 1/2 x)))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (fma.f64 #s(literal 1/2 binary64) x (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
#s(approx (/ -1/8 (sqrt x)) #s(hole binary64 (* -1/8 (sqrt (/ 1 x)))))
#s(approx (/ -1/8 (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)))
#s(approx (/ (/ -1/8 (sqrt x)) x) #s(hole binary64 (* -1/8 (sqrt (/ 1 (pow x 3))))))
#s(approx (/ (/ -1/8 (sqrt x)) x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64)))
#s(approx (sqrt (- x -1)) #s(hole binary64 1))
#s(approx (sqrt (- x -1)) #s(literal 1 binary64))
#s(approx (sqrt (- x -1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (- x -1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
#s(approx (sqrt (- x -1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (- x -1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (sqrt (- x -1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (sqrt (- x -1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (- (sqrt x) (* 1/2 x)) #s(hole binary64 (* x (- (sqrt (/ 1 x)) 1/2))))
#s(approx (- (sqrt x) (* 1/2 x)) (*.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* 1/2 (sqrt (/ 1 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)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt 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)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt 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) (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))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt 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))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) #s(hole binary64 (* x (- 1/2 (sqrt (/ 1 x))))))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) (*.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) #s(hole binary64 (* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) (fma.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x #s(literal 1 binary64)))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) #s(hole binary64 (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) 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))))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) #s(hole binary64 (* 1/2 (sqrt x))))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) #s(hole binary64 (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt 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))
#s(approx (+ (* 1/2 (/ (sqrt x) x)) (/ (/ -1/8 (sqrt x)) x)) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
#s(approx (+ (* 1/2 (/ (sqrt x) x)) (/ (/ -1/8 (sqrt x)) x)) #s(hole binary64 (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) 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))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* 1/2 (sqrt (/ 1 x)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (/.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 (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (/.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))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (neg.f64 (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 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))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* 2 (sqrt x))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))) x))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (*.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) x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)))) x))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (*.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) x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))))) x))
#s(approx (sqrt (- x -1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (- x -1)) (sqrt.f64 x))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (- x -1)) (*.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))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (- x -1)) (*.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))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* 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))))))))))
#s(approx (sqrt (- x -1)) (*.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))
#s(approx (- (sqrt x) (* 1/2 x)) #s(hole binary64 (* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (- (sqrt x) (* 1/2 x)) (*.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -1/2 (sqrt (/ 1 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)) #s(hole binary64 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt 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)) #s(hole binary64 (* -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))))
#s(approx (- (sqrt (+ x 1)) (sqrt 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))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(hole binary64 (* -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))))
#s(approx (- (sqrt (+ x 1)) (sqrt 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) (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))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) #s(hole binary64 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) (*.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) #s(hole binary64 (* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))))
#s(approx (- 1 (- (sqrt x) (* 1/2 x))) (fma.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x #s(literal 1 binary64)))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt x) (sqrt.f64 x))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) #s(hole binary64 (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) #s(hole binary64 (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) 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))))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) #s(hole binary64 (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) #s(hole binary64 (* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt 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))
#s(approx (+ (* 1/2 (/ (sqrt x) x)) (/ (/ -1/8 (sqrt x)) x)) #s(hole binary64 (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
#s(approx (+ (* 1/2 (/ (sqrt x) x)) (/ (/ -1/8 (sqrt x)) x)) #s(hole binary64 (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))))
#s(approx (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) 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))))
#s(approx (/ (sqrt x) x) #s(hole binary64 (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
#s(approx (/ (sqrt x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1/2 (sqrt (/ 1 x)))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (/.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 (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (/.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))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) #s(hole binary64 (* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x))))
#s(approx (/ (- (- x -1) x) (+ (sqrt x) (sqrt (- x -1)))) (/.f64 (fma.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal 5/128 binary64) (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))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -2 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/2 binary64))) x))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (*.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) x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/2 binary64)))) x))
#s(approx (+ (sqrt x) (sqrt (- x -1))) #s(hole binary64 (* -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)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))))
#s(approx (+ (sqrt x) (sqrt (- x -1))) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal -1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/2 binary64))))) x))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (- x -1)) (sqrt.f64 x))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (- x -1)) (*.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))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (- x -1)) (*.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))
#s(approx (sqrt (- x -1)) #s(hole binary64 (* -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)))))))))
#s(approx (sqrt (- x -1)) (*.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))

rewrite136.0ms (3.2%)

Memory
-56.1MiB live, 76.2MiB allocated; 97ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
029147
045143
1182142
01495139
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
16 → 160
Calls
Call 1
Inputs
(-.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)))
(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)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) x) (/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) x) (/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x)))
(/.f64 (sqrt.f64 x) x)
(/.f64 #s(approx (- (- x -1) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
#s(approx (- (- x -1) x) #s(literal 1 binary64))
(+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
(/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x)
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
Outputs
(*.f64 #s(literal -1 binary64) (*.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x))))
(*.f64 #s(literal 1 binary64) (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))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (fma.f64 #s(literal 1/2 binary64) x (sqrt.f64 x)))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal 3/2 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (sqrt.f64 x)) x))
(/.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 3 binary64))) (+.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (sqrt.f64 x) (*.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (neg.f64 (-.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) x (sqrt.f64 x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3/2 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (sqrt.f64 x)) x)))
(/.f64 (-.f64 x (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (fma.f64 #s(literal 1/2 binary64) x (sqrt.f64 x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 3/2 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (sqrt.f64 x)) x))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) (*.f64 (neg.f64 x) #s(literal 1/2 binary64)))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) (*.f64 #s(literal -1/2 binary64) x))
(fma.f64 #s(literal -1/2 binary64) x (sqrt.f64 x))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 x) (*.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x)))
(fma.f64 (sqrt.f64 x) #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)))
(fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))
(-.f64 (/.f64 x (fma.f64 #s(literal 1/2 binary64) x (sqrt.f64 x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x (sqrt.f64 x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (sqrt.f64 x)) x)) (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) x (sqrt.f64 x)) x)))
(-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (*.f64 (sqrt.f64 x) #s(literal 1 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)))
(+.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x)))
(+.f64 (*.f64 #s(literal -1/2 binary64) x) (sqrt.f64 x))
(+.f64 (sqrt.f64 x) (*.f64 (neg.f64 x) #s(literal 1/2 binary64)))
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(neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (neg.f64 x)))
(fma.f64 (/.f64 (sqrt.f64 x) x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) x) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))
(fma.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))
(-.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 x x)) (/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)) (/.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)))
(-.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 (neg.f64 (/.f64 (sqrt.f64 x) x)) #s(literal 1/2 binary64)))
(-.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 x) x)))
(+.f64 (/.f64 (pow.f64 (*.f64 (/.f64 (sqrt.f64 x) x) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (-.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 (/.f64 (sqrt.f64 x) x) #s(literal 1/2 binary64))) (/.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 x x)))) (/.f64 (pow.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 3 binary64)) (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (-.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 (/.f64 (sqrt.f64 x) x) #s(literal 1/2 binary64))) (/.f64 (*.f64 #s(literal 1/4 binary64) x) (*.f64 x x)))))
(+.f64 (*.f64 (/.f64 (sqrt.f64 x) x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))
(+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 (/.f64 (sqrt.f64 x) x) #s(literal 1/2 binary64)))
#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 (neg.f64 (neg.f64 (sqrt.f64 x))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 x))
(/.f64 (sqrt.f64 x) x)
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 x)) x))
(neg.f64 (/.f64 (sqrt.f64 x) (neg.f64 x)))
(*.f64 (/.f64 #s(approx (- (- x -1) x) #s(literal 1 binary64)) (-.f64 x (-.f64 x #s(literal -1 binary64)))) (-.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
(*.f64 (/.f64 #s(approx (- (- x -1) x) #s(literal 1 binary64)) (fma.f64 (sqrt.f64 x) x (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3/2 binary64)))) (-.f64 (+.f64 (-.f64 x #s(literal -1 binary64)) x) (sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) x))))
(/.f64 (neg.f64 (neg.f64 #s(approx (- (- x -1) x) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x)))))
(/.f64 (neg.f64 #s(approx (- (- x -1) x) #s(literal 1 binary64))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))))
(/.f64 #s(approx (- (- x -1) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x)))
(neg.f64 (/.f64 (neg.f64 #s(approx (- (- x -1) x) #s(literal 1 binary64))) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))))
(neg.f64 (/.f64 #s(approx (- (- x -1) x) #s(literal 1 binary64)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x)))))
#s(approx (- (- x -1) x) #s(literal 1 binary64))
(/.f64 (neg.f64 (-.f64 x (-.f64 x #s(literal -1 binary64)))) (neg.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))))
(/.f64 (neg.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3/2 binary64)))) (neg.f64 (-.f64 (+.f64 (-.f64 x #s(literal -1 binary64)) x) (sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) x)))))
(/.f64 (-.f64 x (-.f64 x #s(literal -1 binary64))) (-.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
(/.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3/2 binary64))) (+.f64 (-.f64 x #s(literal -1 binary64)) (-.f64 x (sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) x)))))
(/.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3/2 binary64))) (-.f64 (+.f64 (-.f64 x #s(literal -1 binary64)) x) (sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) x))))
(/.f64 (-.f64 (-.f64 x #s(literal -1 binary64)) x) (-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x)))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(fma.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 x))
(-.f64 (/.f64 x (-.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))) (/.f64 (-.f64 x #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (-.f64 (+.f64 (-.f64 x #s(literal -1 binary64)) x) (sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) x)))) (/.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3/2 binary64)) (-.f64 (+.f64 (-.f64 x #s(literal -1 binary64)) x) (sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) x)))))
(+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))
(+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(/.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)))
(/.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (neg.f64 x))
(/.f64 #s(literal 1/8 binary64) (*.f64 (neg.f64 (sqrt.f64 x)) x))
(/.f64 #s(literal 1/8 binary64) (neg.f64 (pow.f64 x #s(literal 3/2 binary64))))
(/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (neg.f64 (neg.f64 x)))
(/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x)
(/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))
(neg.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) x))
(neg.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (neg.f64 x)))
(*.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64))) (sqrt.f64 (fma.f64 x x (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)))))
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
(exp.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64)))

eval24.0ms (0.6%)

Memory
39.8MiB live, 39.8MiB allocated; 0ms collecting garbage
Compiler

Compiled 5 714 to 853 computations (85.1% saved)

prune24.0ms (0.6%)

Memory
-27.9MiB live, 20.2MiB allocated; 16ms collecting garbage
Pruning

11 alts after pruning (2 fresh and 9 done)

PrunedKeptTotal
New2242226
Fresh000
Picked224
Done178
Total22711238
Accuracy
100.0%
Counts
238 → 11
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.7%
(/.f64 #s(approx (- (- x -1) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
✓49.3%
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓46.6%
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x))
✓3.2%
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
✓46.5%
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
53.9%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) x) (/.f64 #s(literal 1/8 binary64) (*.f64 (neg.f64 (sqrt.f64 x)) x))))
✓53.9%
#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))
✓56.1%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
✓56.1%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
48.4%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))))
✓56.2%
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
Compiler

Compiled 443 to 218 computations (50.8% saved)

regimes10.0ms (0.2%)

Memory
15.2MiB live, 15.2MiB allocated; 0ms collecting garbage
Counts
18 → 1
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (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))))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #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 (sqrt.f64 #s(approx (+ x 1) x)) (sqrt.f64 x))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 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)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(/.f64 #s(approx (- (- x -1) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
(/.f64 (-.f64 (-.f64 x #s(literal -1 binary64)) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
#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))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) x) (/.f64 #s(literal 1/8 binary64) (*.f64 (neg.f64 (sqrt.f64 x)) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) x) (/.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) x)))
Outputs
(/.f64 #s(approx (- (- x -1) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
Calls

2 calls:

5.0ms
x
4.0ms
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Results
AccuracySegmentsBranch
99.7%1(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
99.7%1x
Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes7.0ms (0.2%)

Memory
14.5MiB live, 14.5MiB allocated; 0ms collecting garbage
Counts
12 → 2
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (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))))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #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 (sqrt.f64 #s(approx (+ x 1) x)) (sqrt.f64 x))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 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)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
(-.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))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
Calls

2 calls:

4.0ms
x
3.0ms
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Results
AccuracySegmentsBranch
99.4%2(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
99.4%2x
Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes14.0ms (0.3%)

Memory
-33.7MiB live, 12.8MiB allocated; 2ms collecting garbage
Counts
11 → 2
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (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))))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #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 (sqrt.f64 #s(approx (+ x 1) x)) (sqrt.f64 x))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 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)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
Outputs
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 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:

11.0ms
x
3.0ms
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Results
AccuracySegmentsBranch
99.2%2(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
99.2%2x
Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes6.0ms (0.1%)

Memory
9.3MiB live, 9.3MiB allocated; 0ms collecting garbage
Counts
9 → 2
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (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))))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #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 (sqrt.f64 #s(approx (+ x 1) x)) (sqrt.f64 x))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x))
Outputs
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
Calls

2 calls:

3.0ms
x
2.0ms
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Results
AccuracySegmentsBranch
99.1%2(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
99.1%2x
Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes5.0ms (0.1%)

Memory
7.2MiB live, 7.2MiB allocated; 0ms collecting garbage
Counts
8 → 2
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (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))))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #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 (sqrt.f64 #s(approx (+ x 1) x)) (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 #s(literal 1/2 binary64) (sqrt.f64 x)))
Calls

2 calls:

3.0ms
x
2.0ms
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Results
AccuracySegmentsBranch
99.0%2(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
99.0%2x
Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes4.0ms (0.1%)

Memory
6.4MiB live, 6.4MiB allocated; 0ms collecting garbage
Counts
6 → 1
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (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))))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #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
48.4%1(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
48.4%1x
Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0.1%)

Memory
4.2MiB live, 4.2MiB allocated; 0ms collecting garbage
Accuracy

Total -28.7b remaining (-83.8%)

Threshold costs -28.7b (-83.8%)

Counts
2 → 1
Calls
Call 1
Inputs
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (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
46.5%1(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
46.5%1x
Compiler

Compiled 8 to 7 computations (12.5% saved)

bsearch60.0ms (1.4%)

Memory
-28.7MiB live, 17.4MiB allocated; 3ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
59.0ms
49616452.30864548
3399974483.5015097
Samples
54.0ms112×1valid
Compiler

Compiled 157 to 150 computations (4.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 51.0ms
ival-sqrt: 48.0ms (93.5% of total)
adjust: 2.0ms (3.9% of total)
ival-sub: 1.0ms (1.9% of total)
ival-add: 1.0ms (1.9% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

bsearch15.0ms (0.3%)

Memory
23.5MiB live, 23.5MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
13.0ms
1.3940759168774745e-7
2173.2311582455386
Samples
7.0ms160×0valid
Compiler

Compiled 300 to 270 computations (10% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-sqrt: 2.0ms (51.1% of total)
ival-sub: 1.0ms (25.6% of total)
ival-add: 1.0ms (25.6% 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)

bsearch2.0ms (0%)

Memory
2.6MiB live, 2.6MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
1.0ms
1.3940759168774745e-7
2173.2311582455386
Compiler

Compiled 280 to 250 computations (10.7% saved)

bsearch5.0ms (0.1%)

Memory
8.1MiB live, 8.1MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
4.0ms
1.3940759168774745e-7
2173.2311582455386
Samples
2.0ms48×0valid
Compiler

Compiled 280 to 250 computations (10.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.0ms
ival-sqrt: 1.0ms (85.8% 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)

simplify71.0ms (1.7%)

Memory
-20.4MiB live, 70.6MiB allocated; 26ms collecting garbage
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
045159
158159
271159
388157
4118156
5317156
62582155
77378155
Stop Event
1×node limit
Calls
Call 1
Inputs
(/.f64 #s(approx (- (- x -1) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
(if (<=.f64 x #s(literal 66000000 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 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 5494391545392005/4503599627370496 binary64)) (-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 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 5494391545392005/4503599627370496 binary64)) (-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 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 #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
(/.f64 #s(approx (- (- x -1) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))))
(if (<=.f64 x #s(literal 66000000 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 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 66000000 binary64)) (-.f64 (sqrt.f64 (-.f64 x #s(literal -1 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 5494391545392005/4503599627370496 binary64)) (-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 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 5494391545392005/4503599627370496 binary64)) (-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 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 #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))

derivations169.0ms (3.9%)

Memory
-8.2MiB live, 138.7MiB allocated; 14ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 159 to 45 computations (71.7% saved)

preprocess36.0ms (0.8%)

Memory
18.6MiB live, 64.3MiB allocated; 4ms collecting garbage
Compiler

Compiled 350 to 116 computations (66.9% saved)

end0.0ms (0%)

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

Profiling

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